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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let default_psk = lbytes_empty | let default_psk = | false | null | false | lbytes_empty | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Lib.ByteSequence.lbytes_empty"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val default_psk : Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.SEC) 0 | [] | Spec.Agile.HPKE.default_psk | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | Lib.Sequence.lseq (Lib.IntTypes.int_t Lib.IntTypes.U8 Lib.IntTypes.SEC) 0 | {
"end_col": 30,
"end_line": 306,
"start_col": 18,
"start_line": 306
} |
|
Prims.Tot | val pow2_61:_: unit{pow2 61 == 2305843009213693952} | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952) | val pow2_61:_: unit{pow2 61 == 2305843009213693952}
let pow2_61:_: unit{pow2 61 == 2305843009213693952} = | false | null | false | assert_norm (pow2 61 == 2305843009213693952) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"FStar.Pervasives.assert_norm",
"Prims.eq2",
"Prims.int",
"Prims.pow2"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val pow2_61:_: unit{pow2 61 == 2305843009213693952} | [] | Spec.Agile.HPKE.pow2_61 | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | _: Prims.unit{Prims.pow2 61 == 2305843009213693952} | {
"end_col": 98,
"end_line": 15,
"start_col": 55,
"start_line": 15
} |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce | let base_nonce_of_ctx (cs: ciphersuite) (ctx: encryption_context cs) = | false | null | false | let _, base_nonce, _, _ = ctx in
base_nonce | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_aead_s",
"Spec.Agile.HPKE.nonce_aead_s",
"Spec.Agile.HPKE.seq_aead_s",
"Spec.Agile.HPKE.exporter_secret_s"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val base_nonce_of_ctx : cs: Spec.Agile.HPKE.ciphersuite -> ctx: Spec.Agile.HPKE.encryption_context cs
-> Spec.Agile.HPKE.nonce_aead_s cs | [] | Spec.Agile.HPKE.base_nonce_of_ctx | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> ctx: Spec.Agile.HPKE.encryption_context cs
-> Spec.Agile.HPKE.nonce_aead_s cs | {
"end_col": 45,
"end_line": 391,
"start_col": 68,
"start_line": 390
} |
|
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec | let exp_sec_of_ctx (cs: ciphersuite) (ctx: encryption_context cs) = | false | null | false | let _, _, _, exp_sec = ctx in
exp_sec | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_aead_s",
"Spec.Agile.HPKE.nonce_aead_s",
"Spec.Agile.HPKE.seq_aead_s",
"Spec.Agile.HPKE.exporter_secret_s"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val exp_sec_of_ctx : cs: Spec.Agile.HPKE.ciphersuite -> ctx: Spec.Agile.HPKE.encryption_context cs
-> Spec.Agile.HPKE.exporter_secret_s cs | [] | Spec.Agile.HPKE.exp_sec_of_ctx | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> ctx: Spec.Agile.HPKE.encryption_context cs
-> Spec.Agile.HPKE.exporter_secret_s cs | {
"end_col": 39,
"end_line": 397,
"start_col": 65,
"start_line": 396
} |
|
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key | let key_of_ctx (cs: ciphersuite) (ctx: encryption_context cs) = | false | null | false | let key, _, _, _ = ctx in
key | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_aead_s",
"Spec.Agile.HPKE.nonce_aead_s",
"Spec.Agile.HPKE.seq_aead_s",
"Spec.Agile.HPKE.exporter_secret_s"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val key_of_ctx : cs: Spec.Agile.HPKE.ciphersuite -> ctx: Spec.Agile.HPKE.encryption_context cs
-> Spec.Agile.HPKE.key_aead_s cs | [] | Spec.Agile.HPKE.key_of_ctx | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> ctx: Spec.Agile.HPKE.encryption_context cs
-> Spec.Agile.HPKE.key_aead_s cs | {
"end_col": 31,
"end_line": 388,
"start_col": 61,
"start_line": 387
} |
|
Prims.Tot | val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3) | val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m = | false | null | false | match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.mode",
"Lib.Sequence.create",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Lib.IntTypes.u8",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.size_mode_identifier"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier) | false | true | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier) | [] | Spec.Agile.HPKE.id_of_mode | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | m: Spec.Agile.HPKE.mode -> Lib.ByteSequence.lbytes Spec.Agile.HPKE.size_mode_identifier | {
"end_col": 30,
"end_line": 61,
"start_col": 2,
"start_line": 57
} |
Prims.Tot | val sendExportBase:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs ->
Tot (option (key_dh_public_s cs & lbytes l)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l) | val sendExportBase:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs ->
Tot (option (key_dh_public_s cs & lbytes l))
let sendExportBase cs skE pkR info exp_ctx l = | false | null | false | match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) -> Some (enc, context_export cs ctx exp_ctx l) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.exp_ctx_s",
"Spec.Agile.HPKE.exp_len",
"Spec.Agile.HPKE.setupBaseS",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.encryption_context",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.context_export",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val sendExportBase:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs ->
Tot (option (key_dh_public_s cs & lbytes l)) | [] | Spec.Agile.HPKE.sendExportBase | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
exp_ctx: Spec.Agile.HPKE.exp_ctx_s cs ->
l: Spec.Agile.HPKE.exp_len cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs * Lib.ByteSequence.lbytes l) | {
"end_col": 47,
"end_line": 482,
"start_col": 2,
"start_line": 479
} |
Prims.Tot | val receiveExportBase:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs ->
Tot (option (lbytes l)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l) | val receiveExportBase:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs ->
Tot (option (lbytes l))
let receiveExportBase cs enc skR info exp_ctx l = | false | null | false | match setupBaseR cs enc skR info with
| None -> None
| Some ctx -> Some (context_export cs ctx exp_ctx l) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.exp_ctx_s",
"Spec.Agile.HPKE.exp_len",
"Spec.Agile.HPKE.setupBaseR",
"FStar.Pervasives.Native.None",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.encryption_context",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.context_export",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val receiveExportBase:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs ->
Tot (option (lbytes l)) | [] | Spec.Agile.HPKE.receiveExportBase | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
exp_ctx: Spec.Agile.HPKE.exp_ctx_s cs ->
l: Spec.Agile.HPKE.exp_len cs
-> FStar.Pervasives.Native.option (Lib.ByteSequence.lbytes l) | {
"end_col": 42,
"end_line": 488,
"start_col": 2,
"start_line": 485
} |
Prims.Tot | val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs) | val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs = | false | null | false | Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"FStar.Seq.Base.append",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Agile.HPKE.label_HPKE",
"Lib.Sequence.op_At_Bar",
"Lib.IntTypes.uint_t",
"Prims.op_Addition",
"Spec.Agile.HPKE.id_kem",
"Spec.Agile.HPKE.id_kdf",
"Spec.Agile.HPKE.id_aead",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.size_suite_id_hpke"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke) | false | true | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke) | [] | Spec.Agile.HPKE.suite_id_hpke | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> Lib.ByteSequence.lbytes Spec.Agile.HPKE.size_suite_id_hpke | {
"end_col": 62,
"end_line": 53,
"start_col": 2,
"start_line": 53
} |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length) | let extract_and_expand_dh_pred (cs: ciphersuite) (dh_length: nat) = | false | null | false | labeled_extract_ikm_length_pred (kem_hash_of_cs cs)
(size_suite_id_kem + size_label_eae_prk + dh_length) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Prims.nat",
"Spec.Agile.HPKE.labeled_extract_ikm_length_pred",
"Spec.Agile.HPKE.kem_hash_of_cs",
"Prims.op_Addition",
"Spec.Agile.HPKE.size_suite_id_kem",
"Spec.Agile.HPKE.size_label_eae_prk",
"Prims.bool"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l | false | true | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val extract_and_expand_dh_pred : cs: Spec.Agile.HPKE.ciphersuite -> dh_length: Prims.nat -> Prims.bool | [] | Spec.Agile.HPKE.extract_and_expand_dh_pred | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> dh_length: Prims.nat -> Prims.bool | {
"end_col": 106,
"end_line": 109,
"start_col": 2,
"start_line": 109
} |
|
Prims.Tot | val setupBaseS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx) | val setupBaseS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs))
let setupBaseS cs skE pkR info = | false | null | false | match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.encap",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_kem_s",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.key_schedule",
"Spec.Agile.HPKE.Base",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
/// | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val setupBaseS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs)) | [] | Spec.Agile.HPKE.setupBaseS | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs *
Spec.Agile.HPKE.encryption_context cs) | {
"end_col": 23,
"end_line": 452,
"start_col": 2,
"start_line": 448
} |
Prims.Tot | val context_compute_nonce:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs
-> seq:seq_aead_s cs ->
Tot (nonce_aead_s cs) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce | val context_compute_nonce:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs
-> seq:seq_aead_s cs ->
Tot (nonce_aead_s cs)
let context_compute_nonce cs ctx seq = | false | null | false | let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.seq_aead_s",
"Spec.Loops.seq_map2",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Lib.IntTypes.logxor",
"Lib.Sequence.seq",
"Lib.IntTypes.int_t",
"Prims.l_and",
"Prims.eq2",
"Prims.nat",
"Lib.Sequence.length",
"Spec.Agile.HPKE.size_aead_nonce",
"Prims.l_or",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.pow2",
"Prims.op_Multiply",
"Lib.ByteSequence.nat_from_intseq_be",
"Lib.ByteSequence.nat_to_bytes_be",
"Spec.Agile.HPKE.nonce_aead_s",
"Spec.Agile.HPKE.base_nonce_of_ctx"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val context_compute_nonce:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs
-> seq:seq_aead_s cs ->
Tot (nonce_aead_s cs) | [] | Spec.Agile.HPKE.context_compute_nonce | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
ctx: Spec.Agile.HPKE.encryption_context cs ->
seq: Spec.Agile.HPKE.seq_aead_s cs
-> Spec.Agile.HPKE.nonce_aead_s cs | {
"end_col": 47,
"end_line": 416,
"start_col": 38,
"start_line": 413
} |
Prims.Tot | val sendExportAuth:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & lbytes l)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let sendExportAuth cs skE pkR info exp_ctx l skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l) | val sendExportAuth:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & lbytes l))
let sendExportAuth cs skE pkR info exp_ctx l skS = | false | null | false | match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) -> Some (enc, context_export cs ctx exp_ctx l) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.exp_ctx_s",
"Spec.Agile.HPKE.exp_len",
"Spec.Agile.HPKE.setupAuthS",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.encryption_context",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.context_export",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx)
let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None
let sealAuth cs skE pkR info aad pt skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openAuth cs enc skR info aad ct pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val sendExportAuth:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & lbytes l)) | [] | Spec.Agile.HPKE.sendExportAuth | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
exp_ctx: Spec.Agile.HPKE.exp_ctx_s cs ->
l: Spec.Agile.HPKE.exp_len cs ->
skS: Spec.Agile.HPKE.key_dh_secret_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs * Lib.ByteSequence.lbytes l) | {
"end_col": 47,
"end_line": 578,
"start_col": 2,
"start_line": 575
} |
Prims.Tot | val receiveExportAuthPSK:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (lbytes l)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let receiveExportAuthPSK cs enc skR info exp_ctx l psk psk_id pkS =
match setupAuthPSKR cs enc skR info psk psk_id pkS with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l) | val receiveExportAuthPSK:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (lbytes l))
let receiveExportAuthPSK cs enc skR info exp_ctx l psk psk_id pkS = | false | null | false | match setupAuthPSKR cs enc skR info psk psk_id pkS with
| None -> None
| Some ctx -> Some (context_export cs ctx exp_ctx l) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.exp_ctx_s",
"Spec.Agile.HPKE.exp_len",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.setupAuthPSKR",
"FStar.Pervasives.Native.None",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.encryption_context",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.context_export",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx)
let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None
let sealAuth cs skE pkR info aad pt skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openAuth cs enc skR info aad ct pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportAuth cs skE pkR info exp_ctx l skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportAuth cs enc skR info exp_ctx l pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// AuthPSK mode
///
let setupAuthPSKS cs skE pkR info psk psk_id skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupAuthPSKR cs enc skR info psk psk_id pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealAuthPSK cs skE pkR info aad pt psk psk_id skS =
match setupAuthPSKS cs skE pkR info psk psk_id skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openAuthPSK cs enc skR info aad ct psk psk_id pkS =
match setupAuthPSKR cs enc skR info psk psk_id pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportAuthPSK cs skE pkR info exp_ctx l psk psk_id skS =
match setupAuthPSKS cs skE pkR info psk psk_id skS with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val receiveExportAuthPSK:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (lbytes l)) | [] | Spec.Agile.HPKE.receiveExportAuthPSK | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
exp_ctx: Spec.Agile.HPKE.exp_ctx_s cs ->
l: Spec.Agile.HPKE.exp_len cs ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs ->
pkS: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs)
-> FStar.Pervasives.Native.option (Lib.ByteSequence.lbytes l) | {
"end_col": 42,
"end_line": 631,
"start_col": 2,
"start_line": 628
} |
Prims.Tot | val setupAuthS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx) | val setupAuthS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs))
let setupAuthS cs skE pkR info skS = | false | null | false | match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.auth_encap",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_kem_s",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.key_schedule",
"Spec.Agile.HPKE.Auth",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
/// | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val setupAuthS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs)) | [] | Spec.Agile.HPKE.setupAuthS | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
skS: Spec.Agile.HPKE.key_dh_secret_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs *
Spec.Agile.HPKE.encryption_context cs) | {
"end_col": 23,
"end_line": 548,
"start_col": 2,
"start_line": 544
} |
Prims.Tot | val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32 | val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = | false | null | false | match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32 | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.serialize_public_key",
"Lib.Sequence.sub",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Agile.DH.size_public",
"Lib.ByteSequence.lbytes"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32) | [] | Spec.Agile.HPKE.prepare_dh | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
dh: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs)
-> Lib.ByteSequence.lbytes 32 | {
"end_col": 29,
"end_line": 173,
"start_col": 23,
"start_line": 171
} |
Prims.Pure | val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3 | val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm = | false | null | false | let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3 | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [] | [
"Spec.Agile.HPKE.hash_algorithm",
"Lib.ByteSequence.bytes",
"Spec.Agile.HKDF.extract",
"FStar.Seq.Base.seq",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"FStar.Seq.Base.append",
"Spec.Agile.HPKE.label_version",
"Lib.ByteSequence.lbytes",
"Spec.Hash.Definitions.hash_length"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True) | [] | Spec.Agile.HPKE.labeled_extract | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
a: Spec.Agile.HPKE.hash_algorithm ->
suite_id: Lib.ByteSequence.bytes ->
salt: Lib.ByteSequence.bytes ->
label: Lib.ByteSequence.bytes ->
ikm: Lib.ByteSequence.bytes
-> Prims.Pure (Lib.ByteSequence.lbytes (Spec.Hash.Definitions.hash_length a)) | {
"end_col": 34,
"end_line": 82,
"start_col": 47,
"start_line": 78
} |
Prims.Tot | val sendExportPSK:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (key_dh_public_s cs & lbytes l)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l) | val sendExportPSK:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (key_dh_public_s cs & lbytes l))
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id = | false | null | false | match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) -> Some (enc, context_export cs ctx exp_ctx l) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.exp_ctx_s",
"Spec.Agile.HPKE.exp_len",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.HPKE.setupPSKS",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.encryption_context",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.context_export",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val sendExportPSK:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (key_dh_public_s cs & lbytes l)) | [] | Spec.Agile.HPKE.sendExportPSK | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
exp_ctx: Spec.Agile.HPKE.exp_ctx_s cs ->
l: Spec.Agile.HPKE.exp_len cs ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs * Lib.ByteSequence.lbytes l) | {
"end_col": 47,
"end_line": 531,
"start_col": 2,
"start_line": 528
} |
Prims.Tot | val serialize_public_key:
cs:ciphersuite
-> pk:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (key_dh_public_s cs) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk | val serialize_public_key:
cs:ciphersuite
-> pk:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (key_dh_public_s cs)
let serialize_public_key cs pk = | false | null | false | match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
| DH.DH_P256 -> create 1 (u8 4) @| pk | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Lib.Sequence.op_At_Bar",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Agile.DH.size_public",
"Lib.Sequence.create",
"Lib.IntTypes.u8",
"Spec.Agile.HPKE.key_dh_public_s"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64 | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val serialize_public_key:
cs:ciphersuite
-> pk:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (key_dh_public_s cs) | [] | Spec.Agile.HPKE.serialize_public_key | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
pk: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs)
-> Spec.Agile.HPKE.key_dh_public_s cs | {
"end_col": 39,
"end_line": 137,
"start_col": 33,
"start_line": 134
} |
Prims.Tot | val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let suite_id_kem cs =
Seq.append label_KEM (id_kem cs) | val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs = | false | null | false | Seq.append label_KEM (id_kem cs) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"FStar.Seq.Base.append",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Agile.HPKE.label_KEM",
"Spec.Agile.HPKE.id_kem",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.size_suite_id_kem"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem) | false | true | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem) | [] | Spec.Agile.HPKE.suite_id_kem | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> Lib.ByteSequence.lbytes Spec.Agile.HPKE.size_suite_id_kem | {
"end_col": 34,
"end_line": 49,
"start_col": 2,
"start_line": 49
} |
Prims.Tot | val context_increment_seq:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs ->
Tot (option (encryption_context cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1)) | val context_increment_seq:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs ->
Tot (option (encryption_context cs))
let context_increment_seq cs ctx = | false | null | false | let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else Some (set_seq cs ctx (seq + 1)) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.encryption_context",
"Prims.op_Equality",
"Prims.nat",
"Spec.Agile.HPKE.max_seq",
"FStar.Pervasives.Native.None",
"Prims.bool",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.set_seq",
"Prims.op_Addition",
"FStar.Pervasives.Native.option",
"Spec.Agile.HPKE.seq_aead_s",
"Spec.Agile.HPKE.seq_of_ctx"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val context_increment_seq:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs ->
Tot (option (encryption_context cs)) | [] | Spec.Agile.HPKE.context_increment_seq | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite_not_export_only -> ctx: Spec.Agile.HPKE.encryption_context cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.encryption_context cs) | {
"end_col": 33,
"end_line": 421,
"start_col": 34,
"start_line": 418
} |
Prims.Tot | val setupAuthPSKR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (encryption_context cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let setupAuthPSKR cs enc skR info psk psk_id pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)))
| _ -> None | val setupAuthPSKR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (encryption_context cs))
let setupAuthPSKR cs enc skR info psk psk_id pkS = | false | null | false | let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)))
| _ -> None | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"FStar.Pervasives.Native.Mktuple2",
"FStar.Pervasives.Native.option",
"Spec.Agile.HPKE.key_kem_s",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_schedule",
"Spec.Agile.HPKE.AuthPSK",
"FStar.Pervasives.Native.tuple2",
"FStar.Pervasives.Native.None",
"Spec.Agile.HPKE.auth_decap",
"Spec.Agile.DH.secret_to_public"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx)
let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None
let sealAuth cs skE pkR info aad pt skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openAuth cs enc skR info aad ct pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportAuth cs skE pkR info exp_ctx l skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportAuth cs enc skR info exp_ctx l pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// AuthPSK mode
///
let setupAuthPSKS cs skE pkR info psk psk_id skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val setupAuthPSKR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (encryption_context cs)) | [] | Spec.Agile.HPKE.setupAuthPSKR | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs ->
pkS: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs)
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.encryption_context cs) | {
"end_col": 13,
"end_line": 603,
"start_col": 50,
"start_line": 597
} |
Prims.Pure | val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs) | val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context = | false | null | false | let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs)
(suite_id_kem cs)
eae_prk
label_shared_secret
kem_context
(size_kem_key cs) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [] | [
"Spec.Agile.HPKE.ciphersuite",
"Lib.ByteSequence.bytes",
"Spec.Agile.HPKE.labeled_expand",
"Spec.Agile.HPKE.kem_hash_of_cs",
"Spec.Agile.HPKE.suite_id_kem",
"Spec.Agile.HPKE.label_shared_secret",
"Spec.Agile.HPKE.size_kem_key",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Hash.Definitions.hash_length",
"Spec.Agile.HPKE.labeled_extract",
"Lib.ByteSequence.lbytes_empty",
"Spec.Agile.HPKE.label_eae_prk",
"Spec.Agile.HPKE.key_kem_s"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True) | [] | Spec.Agile.HPKE.extract_and_expand | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> dh: Lib.ByteSequence.bytes -> kem_context: Lib.ByteSequence.bytes
-> Prims.Pure (Spec.Agile.HPKE.key_kem_s cs) | {
"end_col": 112,
"end_line": 126,
"start_col": 42,
"start_line": 124
} |
Prims.Tot | val setupPSKS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx) | val setupPSKS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs))
let setupPSKS cs skE pkR info psk psk_id = | false | null | false | match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.HPKE.encap",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_kem_s",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.key_schedule",
"Spec.Agile.HPKE.PSK",
"Prims.unit",
"Prims._assert",
"Prims.b2t",
"Spec.Agile.HPKE.verify_psk_inputs",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
/// | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val setupPSKS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs)) | [] | Spec.Agile.HPKE.setupPSKS | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs *
Spec.Agile.HPKE.encryption_context cs) | {
"end_col": 23,
"end_line": 500,
"start_col": 2,
"start_line": 495
} |
Prims.Tot | val setupAuthR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (encryption_context cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None | val setupAuthR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (encryption_context cs))
let setupAuthR cs enc skR info pkS = | false | null | false | let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret -> Some (key_schedule cs Auth shared_secret info None)
| _ -> None | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"FStar.Pervasives.Native.Mktuple2",
"FStar.Pervasives.Native.option",
"Spec.Agile.HPKE.key_kem_s",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_schedule",
"Spec.Agile.HPKE.Auth",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.HPKE.auth_decap",
"Spec.Agile.DH.secret_to_public"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val setupAuthR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (encryption_context cs)) | [] | Spec.Agile.HPKE.setupAuthR | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
pkS: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs)
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.encryption_context cs) | {
"end_col": 13,
"end_line": 556,
"start_col": 36,
"start_line": 550
} |
Prims.Pure | val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l | val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l = | false | null | false | let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [] | [
"Spec.Agile.HPKE.hash_algorithm",
"Lib.ByteSequence.bytes",
"Lib.IntTypes.size_nat",
"Spec.Agile.HKDF.expand",
"FStar.Seq.Base.seq",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"FStar.Seq.Base.append",
"Lib.IntTypes.uint_t",
"Spec.Agile.HPKE.label_version",
"Lib.Sequence.seq",
"Prims.l_and",
"Prims.eq2",
"Prims.nat",
"Lib.Sequence.length",
"Prims.l_or",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.pow2",
"Prims.op_Multiply",
"Lib.ByteSequence.nat_from_intseq_be",
"Lib.ByteSequence.nat_to_bytes_be",
"Lib.ByteSequence.lbytes"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True) | [] | Spec.Agile.HPKE.labeled_expand | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
a: Spec.Agile.HPKE.hash_algorithm ->
suite_id: Lib.ByteSequence.bytes ->
prk: Lib.ByteSequence.bytes ->
label: Lib.ByteSequence.bytes ->
info: Lib.ByteSequence.bytes ->
l: Lib.IntTypes.size_nat
-> Prims.Pure (Lib.ByteSequence.lbytes l) | {
"end_col": 35,
"end_line": 106,
"start_col": 48,
"start_line": 100
} |
Prims.Tot | val setupBaseR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs ->
Tot (option (encryption_context cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None | val setupBaseR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs ->
Tot (option (encryption_context cs))
let setupBaseR cs enc skR info = | false | null | false | let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret -> Some (key_schedule cs Base shared_secret info None)
| _ -> None | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"FStar.Pervasives.Native.Mktuple2",
"FStar.Pervasives.Native.option",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.key_kem_s",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_schedule",
"Spec.Agile.HPKE.Base",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.HPKE.decap",
"Spec.Agile.DH.secret_to_public"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val setupBaseR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs ->
Tot (option (encryption_context cs)) | [] | Spec.Agile.HPKE.setupBaseR | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.encryption_context cs) | {
"end_col": 13,
"end_line": 460,
"start_col": 32,
"start_line": 454
} |
Prims.Tot | val id_kem: cs:ciphersuite -> Tot (lbytes 2) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32) | val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = | false | null | false | let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.DH.algorithm",
"Spec.Agile.HPKE.hash_algorithm",
"Spec.Agile.HPKE.aead",
"Spec.Hash.Definitions.hash_alg",
"FStar.Pervasives.Native.Mktuple2",
"Lib.Sequence.op_At_Bar",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Lib.Sequence.create",
"Lib.IntTypes.u8",
"Lib.ByteSequence.lbytes"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val id_kem: cs:ciphersuite -> Tot (lbytes 2) | [] | Spec.Agile.HPKE.id_kem | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> Lib.ByteSequence.lbytes 2 | {
"end_col": 74,
"end_line": 30,
"start_col": 15,
"start_line": 27
} |
Prims.Tot | val setupPSKR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (encryption_context cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None | val setupPSKR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (encryption_context cs))
let setupPSKR cs enc skR info psk psk_id = | false | null | false | let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret -> Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"FStar.Pervasives.Native.Mktuple2",
"FStar.Pervasives.Native.option",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.key_kem_s",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_schedule",
"Spec.Agile.HPKE.PSK",
"FStar.Pervasives.Native.tuple2",
"FStar.Pervasives.Native.None",
"Spec.Agile.HPKE.decap",
"Spec.Agile.DH.secret_to_public"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val setupPSKR:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (encryption_context cs)) | [] | Spec.Agile.HPKE.setupPSKR | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.encryption_context cs) | {
"end_col": 13,
"end_line": 508,
"start_col": 42,
"start_line": 502
} |
Prims.Tot | val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1)) | val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter = | false | null | false | let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes =
labeled_expand (kem_hash_of_cs cs)
(suite_id_kem cs)
dkp_prk
label_candidate
counterbyte
(size_dh_key cs)
in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime
then if (v counter) = 255 then None else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None -> if (v counter) = 255 then None else dkp_nist_p cs dkp_prk (counter +! (u8 1)) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total",
""
] | [
"Spec.Agile.HPKE.ciphersuite",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.size_kem_kdf",
"Lib.IntTypes.uint8",
"Prims.op_BarBar",
"Prims.op_Equality",
"Prims.int",
"Prims.op_GreaterThanOrEqual",
"Spec.P256.PointOps.prime",
"Lib.IntTypes.v",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.key_dh_public_s",
"Prims.bool",
"Spec.Agile.HPKE.dkp_nist_p",
"Lib.IntTypes.op_Plus_Bang",
"Lib.IntTypes.u8",
"FStar.Pervasives.Native.option",
"Spec.Agile.DH.secret_to_public",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.DH.serialized_point",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.serialize_public_key",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.pow2",
"Prims.op_Multiply",
"Lib.Sequence.length",
"Lib.IntTypes.int_t",
"Lib.ByteSequence.nat_from_intseq_be",
"Lib.Sequence.lseq",
"Spec.Agile.HPKE.size_dh_key",
"Prims.l_Forall",
"Prims.l_imp",
"Prims.eq2",
"Lib.Sequence.index",
"Lib.IntTypes.logand",
"FStar.Seq.Base.create",
"Lib.IntTypes.mk_int",
"Lib.Sequence.map2",
"Lib.IntTypes.uint_t",
"Spec.Agile.HPKE.labeled_expand",
"Spec.Agile.HPKE.kem_hash_of_cs",
"Spec.Agile.HPKE.suite_id_kem",
"Spec.Agile.HPKE.label_candidate",
"Lib.Sequence.seq",
"Prims.l_and",
"Prims.l_or",
"Lib.ByteSequence.nat_to_intseq_be"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter) | [
"recursion"
] | Spec.Agile.HPKE.dkp_nist_p | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
dkp_prk: Lib.ByteSequence.lbytes (Spec.Agile.HPKE.size_kem_kdf cs) ->
counter: Lib.IntTypes.uint8
-> Prims.Tot
(FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_secret_s cs *
Spec.Agile.HPKE.key_dh_public_s cs)) | {
"end_col": 52,
"end_line": 154,
"start_col": 39,
"start_line": 141
} |
Prims.Tot | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length) | let extract_and_expand_ctx_pred (cs: ciphersuite) (ctx_length: nat) = | false | null | false | labeled_expand_info_length_pred (kem_hash_of_cs cs)
(size_suite_id_kem + size_label_shared_secret + ctx_length) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Prims.nat",
"Spec.Agile.HPKE.labeled_expand_info_length_pred",
"Spec.Agile.HPKE.kem_hash_of_cs",
"Prims.op_Addition",
"Spec.Agile.HPKE.size_suite_id_kem",
"Spec.Agile.HPKE.size_label_shared_secret",
"Prims.bool"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length) | false | true | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val extract_and_expand_ctx_pred : cs: Spec.Agile.HPKE.ciphersuite -> ctx_length: Prims.nat -> Prims.bool | [] | Spec.Agile.HPKE.extract_and_expand_ctx_pred | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> ctx_length: Prims.nat -> Prims.bool | {
"end_col": 113,
"end_line": 112,
"start_col": 2,
"start_line": 112
} |
|
Prims.Tot | val deserialize_public_key:
cs:ciphersuite
-> pk:key_dh_public_s cs ->
Tot (DH.serialized_point (kem_dh_of_cs cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64 | val deserialize_public_key:
cs:ciphersuite
-> pk:key_dh_public_s cs ->
Tot (DH.serialized_point (kem_dh_of_cs cs))
let deserialize_public_key cs pk = | false | null | false | match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
| DH.DH_P256 -> sub pk 1 64 | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Lib.Sequence.sub",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Agile.HPKE.size_dh_public",
"Spec.Agile.DH.serialized_point"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val deserialize_public_key:
cs:ciphersuite
-> pk:key_dh_public_s cs ->
Tot (DH.serialized_point (kem_dh_of_cs cs)) | [] | Spec.Agile.HPKE.deserialize_public_key | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> pk: Spec.Agile.HPKE.key_dh_public_s cs
-> Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) | {
"end_col": 29,
"end_line": 131,
"start_col": 35,
"start_line": 128
} |
Prims.Tot | val receiveExportPSK:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (lbytes l)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l) | val receiveExportPSK:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (lbytes l))
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id = | false | null | false | match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx -> Some (context_export cs ctx exp_ctx l) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.exp_ctx_s",
"Spec.Agile.HPKE.exp_len",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.HPKE.setupPSKR",
"FStar.Pervasives.Native.None",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.encryption_context",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.context_export",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val receiveExportPSK:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (lbytes l)) | [] | Spec.Agile.HPKE.receiveExportPSK | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
exp_ctx: Spec.Agile.HPKE.exp_ctx_s cs ->
l: Spec.Agile.HPKE.exp_len cs ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs
-> FStar.Pervasives.Native.option (Lib.ByteSequence.lbytes l) | {
"end_col": 42,
"end_line": 537,
"start_col": 2,
"start_line": 534
} |
Prims.Tot | val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context | val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash = | false | null | false | let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.mode",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.size_kdf",
"FStar.Seq.Base.seq",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"FStar.Seq.Base.append",
"Lib.IntTypes.uint_t",
"Lib.Sequence.lseq",
"Spec.Agile.HPKE.size_mode_identifier",
"Spec.Agile.HPKE.id_of_mode",
"Spec.Agile.HPKE.size_ks_ctx"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs)) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs)) | [] | Spec.Agile.HPKE.build_context | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
m: Spec.Agile.HPKE.mode ->
psk_id_hash: Lib.ByteSequence.lbytes (Spec.Agile.HPKE.size_kdf cs) ->
info_hash: Lib.ByteSequence.lbytes (Spec.Agile.HPKE.size_kdf cs)
-> Lib.ByteSequence.lbytes (Spec.Agile.HPKE.size_ks_ctx cs) | {
"end_col": 9,
"end_line": 320,
"start_col": 46,
"start_line": 316
} |
Prims.Tot | val context_export:
cs:ciphersuite
-> ctx:encryption_context cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs ->
Tot (lbytes l) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l | val context_export:
cs:ciphersuite
-> ctx:encryption_context cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs ->
Tot (lbytes l)
let context_export cs ctx exp_ctx l = | false | null | false | let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.exp_ctx_s",
"Spec.Agile.HPKE.exp_len",
"Spec.Agile.HPKE.labeled_expand",
"Spec.Agile.HPKE.hash_of_cs",
"Spec.Agile.HPKE.suite_id_hpke",
"Spec.Agile.HPKE.label_sec",
"Spec.Agile.HPKE.exporter_secret_s",
"Spec.Agile.HPKE.exp_sec_of_ctx",
"Lib.ByteSequence.lbytes"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
/// | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val context_export:
cs:ciphersuite
-> ctx:encryption_context cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs ->
Tot (lbytes l) | [] | Spec.Agile.HPKE.context_export | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
ctx: Spec.Agile.HPKE.encryption_context cs ->
exp_ctx: Spec.Agile.HPKE.exp_ctx_s cs ->
l: Spec.Agile.HPKE.exp_len cs
-> Lib.ByteSequence.lbytes l | {
"end_col": 79,
"end_line": 410,
"start_col": 37,
"start_line": 408
} |
Prims.Tot | val derive_key_pair:
cs:ciphersuite
-> ikm:dkp_ikm_s cs ->
Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0) | val derive_key_pair:
cs:ciphersuite
-> ikm:dkp_ikm_s cs ->
Tot (option (key_dh_secret_s cs & key_dh_public_s cs))
let derive_key_pair cs ikm = | false | null | false | match kem_dh_of_cs cs with
| DH.DH_Curve25519 ->
let dkp_prk =
labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm
in
let sk =
labeled_expand (kem_hash_of_cs cs)
(suite_id_kem cs)
dkp_prk
label_sk
lbytes_empty
(size_dh_key cs)
in
(match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk))
| DH.DH_P256 ->
let dkp_prk =
labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm
in
dkp_nist_p cs dkp_prk (u8 0) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.dkp_ikm_s",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.DH.secret_to_public",
"Spec.Agile.DH.serialized_point",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.key_dh_public_s",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.serialize_public_key",
"FStar.Pervasives.Native.option",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Agile.HPKE.size_dh_key",
"Spec.Agile.HPKE.labeled_expand",
"Spec.Agile.HPKE.kem_hash_of_cs",
"Spec.Agile.HPKE.suite_id_kem",
"Spec.Agile.HPKE.label_sk",
"Lib.ByteSequence.lbytes_empty",
"Spec.Hash.Definitions.hash_length",
"Spec.Agile.HPKE.labeled_extract",
"Spec.Agile.HPKE.label_dkp_prk",
"Spec.Agile.HPKE.dkp_nist_p",
"Lib.IntTypes.u8"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1)) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val derive_key_pair:
cs:ciphersuite
-> ikm:dkp_ikm_s cs ->
Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) | [] | Spec.Agile.HPKE.derive_key_pair | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> ikm: Spec.Agile.HPKE.dkp_ikm_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_secret_s cs *
Spec.Agile.HPKE.key_dh_public_s cs) | {
"end_col": 32,
"end_line": 168,
"start_col": 2,
"start_line": 159
} |
Prims.Tot | val context_seal:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs) ->
Tot (option (encryption_context cs & AEAD.cipher (aead_alg_of cs))) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct) | val context_seal:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs) ->
Tot (option (encryption_context cs & AEAD.cipher (aead_alg_of cs)))
let context_seal cs ctx aad pt = | false | null | false | let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.AEAD.ad",
"Spec.Agile.HPKE.aead_alg_of",
"Spec.Agile.AEAD.plain",
"Spec.Agile.HPKE.context_increment_seq",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.AEAD.cipher",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"FStar.Pervasives.Native.option",
"Spec.Agile.AEAD.encrypted",
"Spec.Agile.AEAD.encrypt",
"Spec.Agile.HPKE.nonce_aead_s",
"Spec.Agile.HPKE.context_compute_nonce",
"Spec.Agile.HPKE.seq_aead_s",
"Spec.Agile.HPKE.seq_of_ctx",
"Spec.Agile.HPKE.key_aead_s",
"Spec.Agile.HPKE.key_of_ctx"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1)) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val context_seal:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs) ->
Tot (option (encryption_context cs & AEAD.cipher (aead_alg_of cs))) | [] | Spec.Agile.HPKE.context_seal | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
ctx: Spec.Agile.HPKE.encryption_context cs ->
aad: Spec.Agile.AEAD.ad (Spec.Agile.HPKE.aead_alg_of cs) ->
pt: Spec.Agile.AEAD.plain (Spec.Agile.HPKE.aead_alg_of cs)
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.encryption_context cs *
Spec.Agile.AEAD.cipher (Spec.Agile.HPKE.aead_alg_of cs)) | {
"end_col": 38,
"end_line": 430,
"start_col": 32,
"start_line": 423
} |
Prims.Tot | val context_open:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs) ->
Tot (option (encryption_context cs & AEAD.plain (aead_alg_of cs))) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt) | val context_open:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs) ->
Tot (option (encryption_context cs & AEAD.plain (aead_alg_of cs)))
let context_open cs ctx aad ct = | false | null | false | let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.AEAD.ad",
"Spec.Agile.HPKE.aead_alg_of",
"Spec.Agile.AEAD.cipher",
"Spec.Agile.AEAD.decrypt",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.AEAD.plain",
"Spec.Agile.AEAD.decrypted",
"Spec.Agile.HPKE.context_increment_seq",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"FStar.Pervasives.Native.option",
"Spec.Agile.HPKE.nonce_aead_s",
"Spec.Agile.HPKE.context_compute_nonce",
"Spec.Agile.HPKE.seq_aead_s",
"Spec.Agile.HPKE.seq_of_ctx",
"Spec.Agile.HPKE.key_aead_s",
"Spec.Agile.HPKE.key_of_ctx"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val context_open:
cs:ciphersuite_not_export_only
-> ctx:encryption_context cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs) ->
Tot (option (encryption_context cs & AEAD.plain (aead_alg_of cs))) | [] | Spec.Agile.HPKE.context_open | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
ctx: Spec.Agile.HPKE.encryption_context cs ->
aad: Spec.Agile.AEAD.ad (Spec.Agile.HPKE.aead_alg_of cs) ->
ct: Spec.Agile.AEAD.cipher (Spec.Agile.HPKE.aead_alg_of cs)
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.encryption_context cs *
Spec.Agile.AEAD.plain (Spec.Agile.HPKE.aead_alg_of cs)) | {
"end_col": 40,
"end_line": 441,
"start_col": 32,
"start_line": 432
} |
Prims.Tot | val id_aead: cs:ciphersuite -> Tot (lbytes 2) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255) | val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = | false | null | false | let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.DH.algorithm",
"Spec.Agile.HPKE.hash_algorithm",
"Spec.Agile.HPKE.aead",
"Spec.Hash.Definitions.hash_alg",
"Lib.Sequence.op_At_Bar",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Lib.Sequence.create",
"Lib.IntTypes.u8",
"Lib.ByteSequence.lbytes"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val id_aead: cs:ciphersuite -> Tot (lbytes 2) | [] | Spec.Agile.HPKE.id_aead | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> Lib.ByteSequence.lbytes 2 | {
"end_col": 56,
"end_line": 45,
"start_col": 16,
"start_line": 40
} |
Prims.Tot | val id_kdf: cs:ciphersuite -> Tot (lbytes 2) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3) | val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = | false | null | false | let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.DH.algorithm",
"Spec.Agile.HPKE.hash_algorithm",
"Spec.Agile.HPKE.aead",
"Spec.Hash.Definitions.hash_alg",
"Lib.Sequence.op_At_Bar",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Lib.Sequence.create",
"Lib.IntTypes.u8",
"Lib.ByteSequence.lbytes"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 20,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val id_kdf: cs:ciphersuite -> Tot (lbytes 2) | [] | Spec.Agile.HPKE.id_kdf | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | cs: Spec.Agile.HPKE.ciphersuite -> Lib.ByteSequence.lbytes 2 | {
"end_col": 55,
"end_line": 37,
"start_col": 15,
"start_line": 33
} |
Prims.Tot | val receiveExportAuth:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (lbytes l)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let receiveExportAuth cs enc skR info exp_ctx l pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l) | val receiveExportAuth:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (lbytes l))
let receiveExportAuth cs enc skR info exp_ctx l pkS = | false | null | false | match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx -> Some (context_export cs ctx exp_ctx l) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.exp_ctx_s",
"Spec.Agile.HPKE.exp_len",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.setupAuthR",
"FStar.Pervasives.Native.None",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.encryption_context",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.context_export",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx)
let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None
let sealAuth cs skE pkR info aad pt skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openAuth cs enc skR info aad ct pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportAuth cs skE pkR info exp_ctx l skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val receiveExportAuth:
cs:ciphersuite
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (lbytes l)) | [] | Spec.Agile.HPKE.receiveExportAuth | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
exp_ctx: Spec.Agile.HPKE.exp_ctx_s cs ->
l: Spec.Agile.HPKE.exp_len cs ->
pkS: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs)
-> FStar.Pervasives.Native.option (Lib.ByteSequence.lbytes l) | {
"end_col": 42,
"end_line": 584,
"start_col": 2,
"start_line": 581
} |
Prims.Tot | val key_schedule_core
(cs: ciphersuite)
(m: mode)
(shared_secret: key_kem_s cs)
(info: info_s cs)
(opsk: option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) &
exporter_secret_s cs &
(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret | val key_schedule_core
(cs: ciphersuite)
(m: mode)
(shared_secret: key_kem_s cs)
(info: info_s cs)
(opsk: option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) &
exporter_secret_s cs &
(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
let key_schedule_core
(cs: ciphersuite)
(m: mode)
(shared_secret: key_kem_s cs)
(info: info_s cs)
(opsk: option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) &
exporter_secret_s cs &
(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) = | false | null | false | let psk, psk_id =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash =
labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id
in
let info_hash =
labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info
in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret =
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs)
in
context, exporter_secret, secret | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.mode",
"Spec.Agile.HPKE.key_kem_s",
"Spec.Agile.HPKE.info_s",
"FStar.Pervasives.Native.option",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Lib.ByteSequence.bytes",
"FStar.Pervasives.Native.Mktuple3",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.size_ks_ctx",
"Spec.Agile.HPKE.exporter_secret_s",
"Spec.Hash.Definitions.hash_length",
"Spec.Agile.HPKE.hash_of_cs",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Agile.HPKE.size_kdf",
"Spec.Agile.HPKE.labeled_expand",
"Spec.Agile.HPKE.suite_id_hpke",
"Spec.Agile.HPKE.label_exp",
"Spec.Agile.HPKE.labeled_extract",
"Spec.Agile.HPKE.label_secret",
"Spec.Agile.HPKE.build_context",
"Lib.ByteSequence.lbytes_empty",
"Spec.Agile.HPKE.label_info_hash",
"Spec.Agile.HPKE.label_psk_id_hash",
"FStar.Pervasives.Native.tuple3",
"Lib.Sequence.seq",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.default_psk",
"Spec.Agile.HPKE.default_psk_id"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val key_schedule_core
(cs: ciphersuite)
(m: mode)
(shared_secret: key_kem_s cs)
(info: info_s cs)
(opsk: option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) &
exporter_secret_s cs &
(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) | [] | Spec.Agile.HPKE.key_schedule_core | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
m: Spec.Agile.HPKE.mode ->
shared_secret: Spec.Agile.HPKE.key_kem_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
opsk: FStar.Pervasives.Native.option (Spec.Agile.HPKE.psk_s cs * Spec.Agile.HPKE.psk_id_s cs)
-> (Lib.ByteSequence.lbytes (Spec.Agile.HPKE.size_ks_ctx cs) *
Spec.Agile.HPKE.exporter_secret_s cs) *
Lib.ByteSequence.lbytes (Spec.Hash.Definitions.hash_length (Spec.Agile.HPKE.hash_of_cs cs)) | {
"end_col": 34,
"end_line": 362,
"start_col": 117,
"start_line": 350
} |
Prims.Tot | val sendExportAuthPSK:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & lbytes l)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let sendExportAuthPSK cs skE pkR info exp_ctx l psk psk_id skS =
match setupAuthPSKS cs skE pkR info psk psk_id skS with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l) | val sendExportAuthPSK:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & lbytes l))
let sendExportAuthPSK cs skE pkR info exp_ctx l psk psk_id skS = | false | null | false | match setupAuthPSKS cs skE pkR info psk psk_id skS with
| None -> None
| Some (enc, ctx) -> Some (enc, context_export cs ctx exp_ctx l) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.exp_ctx_s",
"Spec.Agile.HPKE.exp_len",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.HPKE.setupAuthPSKS",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.encryption_context",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.context_export",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx)
let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None
let sealAuth cs skE pkR info aad pt skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openAuth cs enc skR info aad ct pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportAuth cs skE pkR info exp_ctx l skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportAuth cs enc skR info exp_ctx l pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// AuthPSK mode
///
let setupAuthPSKS cs skE pkR info psk psk_id skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupAuthPSKR cs enc skR info psk psk_id pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealAuthPSK cs skE pkR info aad pt psk psk_id skS =
match setupAuthPSKS cs skE pkR info psk psk_id skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openAuthPSK cs enc skR info aad ct psk psk_id pkS =
match setupAuthPSKR cs enc skR info psk psk_id pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val sendExportAuthPSK:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> exp_ctx:exp_ctx_s cs
-> l:exp_len cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & lbytes l)) | [] | Spec.Agile.HPKE.sendExportAuthPSK | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
exp_ctx: Spec.Agile.HPKE.exp_ctx_s cs ->
l: Spec.Agile.HPKE.exp_len cs ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs ->
skS: Spec.Agile.HPKE.key_dh_secret_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs * Lib.ByteSequence.lbytes l) | {
"end_col": 47,
"end_line": 625,
"start_col": 2,
"start_line": 622
} |
Prims.Tot | val setupAuthPSKS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let setupAuthPSKS cs skE pkR info psk psk_id skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx) | val setupAuthPSKS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs))
let setupAuthPSKS cs skE pkR info psk psk_id skS = | false | null | false | match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.HPKE.auth_encap",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.key_kem_s",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.key_schedule",
"Spec.Agile.HPKE.AuthPSK",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx)
let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None
let sealAuth cs skE pkR info aad pt skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openAuth cs enc skR info aad ct pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportAuth cs skE pkR info exp_ctx l skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportAuth cs enc skR info exp_ctx l pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// AuthPSK mode
/// | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val setupAuthPSKS:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & encryption_context cs)) | [] | Spec.Agile.HPKE.setupAuthPSKS | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs ->
skS: Spec.Agile.HPKE.key_dh_secret_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs *
Spec.Agile.HPKE.encryption_context cs) | {
"end_col": 23,
"end_line": 595,
"start_col": 2,
"start_line": 591
} |
Prims.Tot | val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret) | val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
let decap cs enc skR = | false | null | false | let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2 * size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.dh",
"Spec.Agile.HPKE.kem_dh_of_cs",
"FStar.Pervasives.Native.None",
"Spec.Agile.HPKE.key_kem_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.DH.secret_to_public",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.extract_and_expand",
"Prims.unit",
"Prims._assert",
"Prims.b2t",
"Spec.Agile.HPKE.extract_and_expand_ctx_pred",
"FStar.Seq.Base.length",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.op_Equality",
"Prims.int",
"FStar.Mul.op_Star",
"Spec.Agile.HPKE.size_dh_public",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Spec.Agile.HPKE.prepare_dh",
"Prims.op_Addition",
"Prims.eq2",
"FStar.Seq.Base.seq",
"Lib.Sequence.to_seq",
"FStar.Seq.Base.append",
"Lib.Sequence.concat",
"Spec.Agile.HPKE.serialize_public_key",
"FStar.Pervasives.Native.option",
"Spec.Agile.HPKE.deserialize_public_key",
"FStar.Pervasives.allow_inversion",
"Spec.Hash.Definitions.hash_alg",
"Spec.Agile.DH.algorithm"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs)) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs)) | [] | Spec.Agile.HPKE.decap | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_kem_s cs) | {
"end_col": 26,
"end_line": 225,
"start_col": 22,
"start_line": 209
} |
Prims.Tot | val key_schedule_end
(cs: ciphersuite)
(m: mode)
(context: lbytes (size_ks_ctx cs))
(exporter_secret: exporter_secret_s cs)
(secret: (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret)) | val key_schedule_end
(cs: ciphersuite)
(m: mode)
(context: lbytes (size_ks_ctx cs))
(exporter_secret: exporter_secret_s cs)
(secret: (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
let key_schedule_end
(cs: ciphersuite)
(m: mode)
(context: lbytes (size_ks_ctx cs))
(exporter_secret: exporter_secret_s cs)
(secret: (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs = | false | null | false | if is_valid_not_export_only_ciphersuite cs
then
(let key =
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs)
in
let base_nonce =
labeled_expand (hash_of_cs cs)
(suite_id_hpke cs)
secret
label_base_nonce
context
(size_aead_nonce cs)
in
(key, base_nonce, 0, exporter_secret))
else
(assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret)) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.mode",
"Lib.ByteSequence.lbytes",
"Spec.Agile.HPKE.size_ks_ctx",
"Spec.Agile.HPKE.exporter_secret_s",
"Spec.Hash.Definitions.hash_length",
"Spec.Agile.HPKE.hash_of_cs",
"Spec.Agile.HPKE.is_valid_not_export_only_ciphersuite",
"FStar.Pervasives.Native.Mktuple4",
"Spec.Agile.HPKE.key_aead_s",
"Spec.Agile.HPKE.nonce_aead_s",
"Spec.Agile.HPKE.seq_aead_s",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Agile.HPKE.size_aead_nonce",
"Spec.Agile.HPKE.labeled_expand",
"Spec.Agile.HPKE.suite_id_hpke",
"Spec.Agile.HPKE.label_base_nonce",
"Spec.Agile.HPKE.size_aead_key",
"Spec.Agile.HPKE.label_key",
"Prims.bool",
"Lib.ByteSequence.lbytes_empty",
"Prims.unit",
"Prims._assert",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"Spec.Agile.HPKE.encryption_context"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val key_schedule_end
(cs: ciphersuite)
(m: mode)
(context: lbytes (size_ks_ctx cs))
(exporter_secret: exporter_secret_s cs)
(secret: (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs | [] | Spec.Agile.HPKE.key_schedule_end | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
m: Spec.Agile.HPKE.mode ->
context: Lib.ByteSequence.lbytes (Spec.Agile.HPKE.size_ks_ctx cs) ->
exporter_secret: Spec.Agile.HPKE.exporter_secret_s cs ->
secret:
Lib.ByteSequence.lbytes (Spec.Hash.Definitions.hash_length (Spec.Agile.HPKE.hash_of_cs cs))
-> Spec.Agile.HPKE.encryption_context cs | {
"end_col": 53,
"end_line": 381,
"start_col": 2,
"start_line": 372
} |
Prims.Tot | val sealPSK:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | val sealPSK:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt))
let sealPSK cs skE pkR info aad pt psk psk_id = | false | null | false | match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.AEAD.ad",
"Spec.Agile.HPKE.aead_alg_of",
"Spec.Agile.AEAD.plain",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.HPKE.setupPSKS",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.AEAD.encrypted",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.context_seal",
"Spec.Agile.AEAD.cipher",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val sealPSK:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt)) | [] | Spec.Agile.HPKE.sealPSK | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
aad: Spec.Agile.AEAD.ad (Spec.Agile.HPKE.aead_alg_of cs) ->
pt: Spec.Agile.AEAD.plain (Spec.Agile.HPKE.aead_alg_of cs) ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs *
Spec.Agile.AEAD.encrypted pt) | {
"end_col": 36,
"end_line": 516,
"start_col": 2,
"start_line": 511
} |
Prims.Tot | val sealAuth:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let sealAuth cs skE pkR info aad pt skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | val sealAuth:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt))
let sealAuth cs skE pkR info aad pt skS = | false | null | false | match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.AEAD.ad",
"Spec.Agile.HPKE.aead_alg_of",
"Spec.Agile.AEAD.plain",
"Spec.Agile.HPKE.setupAuthS",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.AEAD.encrypted",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.context_seal",
"Spec.Agile.AEAD.cipher",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx)
let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val sealAuth:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt)) | [] | Spec.Agile.HPKE.sealAuth | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
aad: Spec.Agile.AEAD.ad (Spec.Agile.HPKE.aead_alg_of cs) ->
pt: Spec.Agile.AEAD.plain (Spec.Agile.HPKE.aead_alg_of cs) ->
skS: Spec.Agile.HPKE.key_dh_secret_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs *
Spec.Agile.AEAD.encrypted pt) | {
"end_col": 36,
"end_line": 564,
"start_col": 2,
"start_line": 559
} |
Prims.Tot | val sealAuthPSK:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let sealAuthPSK cs skE pkR info aad pt psk psk_id skS =
match setupAuthPSKS cs skE pkR info psk psk_id skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | val sealAuthPSK:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt))
let sealAuthPSK cs skE pkR info aad pt psk psk_id skS = | false | null | false | match setupAuthPSKS cs skE pkR info psk psk_id skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.AEAD.ad",
"Spec.Agile.HPKE.aead_alg_of",
"Spec.Agile.AEAD.plain",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.HPKE.setupAuthPSKS",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.AEAD.encrypted",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.context_seal",
"Spec.Agile.AEAD.cipher",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx)
let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None
let sealAuth cs skE pkR info aad pt skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openAuth cs enc skR info aad ct pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportAuth cs skE pkR info exp_ctx l skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportAuth cs enc skR info exp_ctx l pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// AuthPSK mode
///
let setupAuthPSKS cs skE pkR info psk psk_id skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupAuthPSKR cs enc skR info psk psk_id pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)))
| _ -> None | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val sealAuthPSK:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> skS:key_dh_secret_s cs ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt)) | [] | Spec.Agile.HPKE.sealAuthPSK | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
aad: Spec.Agile.AEAD.ad (Spec.Agile.HPKE.aead_alg_of cs) ->
pt: Spec.Agile.AEAD.plain (Spec.Agile.HPKE.aead_alg_of cs) ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs ->
skS: Spec.Agile.HPKE.key_dh_secret_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs *
Spec.Agile.AEAD.encrypted pt) | {
"end_col": 36,
"end_line": 611,
"start_col": 2,
"start_line": 606
} |
Prims.Tot | val sealBase:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs) ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | val sealBase:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs) ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt))
let sealBase cs skE pkR info aad pt = | false | null | false | match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.AEAD.ad",
"Spec.Agile.HPKE.aead_alg_of",
"Spec.Agile.AEAD.plain",
"Spec.Agile.HPKE.setupBaseS",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.AEAD.encrypted",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.context_seal",
"Spec.Agile.AEAD.cipher",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val sealBase:
cs:ciphersuite_not_export_only
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> pt:AEAD.plain (aead_alg_of cs) ->
Tot (option (key_dh_public_s cs & AEAD.encrypted #(aead_alg_of cs) pt)) | [] | Spec.Agile.HPKE.sealBase | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
info: Spec.Agile.HPKE.info_s cs ->
aad: Spec.Agile.AEAD.ad (Spec.Agile.HPKE.aead_alg_of cs) ->
pt: Spec.Agile.AEAD.plain (Spec.Agile.HPKE.aead_alg_of cs)
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_dh_public_s cs *
Spec.Agile.AEAD.encrypted pt) | {
"end_col": 36,
"end_line": 468,
"start_col": 2,
"start_line": 463
} |
Prims.Tot | val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret) | val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
let auth_decap cs enc skR pkS = | false | null | false | let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3 * size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs)
(size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs)
(size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.DH.dh",
"FStar.Pervasives.Native.None",
"Spec.Agile.HPKE.key_kem_s",
"Spec.Agile.DH.secret_to_public",
"FStar.Pervasives.Native.Some",
"Spec.Agile.HPKE.extract_and_expand",
"Prims.unit",
"Prims._assert",
"Prims.b2t",
"Spec.Agile.HPKE.extract_and_expand_dh_pred",
"FStar.Seq.Base.length",
"Lib.IntTypes.uint8",
"Spec.Agile.HPKE.labeled_extract_ikm_length_pred",
"Spec.Agile.HPKE.kem_hash_of_cs",
"Prims.op_Addition",
"Spec.Agile.HPKE.size_suite_id_kem",
"Spec.Agile.HPKE.size_label_eae_prk",
"Prims.op_Equality",
"Prims.int",
"Spec.Agile.HPKE.extract_and_expand_ctx_pred",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Agile.HPKE.labeled_expand_info_length_pred",
"Spec.Agile.HPKE.size_label_shared_secret",
"FStar.Mul.op_Star",
"Spec.Agile.HPKE.size_dh_public",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Prims.eq2",
"FStar.Seq.Base.seq",
"Lib.Sequence.to_seq",
"FStar.Seq.Base.append",
"Lib.Sequence.concat",
"Spec.Agile.HPKE.serialize_public_key",
"FStar.Pervasives.Native.option",
"Spec.Agile.HPKE.prepare_dh",
"Spec.Agile.HPKE.deserialize_public_key",
"FStar.Pervasives.allow_inversion",
"Spec.Agile.DH.algorithm"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs)) | [] | Spec.Agile.HPKE.auth_decap | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkS: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs)
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_kem_s cs) | {
"end_col": 28,
"end_line": 302,
"start_col": 31,
"start_line": 277
} |
Prims.Tot | val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc) | val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
let auth_encap cs skE pkR skS = | false | null | false | let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3 * size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs)
(size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs)
(size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.DH.secret_to_public",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_kem_s",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.DH.dh",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.extract_and_expand",
"Prims.unit",
"Prims._assert",
"Prims.b2t",
"Spec.Agile.HPKE.extract_and_expand_dh_pred",
"FStar.Seq.Base.length",
"Lib.IntTypes.uint8",
"Spec.Agile.HPKE.labeled_extract_ikm_length_pred",
"Spec.Agile.HPKE.kem_hash_of_cs",
"Prims.op_Addition",
"Spec.Agile.HPKE.size_suite_id_kem",
"Spec.Agile.HPKE.size_label_eae_prk",
"Prims.op_Equality",
"Prims.int",
"Spec.Agile.HPKE.extract_and_expand_ctx_pred",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Spec.Agile.HPKE.labeled_expand_info_length_pred",
"Spec.Agile.HPKE.size_label_shared_secret",
"FStar.Mul.op_Star",
"Spec.Agile.HPKE.size_dh_public",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Prims.eq2",
"FStar.Seq.Base.seq",
"Lib.Sequence.to_seq",
"FStar.Seq.Base.append",
"Lib.Sequence.concat",
"Spec.Agile.HPKE.serialize_public_key",
"FStar.Pervasives.Native.option",
"Spec.Agile.HPKE.prepare_dh",
"FStar.Pervasives.allow_inversion",
"Spec.Agile.DH.algorithm"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs)) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs)) | [] | Spec.Agile.HPKE.auth_encap | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs) ->
skS: Spec.Agile.HPKE.key_dh_secret_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_kem_s cs *
Spec.Agile.HPKE.key_dh_public_s cs) | {
"end_col": 35,
"end_line": 265,
"start_col": 31,
"start_line": 235
} |
Prims.Tot | val openAuth:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs)
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let openAuth cs enc skR info aad ct pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | val openAuth:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs)
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct))
let openAuth cs enc skR info aad ct pkS = | false | null | false | match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.AEAD.ad",
"Spec.Agile.HPKE.aead_alg_of",
"Spec.Agile.AEAD.cipher",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.setupAuthR",
"FStar.Pervasives.Native.None",
"Spec.Agile.AEAD.decrypted",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.context_open",
"Spec.Agile.AEAD.plain",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx)
let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None
let sealAuth cs skE pkR info aad pt skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val openAuth:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs)
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct)) | [] | Spec.Agile.HPKE.openAuth | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
aad: Spec.Agile.AEAD.ad (Spec.Agile.HPKE.aead_alg_of cs) ->
ct: Spec.Agile.AEAD.cipher (Spec.Agile.HPKE.aead_alg_of cs) ->
pkS: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs)
-> FStar.Pervasives.Native.option (Spec.Agile.AEAD.decrypted ct) | {
"end_col": 29,
"end_line": 572,
"start_col": 2,
"start_line": 567
} |
Prims.Tot | val openAuthPSK:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let openAuthPSK cs enc skR info aad ct psk psk_id pkS =
match setupAuthPSKR cs enc skR info psk psk_id pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | val openAuthPSK:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct))
let openAuthPSK cs enc skR info aad ct psk psk_id pkS = | false | null | false | match setupAuthPSKR cs enc skR info psk psk_id pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.AEAD.ad",
"Spec.Agile.HPKE.aead_alg_of",
"Spec.Agile.AEAD.cipher",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.HPKE.setupAuthPSKR",
"FStar.Pervasives.Native.None",
"Spec.Agile.AEAD.decrypted",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.context_open",
"Spec.Agile.AEAD.plain",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver
let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportPSK cs skE pkR info exp_ctx l psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportPSK cs enc skR info exp_ctx l psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// Auth mode
///
let setupAuthS cs skE pkR info skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Auth shared_secret info None in
Some (enc, enc_ctx)
let setupAuthR cs enc skR info pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Auth shared_secret info None)
| _ -> None
let sealAuth cs skE pkR info aad pt skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openAuth cs enc skR info aad ct pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportAuth cs skE pkR info exp_ctx l skS =
match setupAuthS cs skE pkR info skS with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportAuth cs enc skR info exp_ctx l pkS =
match setupAuthR cs enc skR info pkS with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// AuthPSK mode
///
let setupAuthPSKS cs skE pkR info psk psk_id skS =
match auth_encap cs skE pkR skS with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupAuthPSKR cs enc skR info psk psk_id pkS =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = auth_decap cs enc skR pkS in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs AuthPSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealAuthPSK cs skE pkR info aad pt psk psk_id skS =
match setupAuthPSKS cs skE pkR info psk psk_id skS with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val openAuthPSK:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs
-> pkS:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct)) | [] | Spec.Agile.HPKE.openAuthPSK | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
aad: Spec.Agile.AEAD.ad (Spec.Agile.HPKE.aead_alg_of cs) ->
ct: Spec.Agile.AEAD.cipher (Spec.Agile.HPKE.aead_alg_of cs) ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs ->
pkS: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs)
-> FStar.Pervasives.Native.option (Spec.Agile.AEAD.decrypted ct) | {
"end_col": 29,
"end_line": 619,
"start_col": 2,
"start_line": 614
} |
Prims.Tot | val openPSK:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let openPSK cs enc skR info aad ct psk psk_id =
match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | val openPSK:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct))
let openPSK cs enc skR info aad ct psk psk_id = | false | null | false | match setupPSKR cs enc skR info psk psk_id with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.AEAD.ad",
"Spec.Agile.HPKE.aead_alg_of",
"Spec.Agile.AEAD.cipher",
"Spec.Agile.HPKE.psk_s",
"Spec.Agile.HPKE.psk_id_s",
"Spec.Agile.HPKE.setupPSKR",
"FStar.Pervasives.Native.None",
"Spec.Agile.AEAD.decrypted",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.context_open",
"Spec.Agile.AEAD.plain",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt
let sendExportBase cs skE pkR info exp_ctx l =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
Some (enc, context_export cs ctx exp_ctx l)
let receiveExportBase cs enc skR info exp_ctx l =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
Some (context_export cs ctx exp_ctx l)
///
/// PSK mode
///
let setupPSKS cs skE pkR info psk psk_id =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
assert (verify_psk_inputs cs PSK (Some (psk, psk_id)));
let enc_ctx = key_schedule cs PSK shared_secret info (Some (psk, psk_id)) in
Some (enc, enc_ctx)
let setupPSKR cs enc skR info psk psk_id =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs PSK shared_secret info (Some (psk, psk_id)))
| _ -> None
let sealPSK cs skE pkR info aad pt psk psk_id =
match setupPSKS cs skE pkR info psk psk_id with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct)
#restart-solver | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val openPSK:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs)
-> psk:psk_s cs
-> psk_id:psk_id_s cs ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct)) | [] | Spec.Agile.HPKE.openPSK | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
aad: Spec.Agile.AEAD.ad (Spec.Agile.HPKE.aead_alg_of cs) ->
ct: Spec.Agile.AEAD.cipher (Spec.Agile.HPKE.aead_alg_of cs) ->
psk: Spec.Agile.HPKE.psk_s cs ->
psk_id: Spec.Agile.HPKE.psk_id_s cs
-> FStar.Pervasives.Native.option (Spec.Agile.AEAD.decrypted ct) | {
"end_col": 29,
"end_line": 525,
"start_col": 2,
"start_line": 520
} |
Prims.Tot | val openBase:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs) ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let openBase cs enc skR info aad ct =
match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | val openBase:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs) ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct))
let openBase cs enc skR info aad ct = | false | null | false | match setupBaseR cs enc skR info with
| None -> None
| Some ctx ->
match context_open cs ctx aad ct with
| None -> None
| Some (_, pt) -> Some pt | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite_not_export_only",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.HPKE.info_s",
"Spec.Agile.AEAD.ad",
"Spec.Agile.HPKE.aead_alg_of",
"Spec.Agile.AEAD.cipher",
"Spec.Agile.HPKE.setupBaseR",
"FStar.Pervasives.Native.None",
"Spec.Agile.AEAD.decrypted",
"Spec.Agile.HPKE.encryption_context",
"Spec.Agile.HPKE.context_open",
"Spec.Agile.AEAD.plain",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.option"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc)
val decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs ->
Tot (option (key_kem_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let decap cs enc skR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let _ = allow_inversion Spec.Agile.Hash.hash_alg in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some dh ->
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret = extract_and_expand cs dhm kem_context in
Some (shared_secret)
val auth_encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs)
-> skS:key_dh_secret_s cs ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_encap cs skE pkR skS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skS pkR with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
// TODO Do not put 32 literally
let dh = concat #uint8 #32 #32 esm ssm in
let enc = serialize_public_key cs pkE in
match DH.secret_to_public (kem_dh_of_cs cs) skS with
| None -> None
| Some pkS ->
let pkSm = serialize_public_key cs pkS in
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
// TODO Do not put 64 literally
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret, enc)
#reset-options
val auth_decap:
cs: ciphersuite
-> enc: key_dh_public_s cs
-> skR: key_dh_secret_s cs
-> pkS: DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs))
#restart-solver
#set-options "--z3rlimit 100 --fuel 0 --ifuel 0"
let auth_decap cs enc skR pkS =
let _ = allow_inversion Spec.Agile.DH.algorithm in
let pkE = deserialize_public_key cs enc in
match DH.dh (kem_dh_of_cs cs) skR pkE with
| None -> None
| Some es ->
match DH.dh (kem_dh_of_cs cs) skR pkS with
| None -> None
| Some ss ->
let esm = prepare_dh cs es in
let ssm = prepare_dh cs ss in
let dh = concat #uint8 #32 #32 esm ssm in
match DH.secret_to_public (kem_dh_of_cs cs) skR with
| None -> None
| Some pkR ->
let pkRm = serialize_public_key cs pkR in
let pkSm = serialize_public_key cs pkS in
let kem_context = concat enc (concat pkRm pkSm) in
assert (Seq.length kem_context = 3*size_dh_public cs);
assert (labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + Seq.length kem_context));
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
assert (Seq.length dh = 64);
assert (labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + Seq.length dh));
assert (extract_and_expand_dh_pred cs (Seq.length dh));
let shared_secret = extract_and_expand cs dh kem_context in
Some (shared_secret)
#reset-options
let default_psk = lbytes_empty
let default_psk_id = lbytes_empty
val build_context:
cs:ciphersuite
-> m:mode
-> psk_id_hash:lbytes (size_kdf cs)
-> info_hash:lbytes (size_kdf cs) ->
Tot (lbytes (size_ks_ctx cs))
let build_context cs m psk_id_hash info_hash =
let context = id_of_mode m in
let context = Seq.append context psk_id_hash in
let context = Seq.append context info_hash in
context
let verify_psk_inputs (cs:ciphersuite) (m:mode) (opsk:option(psk_s cs & psk_id_s cs)) : bool =
match (m, opsk) with
| Base, None -> true
| PSK, Some _ -> true
| Auth, None -> true
| AuthPSK, Some _ -> true
| _, _ -> false
// key and nonce are zero-length if AEAD is Export-Only
let encryption_context (cs:ciphersuite) = key_aead_s cs & nonce_aead_s cs & seq_aead_s cs & exporter_secret_s cs
val key_schedule:
cs:ciphersuite
-> m:mode
-> shared_secret:key_kem_s cs
-> info:info_s cs
-> opsk:option (psk_s cs & psk_id_s cs) ->
Pure (encryption_context cs)
(requires verify_psk_inputs cs m opsk)
(ensures fun _ -> True)
#set-options "--z3rlimit 500 --fuel 0 --ifuel 2"
let key_schedule_core
(cs:ciphersuite)
(m:mode)
(shared_secret:key_kem_s cs)
(info:info_s cs)
(opsk:option (psk_s cs & psk_id_s cs))
: (lbytes (size_ks_ctx cs) & exporter_secret_s cs & (lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs)))) =
let (psk, psk_id) =
match opsk with
| None -> (default_psk, default_psk_id)
| Some (psk, psk_id) -> (psk, psk_id)
in
let psk_id_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_psk_id_hash psk_id in
let info_hash = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) lbytes_empty label_info_hash info in
let context = build_context cs m psk_id_hash info_hash in
let secret = labeled_extract (hash_of_cs cs) (suite_id_hpke cs) shared_secret label_secret psk in
let exporter_secret = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_exp context (size_kdf cs) in
context, exporter_secret, secret
let key_schedule_end
(cs:ciphersuite)
(m:mode)
(context:lbytes (size_ks_ctx cs))
(exporter_secret:exporter_secret_s cs)
(secret:(lbytes (Spec.Hash.Definitions.hash_length (hash_of_cs cs))))
: encryption_context cs
=
if is_valid_not_export_only_ciphersuite cs then (
let key = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_key context (size_aead_key cs) in
let base_nonce = labeled_expand (hash_of_cs cs) (suite_id_hpke cs) secret label_base_nonce context (size_aead_nonce cs) in
(key, base_nonce, 0, exporter_secret)
) else (
(* if AEAD is Export-Only, then skip computation of key and base_nonce *)
assert (size_aead_key cs = 0);
assert (size_aead_nonce cs = 0);
(lbytes_empty, lbytes_empty, 0, exporter_secret))
let key_schedule cs m shared_secret info opsk =
let context, exporter_secret, secret = key_schedule_core cs m shared_secret info opsk in
key_schedule_end cs m context exporter_secret secret
let key_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let key, _, _, _ = ctx in key
let base_nonce_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, base_nonce, _, _ = ctx in base_nonce
let seq_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, seq, _ = ctx in seq
let exp_sec_of_ctx (cs:ciphersuite) (ctx:encryption_context cs) =
let _, _, _, exp_sec = ctx in exp_sec
let set_seq (cs:ciphersuite) (ctx:encryption_context cs) (seq:seq_aead_s cs) =
let key, base_nonce, _, exp_sec = ctx in
(key, base_nonce, seq, exp_sec)
///
/// Encryption Context
///
let context_export cs ctx exp_ctx l =
let exp_sec = exp_sec_of_ctx cs ctx in
labeled_expand (hash_of_cs cs) (suite_id_hpke cs) exp_sec label_sec exp_ctx l
let context_compute_nonce cs ctx seq =
let base_nonce = base_nonce_of_ctx cs ctx in
let enc_seq = nat_to_bytes_be (size_aead_nonce cs) seq in
Spec.Loops.seq_map2 logxor enc_seq base_nonce
let context_increment_seq cs ctx =
let seq = seq_of_ctx cs ctx in
if seq = max_seq cs then None else
Some (set_seq cs ctx (seq + 1))
let context_seal cs ctx aad pt =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
let ct = AEAD.encrypt key nonce aad pt in
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, ct)
let context_open cs ctx aad ct =
let key = key_of_ctx cs ctx in
let seq = seq_of_ctx cs ctx in
let nonce = context_compute_nonce cs ctx seq in
match AEAD.decrypt key nonce aad ct with
| None -> None
| Some pt ->
match context_increment_seq cs ctx with
| None -> None
| Some new_ctx -> Some (new_ctx, pt)
///
/// Base Mode
///
let setupBaseS cs skE pkR info =
match encap cs skE pkR with
| None -> None
| Some (shared_secret, enc) ->
let enc_ctx = key_schedule cs Base shared_secret info None in
Some (enc, enc_ctx)
let setupBaseR cs enc skR info =
let pkR = DH.secret_to_public (kem_dh_of_cs cs) skR in
let shared_secret = decap cs enc skR in
match pkR, shared_secret with
| Some pkR, Some shared_secret ->
Some (key_schedule cs Base shared_secret info None)
| _ -> None
let sealBase cs skE pkR info aad pt =
match setupBaseS cs skE pkR info with
| None -> None
| Some (enc, ctx) ->
match context_seal cs ctx aad pt with
| None -> None
| Some (_, ct) -> Some (enc, ct) | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 2,
"max_fuel": 0,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 500,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val openBase:
cs:ciphersuite_not_export_only
-> enc:key_dh_public_s cs
-> skR:key_dh_secret_s cs
-> info:info_s cs
-> aad:AEAD.ad (aead_alg_of cs)
-> ct:AEAD.cipher (aead_alg_of cs) ->
Tot (option (AEAD.decrypted #(aead_alg_of cs) ct)) | [] | Spec.Agile.HPKE.openBase | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite_not_export_only ->
enc: Spec.Agile.HPKE.key_dh_public_s cs ->
skR: Spec.Agile.HPKE.key_dh_secret_s cs ->
info: Spec.Agile.HPKE.info_s cs ->
aad: Spec.Agile.AEAD.ad (Spec.Agile.HPKE.aead_alg_of cs) ->
ct: Spec.Agile.AEAD.cipher (Spec.Agile.HPKE.aead_alg_of cs)
-> FStar.Pervasives.Native.option (Spec.Agile.AEAD.decrypted ct) | {
"end_col": 29,
"end_line": 476,
"start_col": 2,
"start_line": 471
} |
Prims.Tot | val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs)) | [
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "Spec.Agile.HKDF",
"short_module": "HKDF"
},
{
"abbrev": true,
"full_module": "Spec.Agile.Hash",
"short_module": "Hash"
},
{
"abbrev": true,
"full_module": "Spec.Agile.AEAD",
"short_module": "AEAD"
},
{
"abbrev": true,
"full_module": "Spec.Agile.DH",
"short_module": "DH"
},
{
"abbrev": false,
"full_module": "Lib.ByteSequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.RawIntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "Spec.Agile",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let encap cs skE pkR =
let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2*size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc) | val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
let encap cs skE pkR = | false | null | false | let _ = allow_inversion Spec.Agile.DH.algorithm in
match DH.secret_to_public (kem_dh_of_cs cs) skE with
| None -> None
| Some pkE ->
let enc = serialize_public_key cs pkE in
match DH.dh (kem_dh_of_cs cs) skE pkR with
| None -> None
| Some dh ->
let pkRm = serialize_public_key cs pkR in
let kem_context = concat enc pkRm in
let dhm = prepare_dh cs dh in
assert (Seq.length kem_context = 2 * size_dh_public cs);
assert (extract_and_expand_ctx_pred cs (Seq.length kem_context));
let shared_secret:key_kem_s cs = extract_and_expand cs dhm kem_context in
Some (shared_secret, enc) | {
"checked_file": "Spec.Agile.HPKE.fst.checked",
"dependencies": [
"Spec.P256.fst.checked",
"Spec.Loops.fst.checked",
"Spec.Hash.Definitions.fst.checked",
"Spec.Agile.HMAC.fsti.checked",
"Spec.Agile.HKDF.fsti.checked",
"Spec.Agile.Hash.fsti.checked",
"Spec.Agile.DH.fst.checked",
"Spec.Agile.AEAD.fsti.checked",
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.RawIntTypes.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Lib.ByteSequence.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": true,
"source_file": "Spec.Agile.HPKE.fst"
} | [
"total"
] | [
"Spec.Agile.HPKE.ciphersuite",
"Spec.Agile.HPKE.key_dh_secret_s",
"Spec.Agile.DH.serialized_point",
"Spec.Agile.HPKE.kem_dh_of_cs",
"Spec.Agile.DH.secret_to_public",
"FStar.Pervasives.Native.None",
"FStar.Pervasives.Native.tuple2",
"Spec.Agile.HPKE.key_kem_s",
"Spec.Agile.HPKE.key_dh_public_s",
"Spec.Agile.DH.dh",
"FStar.Pervasives.Native.Some",
"FStar.Pervasives.Native.Mktuple2",
"Spec.Agile.HPKE.extract_and_expand",
"Prims.unit",
"Prims._assert",
"Prims.b2t",
"Spec.Agile.HPKE.extract_and_expand_ctx_pred",
"FStar.Seq.Base.length",
"Lib.IntTypes.uint_t",
"Lib.IntTypes.U8",
"Lib.IntTypes.SEC",
"Prims.op_Equality",
"Prims.int",
"FStar.Mul.op_Star",
"Spec.Agile.HPKE.size_dh_public",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Spec.Agile.HPKE.prepare_dh",
"Prims.op_Addition",
"Prims.eq2",
"FStar.Seq.Base.seq",
"Lib.Sequence.to_seq",
"FStar.Seq.Base.append",
"Lib.Sequence.concat",
"Spec.Agile.HPKE.serialize_public_key",
"FStar.Pervasives.Native.option",
"FStar.Pervasives.allow_inversion",
"Spec.Agile.DH.algorithm"
] | [] | module Spec.Agile.HPKE
open FStar.Mul
open Lib.IntTypes
open Lib.RawIntTypes
open Lib.Sequence
open Lib.ByteSequence
module DH = Spec.Agile.DH
module AEAD = Spec.Agile.AEAD
module Hash = Spec.Agile.Hash
module HKDF = Spec.Agile.HKDF
let pow2_61 : _:unit{pow2 61 == 2305843009213693952} = assert_norm(pow2 61 == 2305843009213693952)
let pow2_35_less_than_pow2_61 : _:unit{pow2 32 * pow2 3 <= pow2 61 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 61 - 1)
let pow2_35_less_than_pow2_125 : _:unit{pow2 32 * pow2 3 <= pow2 125 - 1} = assert_norm(pow2 32 * pow2 3 <= pow2 125 - 1)
#set-options "--z3rlimit 20 --fuel 0 --ifuel 1"
/// Types
val id_kem: cs:ciphersuite -> Tot (lbytes 2)
let id_kem cs = let kem_dh, kem_hash, _, _ = cs in
match kem_dh, kem_hash with
| DH.DH_P256, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 16)
| DH.DH_Curve25519, Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 32)
val id_kdf: cs:ciphersuite -> Tot (lbytes 2)
let id_kdf cs = let _, _, _, h = cs in
match h with
| Hash.SHA2_256 -> create 1 (u8 0) @| create 1 (u8 1)
| Hash.SHA2_384 -> create 1 (u8 0) @| create 1 (u8 2)
| Hash.SHA2_512 -> create 1 (u8 0) @| create 1 (u8 3)
val id_aead: cs:ciphersuite -> Tot (lbytes 2)
let id_aead cs = let _, _, a, _ = cs in
match a with
| Seal AEAD.AES128_GCM -> create 1 (u8 0) @| create 1 (u8 1)
| Seal AEAD.AES256_GCM -> create 1 (u8 0) @| create 1 (u8 2)
| Seal AEAD.CHACHA20_POLY1305 -> create 1 (u8 0) @| create 1 (u8 3)
| ExportOnly -> create 1 (u8 255) @| create 1 (u8 255)
val suite_id_kem: cs:ciphersuite -> Tot (lbytes size_suite_id_kem)
let suite_id_kem cs =
Seq.append label_KEM (id_kem cs)
val suite_id_hpke: cs:ciphersuite -> Tot (lbytes size_suite_id_hpke)
let suite_id_hpke cs =
Seq.append label_HPKE (id_kem cs @| id_kdf cs @| id_aead cs)
val id_of_mode: m:mode -> Tot (lbytes size_mode_identifier)
let id_of_mode m =
match m with
| Base -> create 1 (u8 0)
| PSK -> create 1 (u8 1)
| Auth -> create 1 (u8 2)
| AuthPSK -> create 1 (u8 3)
val labeled_extract:
a:hash_algorithm
-> suite_id:bytes
-> salt:bytes
-> label:bytes
-> ikm:bytes ->
Pure (lbytes (Spec.Hash.Definitions.hash_length a))
(requires
Spec.Agile.HMAC.keysized a (Seq.length salt) /\
labeled_extract_ikm_length_pred a (Seq.length suite_id + Seq.length label + Seq.length ikm))
(ensures fun _ -> True)
let labeled_extract a suite_id salt label ikm =
let labeled_ikm1 = Seq.append label_version suite_id in
let labeled_ikm2 = Seq.append labeled_ikm1 label in
let labeled_ikm3 = Seq.append labeled_ikm2 ikm in
HKDF.extract a salt labeled_ikm3
val labeled_expand:
a:hash_algorithm
-> suite_id:bytes
-> prk:bytes
-> label:bytes
-> info:bytes
-> l:size_nat ->
Pure (lbytes l)
(requires
Spec.Hash.Definitions.hash_length a <= Seq.length prk /\
Spec.Agile.HMAC.keysized a (Seq.length prk) /\
labeled_expand_info_length_pred a (Seq.length suite_id + Seq.length label + Seq.length info) /\
HKDF.expand_output_length_pred a l)
(ensures fun _ -> True)
let labeled_expand a suite_id prk label info l =
let labeled_info1 = nat_to_bytes_be 2 l in
let labeled_info2 = Seq.append labeled_info1 label_version in
let labeled_info3 = Seq.append labeled_info2 suite_id in
let labeled_info4 = Seq.append labeled_info3 label in
let labeled_info5 = Seq.append labeled_info4 info in
HKDF.expand a prk labeled_info5 l
let extract_and_expand_dh_pred (cs:ciphersuite) (dh_length:nat) =
labeled_extract_ikm_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_eae_prk + dh_length)
let extract_and_expand_ctx_pred (cs:ciphersuite) (ctx_length:nat) =
labeled_expand_info_length_pred (kem_hash_of_cs cs) (size_suite_id_kem + size_label_shared_secret + ctx_length)
val extract_and_expand:
cs:ciphersuite
-> dh:bytes
-> kem_context:bytes ->
Pure (key_kem_s cs)
(requires
extract_and_expand_dh_pred cs (Seq.length dh) /\
extract_and_expand_ctx_pred cs (Seq.length kem_context))
(ensures fun _ -> True)
let extract_and_expand cs dh kem_context =
let eae_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_eae_prk dh in
labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) eae_prk label_shared_secret kem_context (size_kem_key cs)
let deserialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Extract the point coordinates by removing the first representation byte
| DH.DH_P256 -> sub pk 1 64
let serialize_public_key cs pk = match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> pk
// Add the first representation byte to the point coordinates
| DH.DH_P256 -> create 1 (u8 4) @| pk
val dkp_nist_p: cs:ciphersuite -> lbytes (size_kem_kdf cs) -> counter:uint8 -> Tot (option (key_dh_secret_s cs & key_dh_public_s cs)) (decreases 255 - v counter)
let rec dkp_nist_p cs dkp_prk counter =
let counterbyte = nat_to_intseq_be #U8 #SEC 1 (v counter) in
let bytes = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_candidate counterbyte (size_dh_key cs) in
let bytes = Lib.Sequence.map2 (logand #U8 #SEC) bytes (Seq.create (size_dh_key cs) (u8 255)) in
let sk = nat_from_intseq_be #U8 #SEC bytes in
if sk = 0 || sk >= Spec.P256.prime then
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
else
match DH.secret_to_public (kem_dh_of_cs cs) bytes with
| Some pk -> Some (bytes, serialize_public_key cs pk)
| None ->
if (v counter) = 255 then None
else dkp_nist_p cs dkp_prk (counter +! (u8 1))
let derive_key_pair cs ikm =
match kem_dh_of_cs cs with
| DH.DH_Curve25519 -> begin
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
let sk = labeled_expand (kem_hash_of_cs cs) (suite_id_kem cs) dkp_prk label_sk lbytes_empty (size_dh_key cs) in
match DH.secret_to_public (kem_dh_of_cs cs) sk with
| Some pk -> Some (sk, serialize_public_key cs pk)
end
| DH.DH_P256 ->
let dkp_prk = labeled_extract (kem_hash_of_cs cs) (suite_id_kem cs) lbytes_empty label_dkp_prk ikm in
dkp_nist_p cs dkp_prk (u8 0)
val prepare_dh: cs:ciphersuite -> DH.serialized_point (kem_dh_of_cs cs) -> Tot (lbytes 32)
let prepare_dh cs dh = match (kem_dh_of_cs cs) with
| DH.DH_Curve25519 -> serialize_public_key cs dh
| DH.DH_P256 -> sub dh 0 32
val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs))
#restart-solver | false | false | Spec.Agile.HPKE.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 100,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val encap:
cs:ciphersuite
-> skE:key_dh_secret_s cs
-> pkR:DH.serialized_point (kem_dh_of_cs cs) ->
Tot (option (key_kem_s cs & key_dh_public_s cs)) | [] | Spec.Agile.HPKE.encap | {
"file_name": "specs/Spec.Agile.HPKE.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
cs: Spec.Agile.HPKE.ciphersuite ->
skE: Spec.Agile.HPKE.key_dh_secret_s cs ->
pkR: Spec.Agile.DH.serialized_point (Spec.Agile.HPKE.kem_dh_of_cs cs)
-> FStar.Pervasives.Native.option (Spec.Agile.HPKE.key_kem_s cs *
Spec.Agile.HPKE.key_dh_public_s cs) | {
"end_col": 31,
"end_line": 199,
"start_col": 22,
"start_line": 184
} |
Prims.Tot | val add (#a: eqtype) (x: a) (s: set a) : set a | [
{
"abbrev": true,
"full_module": "FStar.FunctionalExtensionality",
"short_module": "F"
},
{
"abbrev": false,
"full_module": "FStar.FunctionalExtensionality",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let add (#a:eqtype) (x:a) (s:set a) : set a =
union s (singleton x) | val add (#a: eqtype) (x: a) (s: set a) : set a
let add (#a: eqtype) (x: a) (s: set a) : set a = | false | null | false | union s (singleton x) | {
"checked_file": "FStar.Set.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Set.fsti"
} | [
"total"
] | [
"Prims.eqtype",
"FStar.Set.set",
"FStar.Set.union",
"FStar.Set.singleton"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy, Aseem Rastogi,
Microsoft Research, University of Maryland
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Set
(** Computational sets (on eqtypes): membership is a boolean function *)
#set-options "--initial_fuel 0 --max_fuel 0 --initial_ifuel 0 --max_ifuel 0"
val set (a:eqtype)
: Type0
val equal (#a:eqtype) (s1:set a) (s2:set a)
: Type0
(* destructors *)
val mem (#a:eqtype) (x:a) (s:set a)
: Tot bool
(* constructors *)
val empty (#a:eqtype)
: Tot (set a)
val singleton (#a:eqtype) (x:a)
: Tot (set a)
val union : #a:eqtype -> set a -> set a -> Tot (set a)
val intersect : #a:eqtype -> set a -> set a -> Tot (set a)
val complement : #a:eqtype -> set a -> Tot (set a)
val intension : #a:eqtype -> (a -> Tot bool) -> GTot (set a)
(* Derived functions *)
let disjoint (#a:eqtype) (s1: set a) (s2: set a) =
equal (intersect s1 s2) empty
let subset (#a:eqtype) (s1:set a) (s2:set a) =
forall x. mem x s1 ==> mem x s2 | false | false | FStar.Set.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val add (#a: eqtype) (x: a) (s: set a) : set a | [] | FStar.Set.add | {
"file_name": "ulib/FStar.Set.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | x: a -> s: FStar.Set.set a -> FStar.Set.set a | {
"end_col": 23,
"end_line": 54,
"start_col": 2,
"start_line": 54
} |
Prims.Tot | [
{
"abbrev": true,
"full_module": "FStar.FunctionalExtensionality",
"short_module": "F"
},
{
"abbrev": false,
"full_module": "FStar.FunctionalExtensionality",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let subset (#a:eqtype) (s1:set a) (s2:set a) =
forall x. mem x s1 ==> mem x s2 | let subset (#a: eqtype) (s1 s2: set a) = | false | null | false | forall x. mem x s1 ==> mem x s2 | {
"checked_file": "FStar.Set.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Set.fsti"
} | [
"total"
] | [
"Prims.eqtype",
"FStar.Set.set",
"Prims.l_Forall",
"Prims.l_imp",
"Prims.b2t",
"FStar.Set.mem",
"Prims.logical"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy, Aseem Rastogi,
Microsoft Research, University of Maryland
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Set
(** Computational sets (on eqtypes): membership is a boolean function *)
#set-options "--initial_fuel 0 --max_fuel 0 --initial_ifuel 0 --max_ifuel 0"
val set (a:eqtype)
: Type0
val equal (#a:eqtype) (s1:set a) (s2:set a)
: Type0
(* destructors *)
val mem (#a:eqtype) (x:a) (s:set a)
: Tot bool
(* constructors *)
val empty (#a:eqtype)
: Tot (set a)
val singleton (#a:eqtype) (x:a)
: Tot (set a)
val union : #a:eqtype -> set a -> set a -> Tot (set a)
val intersect : #a:eqtype -> set a -> set a -> Tot (set a)
val complement : #a:eqtype -> set a -> Tot (set a)
val intension : #a:eqtype -> (a -> Tot bool) -> GTot (set a)
(* Derived functions *)
let disjoint (#a:eqtype) (s1: set a) (s2: set a) =
equal (intersect s1 s2) empty | false | false | FStar.Set.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val subset : s1: FStar.Set.set a -> s2: FStar.Set.set a -> Prims.logical | [] | FStar.Set.subset | {
"file_name": "ulib/FStar.Set.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Set.set a -> s2: FStar.Set.set a -> Prims.logical | {
"end_col": 33,
"end_line": 51,
"start_col": 2,
"start_line": 51
} |
|
Prims.Tot | val remove (#a: eqtype) (x: a) (s: set a) : set a | [
{
"abbrev": true,
"full_module": "FStar.FunctionalExtensionality",
"short_module": "F"
},
{
"abbrev": false,
"full_module": "FStar.FunctionalExtensionality",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let remove (#a:eqtype) (x:a) (s:set a) : set a =
intersect s (complement (singleton x)) | val remove (#a: eqtype) (x: a) (s: set a) : set a
let remove (#a: eqtype) (x: a) (s: set a) : set a = | false | null | false | intersect s (complement (singleton x)) | {
"checked_file": "FStar.Set.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Set.fsti"
} | [
"total"
] | [
"Prims.eqtype",
"FStar.Set.set",
"FStar.Set.intersect",
"FStar.Set.complement",
"FStar.Set.singleton"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy, Aseem Rastogi,
Microsoft Research, University of Maryland
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Set
(** Computational sets (on eqtypes): membership is a boolean function *)
#set-options "--initial_fuel 0 --max_fuel 0 --initial_ifuel 0 --max_ifuel 0"
val set (a:eqtype)
: Type0
val equal (#a:eqtype) (s1:set a) (s2:set a)
: Type0
(* destructors *)
val mem (#a:eqtype) (x:a) (s:set a)
: Tot bool
(* constructors *)
val empty (#a:eqtype)
: Tot (set a)
val singleton (#a:eqtype) (x:a)
: Tot (set a)
val union : #a:eqtype -> set a -> set a -> Tot (set a)
val intersect : #a:eqtype -> set a -> set a -> Tot (set a)
val complement : #a:eqtype -> set a -> Tot (set a)
val intension : #a:eqtype -> (a -> Tot bool) -> GTot (set a)
(* Derived functions *)
let disjoint (#a:eqtype) (s1: set a) (s2: set a) =
equal (intersect s1 s2) empty
let subset (#a:eqtype) (s1:set a) (s2:set a) =
forall x. mem x s1 ==> mem x s2
let add (#a:eqtype) (x:a) (s:set a) : set a =
union s (singleton x) | false | false | FStar.Set.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val remove (#a: eqtype) (x: a) (s: set a) : set a | [] | FStar.Set.remove | {
"file_name": "ulib/FStar.Set.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | x: a -> s: FStar.Set.set a -> FStar.Set.set a | {
"end_col": 40,
"end_line": 57,
"start_col": 2,
"start_line": 57
} |
Prims.Tot | [
{
"abbrev": true,
"full_module": "FStar.FunctionalExtensionality",
"short_module": "F"
},
{
"abbrev": false,
"full_module": "FStar.FunctionalExtensionality",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let as_set (#a:eqtype) (l:list a) = normalize_term (as_set' l) | let as_set (#a: eqtype) (l: list a) = | false | null | false | normalize_term (as_set' l) | {
"checked_file": "FStar.Set.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Set.fsti"
} | [
"total"
] | [
"Prims.eqtype",
"Prims.list",
"FStar.Pervasives.normalize_term",
"FStar.Set.set",
"FStar.Set.as_set'"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy, Aseem Rastogi,
Microsoft Research, University of Maryland
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Set
(** Computational sets (on eqtypes): membership is a boolean function *)
#set-options "--initial_fuel 0 --max_fuel 0 --initial_ifuel 0 --max_ifuel 0"
val set (a:eqtype)
: Type0
val equal (#a:eqtype) (s1:set a) (s2:set a)
: Type0
(* destructors *)
val mem (#a:eqtype) (x:a) (s:set a)
: Tot bool
(* constructors *)
val empty (#a:eqtype)
: Tot (set a)
val singleton (#a:eqtype) (x:a)
: Tot (set a)
val union : #a:eqtype -> set a -> set a -> Tot (set a)
val intersect : #a:eqtype -> set a -> set a -> Tot (set a)
val complement : #a:eqtype -> set a -> Tot (set a)
val intension : #a:eqtype -> (a -> Tot bool) -> GTot (set a)
(* Derived functions *)
let disjoint (#a:eqtype) (s1: set a) (s2: set a) =
equal (intersect s1 s2) empty
let subset (#a:eqtype) (s1:set a) (s2:set a) =
forall x. mem x s1 ==> mem x s2
let add (#a:eqtype) (x:a) (s:set a) : set a =
union s (singleton x)
let remove (#a:eqtype) (x:a) (s:set a) : set a =
intersect s (complement (singleton x))
(* Properties *)
val mem_empty: #a:eqtype -> x:a -> Lemma
(requires True)
(ensures (not (mem x empty)))
[SMTPat (mem x empty)]
val mem_singleton: #a:eqtype -> x:a -> y:a -> Lemma
(requires True)
(ensures (mem y (singleton x) = (x=y)))
[SMTPat (mem y (singleton x))]
val mem_union: #a:eqtype -> x:a -> s1:set a -> s2:set a -> Lemma
(requires True)
(ensures (mem x (union s1 s2) = (mem x s1 || mem x s2)))
[SMTPat (mem x (union s1 s2))]
val mem_intersect: #a:eqtype -> x:a -> s1:set a -> s2:set a -> Lemma
(requires True)
(ensures (mem x (intersect s1 s2) = (mem x s1 && mem x s2)))
[SMTPat (mem x (intersect s1 s2))]
val mem_complement: #a:eqtype -> x:a -> s:set a -> Lemma
(requires True)
(ensures (mem x (complement s) = not (mem x s)))
[SMTPat (mem x (complement s))]
val mem_intension: #a:eqtype -> x:a -> f:(a -> Tot bool) -> Lemma
(requires True)
(ensures (mem x (intension f) = f x))
val mem_subset: #a:eqtype -> s1:set a -> s2:set a -> Lemma
(requires (forall x. mem x s1 ==> mem x s2))
(ensures (subset s1 s2))
[SMTPat (subset s1 s2)]
val subset_mem: #a:eqtype -> s1:set a -> s2:set a -> Lemma
(requires (subset s1 s2))
(ensures (forall x. mem x s1 ==> mem x s2))
[SMTPat (subset s1 s2)]
(* extensionality *)
val lemma_equal_intro: #a:eqtype -> s1:set a -> s2:set a -> Lemma
(requires (forall x. mem x s1 = mem x s2))
(ensures (equal s1 s2))
[SMTPat (equal s1 s2)]
val lemma_equal_elim: #a:eqtype -> s1:set a -> s2:set a -> Lemma
(requires (equal s1 s2))
(ensures (s1 == s2))
[SMTPat (equal s1 s2)]
val lemma_equal_refl: #a:eqtype -> s1:set a -> s2:set a -> Lemma
(requires (s1 == s2))
(ensures (equal s1 s2))
[SMTPat (equal s1 s2)]
val disjoint_not_in_both (a:eqtype) (s1:set a) (s2:set a)
: Lemma
(requires (disjoint s1 s2))
(ensures (forall (x:a).{:pattern (mem x s1) \/ (mem x s2)} mem x s1 ==> ~(mem x s2)))
[SMTPat (disjoint s1 s2)]
(* Converting lists to sets *)
(* WHY IS THIS HERE? It is not strictly part of the interface *)
#reset-options //restore fuel usage here
let rec as_set' (#a:eqtype) (l:list a) : set a =
match l with
| [] -> empty
| hd::tl -> union (singleton hd) (as_set' tl) | false | false | FStar.Set.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val as_set : l: Prims.list a -> FStar.Set.set a | [] | FStar.Set.as_set | {
"file_name": "ulib/FStar.Set.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | l: Prims.list a -> FStar.Set.set a | {
"end_col": 62,
"end_line": 131,
"start_col": 36,
"start_line": 131
} |
|
Prims.Tot | [
{
"abbrev": true,
"full_module": "FStar.FunctionalExtensionality",
"short_module": "F"
},
{
"abbrev": false,
"full_module": "FStar.FunctionalExtensionality",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let disjoint (#a:eqtype) (s1: set a) (s2: set a) =
equal (intersect s1 s2) empty | let disjoint (#a: eqtype) (s1 s2: set a) = | false | null | false | equal (intersect s1 s2) empty | {
"checked_file": "FStar.Set.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Set.fsti"
} | [
"total"
] | [
"Prims.eqtype",
"FStar.Set.set",
"FStar.Set.equal",
"FStar.Set.intersect",
"FStar.Set.empty"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy, Aseem Rastogi,
Microsoft Research, University of Maryland
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Set
(** Computational sets (on eqtypes): membership is a boolean function *)
#set-options "--initial_fuel 0 --max_fuel 0 --initial_ifuel 0 --max_ifuel 0"
val set (a:eqtype)
: Type0
val equal (#a:eqtype) (s1:set a) (s2:set a)
: Type0
(* destructors *)
val mem (#a:eqtype) (x:a) (s:set a)
: Tot bool
(* constructors *)
val empty (#a:eqtype)
: Tot (set a)
val singleton (#a:eqtype) (x:a)
: Tot (set a)
val union : #a:eqtype -> set a -> set a -> Tot (set a)
val intersect : #a:eqtype -> set a -> set a -> Tot (set a)
val complement : #a:eqtype -> set a -> Tot (set a)
val intension : #a:eqtype -> (a -> Tot bool) -> GTot (set a)
(* Derived functions *) | false | false | FStar.Set.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 0,
"initial_ifuel": 0,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val disjoint : s1: FStar.Set.set a -> s2: FStar.Set.set a -> Type0 | [] | FStar.Set.disjoint | {
"file_name": "ulib/FStar.Set.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s1: FStar.Set.set a -> s2: FStar.Set.set a -> Type0 | {
"end_col": 31,
"end_line": 48,
"start_col": 2,
"start_line": 48
} |
|
Prims.Tot | val as_set' (#a: eqtype) (l: list a) : set a | [
{
"abbrev": true,
"full_module": "FStar.FunctionalExtensionality",
"short_module": "F"
},
{
"abbrev": false,
"full_module": "FStar.FunctionalExtensionality",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec as_set' (#a:eqtype) (l:list a) : set a =
match l with
| [] -> empty
| hd::tl -> union (singleton hd) (as_set' tl) | val as_set' (#a: eqtype) (l: list a) : set a
let rec as_set' (#a: eqtype) (l: list a) : set a = | false | null | false | match l with
| [] -> empty
| hd :: tl -> union (singleton hd) (as_set' tl) | {
"checked_file": "FStar.Set.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.Pervasives.fsti.checked"
],
"interface_file": false,
"source_file": "FStar.Set.fsti"
} | [
"total"
] | [
"Prims.eqtype",
"Prims.list",
"FStar.Set.empty",
"FStar.Set.union",
"FStar.Set.singleton",
"FStar.Set.as_set'",
"FStar.Set.set"
] | [] | (*
Copyright 2008-2014 Nikhil Swamy, Aseem Rastogi,
Microsoft Research, University of Maryland
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*)
module FStar.Set
(** Computational sets (on eqtypes): membership is a boolean function *)
#set-options "--initial_fuel 0 --max_fuel 0 --initial_ifuel 0 --max_ifuel 0"
val set (a:eqtype)
: Type0
val equal (#a:eqtype) (s1:set a) (s2:set a)
: Type0
(* destructors *)
val mem (#a:eqtype) (x:a) (s:set a)
: Tot bool
(* constructors *)
val empty (#a:eqtype)
: Tot (set a)
val singleton (#a:eqtype) (x:a)
: Tot (set a)
val union : #a:eqtype -> set a -> set a -> Tot (set a)
val intersect : #a:eqtype -> set a -> set a -> Tot (set a)
val complement : #a:eqtype -> set a -> Tot (set a)
val intension : #a:eqtype -> (a -> Tot bool) -> GTot (set a)
(* Derived functions *)
let disjoint (#a:eqtype) (s1: set a) (s2: set a) =
equal (intersect s1 s2) empty
let subset (#a:eqtype) (s1:set a) (s2:set a) =
forall x. mem x s1 ==> mem x s2
let add (#a:eqtype) (x:a) (s:set a) : set a =
union s (singleton x)
let remove (#a:eqtype) (x:a) (s:set a) : set a =
intersect s (complement (singleton x))
(* Properties *)
val mem_empty: #a:eqtype -> x:a -> Lemma
(requires True)
(ensures (not (mem x empty)))
[SMTPat (mem x empty)]
val mem_singleton: #a:eqtype -> x:a -> y:a -> Lemma
(requires True)
(ensures (mem y (singleton x) = (x=y)))
[SMTPat (mem y (singleton x))]
val mem_union: #a:eqtype -> x:a -> s1:set a -> s2:set a -> Lemma
(requires True)
(ensures (mem x (union s1 s2) = (mem x s1 || mem x s2)))
[SMTPat (mem x (union s1 s2))]
val mem_intersect: #a:eqtype -> x:a -> s1:set a -> s2:set a -> Lemma
(requires True)
(ensures (mem x (intersect s1 s2) = (mem x s1 && mem x s2)))
[SMTPat (mem x (intersect s1 s2))]
val mem_complement: #a:eqtype -> x:a -> s:set a -> Lemma
(requires True)
(ensures (mem x (complement s) = not (mem x s)))
[SMTPat (mem x (complement s))]
val mem_intension: #a:eqtype -> x:a -> f:(a -> Tot bool) -> Lemma
(requires True)
(ensures (mem x (intension f) = f x))
val mem_subset: #a:eqtype -> s1:set a -> s2:set a -> Lemma
(requires (forall x. mem x s1 ==> mem x s2))
(ensures (subset s1 s2))
[SMTPat (subset s1 s2)]
val subset_mem: #a:eqtype -> s1:set a -> s2:set a -> Lemma
(requires (subset s1 s2))
(ensures (forall x. mem x s1 ==> mem x s2))
[SMTPat (subset s1 s2)]
(* extensionality *)
val lemma_equal_intro: #a:eqtype -> s1:set a -> s2:set a -> Lemma
(requires (forall x. mem x s1 = mem x s2))
(ensures (equal s1 s2))
[SMTPat (equal s1 s2)]
val lemma_equal_elim: #a:eqtype -> s1:set a -> s2:set a -> Lemma
(requires (equal s1 s2))
(ensures (s1 == s2))
[SMTPat (equal s1 s2)]
val lemma_equal_refl: #a:eqtype -> s1:set a -> s2:set a -> Lemma
(requires (s1 == s2))
(ensures (equal s1 s2))
[SMTPat (equal s1 s2)]
val disjoint_not_in_both (a:eqtype) (s1:set a) (s2:set a)
: Lemma
(requires (disjoint s1 s2))
(ensures (forall (x:a).{:pattern (mem x s1) \/ (mem x s2)} mem x s1 ==> ~(mem x s2)))
[SMTPat (disjoint s1 s2)]
(* Converting lists to sets *)
(* WHY IS THIS HERE? It is not strictly part of the interface *)
#reset-options //restore fuel usage here | false | false | FStar.Set.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val as_set' (#a: eqtype) (l: list a) : set a | [
"recursion"
] | FStar.Set.as_set' | {
"file_name": "ulib/FStar.Set.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | l: Prims.list a -> FStar.Set.set a | {
"end_col": 47,
"end_line": 128,
"start_col": 2,
"start_line": 126
} |
FStar.Pervasives.Lemma | val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24 | val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 = | false | null | true | let f20, f21, f22, f23, f24 = f2 in
let m20, m21, m22, m23, m24 = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.scale32_5",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"Prims.nat",
"Hacl.Poly1305.Field32xN.Lemmas0.smul_felem5_fits_lemma1",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2)) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2)) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_felem5_fits_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
u1: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 u1 m1} ->
f2: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Spec.Poly1305.Field32xN.felem_fits5 f2 m2}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5 (Hacl.Spec.Poly1305.Field32xN.smul_felem5 u1 f2)
(m1 *^ m2)) | {
"end_col": 44,
"end_line": 197,
"start_col": 45,
"start_line": 190
} |
FStar.Pervasives.Lemma | val lemma_prime: unit -> Lemma (pow2 130 % prime = 5) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime | val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () = | false | null | true | assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Prims.unit",
"FStar.Math.Lemmas.modulo_lemma",
"Hacl.Spec.Poly1305.Vec.prime",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.op_Equality",
"Prims.int",
"Prims.op_Modulus",
"Prims.pow2"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_prime: unit -> Lemma (pow2 130 % prime = 5) | [] | Hacl.Poly1305.Field32xN.Lemmas0.lemma_prime | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | _: Prims.unit -> FStar.Pervasives.Lemma (ensures Prims.pow2 130 % Hacl.Spec.Poly1305.Vec.prime = 5) | {
"end_col": 40,
"end_line": 18,
"start_col": 2,
"start_line": 16
} |
FStar.Pervasives.Lemma | val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32) | val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b = | false | null | true | assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.scale64",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.small_mod",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Prims.pow2",
"Prims.unit",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_LessThan",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Prims._assert",
"Prims.op_LessThanOrEqual",
"FStar.Math.Lemmas.lemma_mult_le_right"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26) | [] | Hacl.Poly1305.Field32xN.Lemmas0.add5_lemma1 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
ma: Hacl.Spec.Poly1305.Field32xN.scale64 ->
mb: Hacl.Spec.Poly1305.Field32xN.scale64 ->
a: Lib.IntTypes.uint64 ->
b: Lib.IntTypes.uint64
-> FStar.Pervasives.Lemma
(requires
Lib.IntTypes.v a <= ma * Hacl.Spec.Poly1305.Field32xN.max26 /\
Lib.IntTypes.v b <= mb * Hacl.Spec.Poly1305.Field32xN.max26 /\ ma + mb <= 64)
(ensures
Lib.IntTypes.v (a +. b) == Lib.IntTypes.v a + Lib.IntTypes.v b /\
Lib.IntTypes.v (a +. b) <= (ma + mb) * Hacl.Spec.Poly1305.Field32xN.max26) | {
"end_col": 45,
"end_line": 72,
"start_col": 2,
"start_line": 68
} |
FStar.Pervasives.Lemma | val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64) | val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b = | false | null | true | lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= ((m1 * m2) * max26) * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"FStar.Math.Lemmas.modulo_lemma",
"Prims.pow2",
"Prims.unit",
"Prims._assert",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_mult_le"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_mod_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
a: Prims.nat{a <= m1 * Hacl.Spec.Poly1305.Field32xN.max26} ->
b: Prims.nat{b <= m2 * Hacl.Spec.Poly1305.Field32xN.max26}
-> FStar.Pervasives.Lemma (ensures a * b % Prims.pow2 64 == a * b) | {
"end_col": 50,
"end_line": 44,
"start_col": 2,
"start_line": 42
} |
FStar.Pervasives.Lemma | val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4 | val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 = | false | null | true | let f20, f21, f22, f23, f24 = f2 in
let m20, m21, m22, m23, m24 = m2 in
let a0, a1, a2, a3, a4 = acc1 in
let m30, m31, m32, m33, m34 = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.scale32_5",
"Hacl.Spec.Poly1305.Field32xN.scale64_5",
"Hacl.Spec.Poly1305.Field32xN.op_Less_Equals_Star",
"Hacl.Spec.Poly1305.Field32xN.op_Plus_Star",
"Hacl.Spec.Poly1305.Field32xN.op_Star_Hat",
"Hacl.Spec.Poly1305.Field32xN.s64x5",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5",
"Prims.nat",
"Hacl.Poly1305.Field32xN.Lemmas0.smul_add_felem5_fits_lemma1",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2)) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2)) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_add_felem5_fits_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
u1: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 u1 m1} ->
f2: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Spec.Poly1305.Field32xN.felem_fits5 f2 m2} ->
acc1:
Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
{Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5 acc1 m3}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5 (Hacl.Spec.Poly1305.Field32xN.smul_add_felem5 u1
f2
acc1)
(m3 +* m1 *^ m2)) | {
"end_col": 56,
"end_line": 339,
"start_col": 58,
"start_line": 330
} |
FStar.Pervasives.Lemma | val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64) | val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c = | false | null | true | assert_norm (((m3 + m1 * m2) * max26) * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= (m3 * max26) * max26 + ((m1 * m2) * max26) * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.scale64",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Prims.nat",
"Hacl.Spec.Poly1305.Field32xN.max26",
"FStar.Math.Lemmas.modulo_lemma",
"Prims.pow2",
"Prims.unit",
"Prims._assert",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_mult_le",
"FStar.Pervasives.assert_norm",
"Prims.op_LessThan"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 0,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_add_mod_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
a: Prims.nat{a <= m1 * Hacl.Spec.Poly1305.Field32xN.max26} ->
b: Prims.nat{b <= m2 * Hacl.Spec.Poly1305.Field32xN.max26} ->
c:
Prims.nat{c <= (m3 * Hacl.Spec.Poly1305.Field32xN.max26) * Hacl.Spec.Poly1305.Field32xN.max26}
-> FStar.Pervasives.Lemma (ensures (c + a * b % Prims.pow2 64) % Prims.pow2 64 == c + a * b) | {
"end_col": 54,
"end_line": 60,
"start_col": 2,
"start_line": 57
} |
FStar.Pervasives.Lemma | val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26) | val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i = | false | null | true | let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[ i ] (uint64xN_v f2).[ i ];
assert ((uint64xN_v o).[ i ] == (uint64xN_v u1).[ i ] * (uint64xN_v f2).[ i ]);
lemma_mult_le (uint64xN_v u1).[ i ] (m1 * max26) (uint64xN_v f2).[ i ] (m2 * max26) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_mult_le",
"Lib.Sequence.op_String_Access",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Prims.unit",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Hacl.Poly1305.Field32xN.Lemmas0.smul_mod_lemma",
"Lib.IntVector.vec_t",
"Lib.IntTypes.U64",
"Lib.Sequence.lseq",
"Lib.IntTypes.int_t",
"Lib.IntTypes.SEC",
"Lib.IntVector.vec_v",
"Lib.Sequence.map2",
"Lib.IntTypes.mul_mod",
"Lib.IntVector.vec_mul_mod"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_felem5_fits_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
u1: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 u1 m1} ->
f2: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 f2 m2} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v (Lib.IntVector.vec_mul_mod f2 u1)).[ i ] <=
((m1 * m2) * Hacl.Spec.Poly1305.Field32xN.max26) * Hacl.Spec.Poly1305.Field32xN.max26) | {
"end_col": 81,
"end_line": 116,
"start_col": 49,
"start_line": 112
} |
FStar.Pervasives.Lemma | val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) | val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 = | false | null | true | FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.scale32_5",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"Lib.Sequence.eq_intro",
"Prims.nat",
"Hacl.Spec.Poly1305.Field32xN.fas_nat5",
"Hacl.Spec.Poly1305.Field32xN.smul_felem5",
"Lib.Sequence.map2",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Prims.unit",
"FStar.Classical.forall_intro",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.eq2",
"Prims.int",
"Lib.Sequence.op_String_Access",
"Hacl.Poly1305.Field32xN.Lemmas0.smul_felem5_eval_lemma_i"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_felem5_eval_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
u1: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 u1 m1} ->
f2: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Spec.Poly1305.Field32xN.felem_fits5 f2 m2}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.fas_nat5 (Hacl.Spec.Poly1305.Field32xN.smul_felem5 u1 f2) ==
Lib.Sequence.map2 (fun a b -> a * b)
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v u1)
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 f2)) | {
"end_col": 74,
"end_line": 212,
"start_col": 2,
"start_line": 210
} |
FStar.Pervasives.Lemma | val mul_felem5_lemma:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_pfelem5 f1) `pfmul` (as_pfelem5 r) ==
(v f10 * as_nat5 (r0, r1, r2, r3, r4) +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let mul_felem5_lemma f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
mul_felem5_lemma_4 f1 r;
FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime;
FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime | val mul_felem5_lemma:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_pfelem5 f1) `pfmul` (as_pfelem5 r) ==
(v f10 * as_nat5 (r0, r1, r2, r3, r4) +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)
let mul_felem5_lemma f1 r = | false | null | true | let f10, f11, f12, f13, f14 = f1 in
let r0, r1, r2, r3, r4 = r in
mul_felem5_lemma_4 f1 r;
FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime;
FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"Prims.op_Modulus",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.unit",
"FStar.Math.Lemmas.lemma_mod_mul_distr_l",
"Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_lemma_4"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime)
val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime))
let lemma_fmul5_pow52 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow52 * as_nat5 r) % prime;
(==) { assert_norm (pow52 == pow26 * pow26) }
(pow26 * pow26 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
(==) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)
val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime))
let lemma_fmul5_pow78 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow78 * as_nat5 r) % prime;
(==) { assert_norm (pow78 == pow26 * pow52) }
(pow26 * pow52 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow52 * as_nat5 r) prime }
(pow26 * (pow52 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow52 r }
(pow26 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(pow26 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
(==) { lemma_fmul5_pow26 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) }
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime;
};
assert ((pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)
val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime))
let lemma_fmul5_pow104 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow104 * as_nat5 r) % prime;
(==) { assert_norm (pow104 == pow26 * pow78) }
(pow26 * pow78 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow78 * as_nat5 r) prime }
(pow26 * (pow78 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow78 r }
(pow26 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(pow26 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
(==) { lemma_fmul5_pow26 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) }
as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime;
};
assert ((pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime)
val mul_felem5_lemma_1:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_1 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp = v f10 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { }
(v f10 + v f11 * pow26 + v f12 * pow52 + v f13 * pow78 + v f14 * pow104) * as_nat5 r % prime;
(==) { lemma_mul5_distr_r (v f10) (v f11 * pow26) (v f12 * pow52) (v f13 * pow78) (v f14 * pow104) (as_nat5 r) }
(v f10 * as_nat5 r + v f11 * pow26 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * pow26 * as_nat5 r) prime }
(tmp + (v f11 * pow26 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f11) pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow26 * as_nat5 r) prime }
(tmp + v f11 * (pow26 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow26 r }
(tmp + v f11 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime)
val mul_felem5_lemma_2:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_2 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_1 f1 r }
(tmp + v f12 * pow52 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * pow52 * as_nat5 r) prime }
(tmp + (v f12 * pow52 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f12) pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (pow52 * as_nat5 r) prime }
(tmp + v f12 * (pow52 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow52 r }
(tmp + v f12 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime)
val mul_felem5_lemma_3:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_3 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_2 f1 r }
(tmp + v f13 * pow78 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f13 * pow78 * as_nat5 r) prime }
(tmp + (v f13 * pow78 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f13) pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (pow78 * as_nat5 r) prime }
(tmp + v f13 * (pow78 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow78 r }
(tmp + v f13 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime)
val mul_felem5_lemma_4:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)
let mul_felem5_lemma_4 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_3 f1 r }
(tmp + v f14 * pow104 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f14 * pow104 * as_nat5 r) prime }
(tmp + (v f14 * pow104 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f14) pow104 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (pow104 * as_nat5 r) prime }
(tmp + v f14 * (pow104 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow104 r }
(tmp + v f14 * (as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) prime }
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) prime }
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)
val mul_felem5_lemma:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_pfelem5 f1) `pfmul` (as_pfelem5 r) ==
(v f10 * as_nat5 (r0, r1, r2, r3, r4) +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val mul_felem5_lemma:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_pfelem5 f1) `pfmul` (as_pfelem5 r) ==
(v f10 * as_nat5 (r0, r1, r2, r3, r4) +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f1:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 f1 (3, 3, 3, 3, 3)} ->
r:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 r (2, 2, 2, 2, 2)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = f1 in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in
let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in
Hacl.Spec.Poly1305.Vec.pfmul (Hacl.Spec.Poly1305.Field32xN.as_pfelem5 f1)
(Hacl.Spec.Poly1305.Field32xN.as_pfelem5 r) ==
(Lib.IntTypes.v f10 * Hacl.Spec.Poly1305.Field32xN.as_nat5 (r0, r1, r2, r3, r4) +
Lib.IntTypes.v f11 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r4 *! Lib.IntTypes.u64 5, r0, r1, r2, r3) +
Lib.IntTypes.v f12 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0,
r1,
r2) +
Lib.IntTypes.v f13 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r2 *! Lib.IntTypes.u64 5,
r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0,
r1) +
Lib.IntTypes.v f14 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r1 *! Lib.IntTypes.u64 5,
r2 *! Lib.IntTypes.u64 5,
r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0)) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)
<:
Type0)) | {
"end_col": 80,
"end_line": 653,
"start_col": 27,
"start_line": 648
} |
FStar.Pervasives.Lemma | val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3 | val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 = | false | null | true | match w with
| 1 -> smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.scale64",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1",
"Hacl.Poly1305.Field32xN.Lemmas0.smul_add_felem5_fits_lemma_i",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2)) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2)) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_add_felem5_fits_lemma1 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
u1: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 u1 m1} ->
f2: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 f2 m2} ->
acc1:
Hacl.Spec.Poly1305.Field32xN.uint64xN w
{Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1 acc1 m3}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1 (Lib.IntVector.vec_add_mod acc1
(Lib.IntVector.vec_mul_mod f2 u1))
(m3 + m1 * m2)) | {
"end_col": 60,
"end_line": 317,
"start_col": 2,
"start_line": 307
} |
FStar.Pervasives.Lemma | val precomp_r5_as_tup64:
#w:lanes
-> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}
-> i:nat{i < w} ->
Lemma
(let r5 = precomp_r5 r in
let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
tr50 == tr0 *! u64 5 /\
tr51 == tr1 *! u64 5 /\
tr52 == tr2 *! u64 5 /\
tr53 == tr3 *! u64 5 /\
tr54 == tr4 *! u64 5) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let precomp_r5_as_tup64 #w r i =
let r5 = precomp_r5 r in
let (r50, r51, r52, r53, r54) = r5 in
let (r0, r1, r2, r3, r4) = r in
let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (5 * v tr0) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr1) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr2) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr3) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr4) (pow2 64);
assert (v tr50 == v (tr0 *! u64 5));
assert (v tr51 == v (tr1 *! u64 5));
assert (v tr52 == v (tr2 *! u64 5));
assert (v tr53 == v (tr3 *! u64 5));
assert (v tr54 == v (tr4 *! u64 5)) | val precomp_r5_as_tup64:
#w:lanes
-> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}
-> i:nat{i < w} ->
Lemma
(let r5 = precomp_r5 r in
let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
tr50 == tr0 *! u64 5 /\
tr51 == tr1 *! u64 5 /\
tr52 == tr2 *! u64 5 /\
tr53 == tr3 *! u64 5 /\
tr54 == tr4 *! u64 5)
let precomp_r5_as_tup64 #w r i = | false | null | true | let r5 = precomp_r5 r in
let r50, r51, r52, r53, r54 = r5 in
let r0, r1, r2, r3, r4 = r in
let tr50, tr51, tr52, tr53, tr54 = as_tup64_i r5 i in
let tr0, tr1, tr2, tr3, tr4 = as_tup64_i r i in
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (5 * v tr0) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr1) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr2) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr3) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr4) (pow2 64);
assert (v tr50 == v (tr0 *! u64 5));
assert (v tr51 == v (tr1 *! u64 5));
assert (v tr52 == v (tr2 *! u64 5));
assert (v tr53 == v (tr3 *! u64 5));
assert (v tr54 == v (tr4 *! u64 5)) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Lib.IntTypes.range_t",
"Lib.IntTypes.U64",
"Lib.IntTypes.v",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Star_Bang",
"Lib.IntTypes.u64",
"Prims.unit",
"FStar.Math.Lemmas.modulo_lemma",
"FStar.Mul.op_Star",
"Prims.pow2",
"FStar.Pervasives.assert_norm",
"Prims.op_Equality",
"Prims.int",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Prims.op_Subtraction",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"Hacl.Spec.Poly1305.Field32xN.precomp_r5"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime)
val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime))
let lemma_fmul5_pow52 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow52 * as_nat5 r) % prime;
(==) { assert_norm (pow52 == pow26 * pow26) }
(pow26 * pow26 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
(==) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)
val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime))
let lemma_fmul5_pow78 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow78 * as_nat5 r) % prime;
(==) { assert_norm (pow78 == pow26 * pow52) }
(pow26 * pow52 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow52 * as_nat5 r) prime }
(pow26 * (pow52 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow52 r }
(pow26 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(pow26 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
(==) { lemma_fmul5_pow26 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) }
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime;
};
assert ((pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)
val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime))
let lemma_fmul5_pow104 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow104 * as_nat5 r) % prime;
(==) { assert_norm (pow104 == pow26 * pow78) }
(pow26 * pow78 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow78 * as_nat5 r) prime }
(pow26 * (pow78 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow78 r }
(pow26 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(pow26 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
(==) { lemma_fmul5_pow26 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) }
as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime;
};
assert ((pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime)
val mul_felem5_lemma_1:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_1 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp = v f10 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { }
(v f10 + v f11 * pow26 + v f12 * pow52 + v f13 * pow78 + v f14 * pow104) * as_nat5 r % prime;
(==) { lemma_mul5_distr_r (v f10) (v f11 * pow26) (v f12 * pow52) (v f13 * pow78) (v f14 * pow104) (as_nat5 r) }
(v f10 * as_nat5 r + v f11 * pow26 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * pow26 * as_nat5 r) prime }
(tmp + (v f11 * pow26 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f11) pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow26 * as_nat5 r) prime }
(tmp + v f11 * (pow26 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow26 r }
(tmp + v f11 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime)
val mul_felem5_lemma_2:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_2 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_1 f1 r }
(tmp + v f12 * pow52 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * pow52 * as_nat5 r) prime }
(tmp + (v f12 * pow52 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f12) pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (pow52 * as_nat5 r) prime }
(tmp + v f12 * (pow52 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow52 r }
(tmp + v f12 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime)
val mul_felem5_lemma_3:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_3 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_2 f1 r }
(tmp + v f13 * pow78 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f13 * pow78 * as_nat5 r) prime }
(tmp + (v f13 * pow78 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f13) pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (pow78 * as_nat5 r) prime }
(tmp + v f13 * (pow78 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow78 r }
(tmp + v f13 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime)
val mul_felem5_lemma_4:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)
let mul_felem5_lemma_4 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_3 f1 r }
(tmp + v f14 * pow104 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f14 * pow104 * as_nat5 r) prime }
(tmp + (v f14 * pow104 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f14) pow104 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (pow104 * as_nat5 r) prime }
(tmp + v f14 * (pow104 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow104 r }
(tmp + v f14 * (as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) prime }
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) prime }
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)
val mul_felem5_lemma:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_pfelem5 f1) `pfmul` (as_pfelem5 r) ==
(v f10 * as_nat5 (r0, r1, r2, r3, r4) +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)
let mul_felem5_lemma f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
mul_felem5_lemma_4 f1 r;
FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime;
FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime
val precomp_r5_as_tup64:
#w:lanes
-> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}
-> i:nat{i < w} ->
Lemma
(let r5 = precomp_r5 r in
let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
tr50 == tr0 *! u64 5 /\
tr51 == tr1 *! u64 5 /\
tr52 == tr2 *! u64 5 /\
tr53 == tr3 *! u64 5 /\
tr54 == tr4 *! u64 5) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val precomp_r5_as_tup64:
#w:lanes
-> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}
-> i:nat{i < w} ->
Lemma
(let r5 = precomp_r5 r in
let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
tr50 == tr0 *! u64 5 /\
tr51 == tr1 *! u64 5 /\
tr52 == tr2 *! u64 5 /\
tr53 == tr3 *! u64 5 /\
tr54 == tr4 *! u64 5) | [] | Hacl.Poly1305.Field32xN.Lemmas0.precomp_r5_as_tup64 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
r:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 r (2, 2, 2, 2, 2)} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(let r5 = Hacl.Spec.Poly1305.Field32xN.precomp_r5 r in
let _ = Hacl.Spec.Poly1305.Field32xN.as_tup64_i r5 i in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ tr50 tr51 tr52 tr53 tr54 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.as_tup64_i r i in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ tr0 tr1 tr2 tr3 tr4 = _ in
tr50 == tr0 *! Lib.IntTypes.u64 5 /\ tr51 == tr1 *! Lib.IntTypes.u64 5 /\
tr52 == tr2 *! Lib.IntTypes.u64 5 /\ tr53 == tr3 *! Lib.IntTypes.u64 5 /\
tr54 == tr4 *! Lib.IntTypes.u64 5)
<:
Type0)
<:
Type0)) | {
"end_col": 37,
"end_line": 686,
"start_col": 32,
"start_line": 670
} |
FStar.Pervasives.Lemma | val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3 | val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 = | false | null | true | match w with
| 1 -> smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3 | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Poly1305.Field32xN.Lemmas0.smul_felem5_fits_lemma_i",
"Prims.unit"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2)) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2)) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_felem5_fits_lemma1 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
u1: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 u1 m1} ->
f2: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 f2 m2}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1 (Lib.IntVector.vec_mul_mod f2 u1) (m1 * m2)) | {
"end_col": 47,
"end_line": 179,
"start_col": 2,
"start_line": 169
} |
FStar.Pervasives.Lemma | val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp | val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 = | false | null | true | let tmp =
map2 #nat
#nat
#nat
(fun a b -> a + b)
(fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.scale32_5",
"Hacl.Spec.Poly1305.Field32xN.scale64_5",
"Hacl.Spec.Poly1305.Field32xN.op_Less_Equals_Star",
"Hacl.Spec.Poly1305.Field32xN.op_Plus_Star",
"Hacl.Spec.Poly1305.Field32xN.op_Star_Hat",
"Hacl.Spec.Poly1305.Field32xN.s64x5",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5",
"Lib.Sequence.eq_intro",
"Prims.nat",
"Hacl.Spec.Poly1305.Field32xN.fas_nat5",
"Hacl.Spec.Poly1305.Field32xN.smul_add_felem5",
"Prims.unit",
"FStar.Classical.forall_intro",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.eq2",
"Prims.int",
"Lib.Sequence.op_String_Access",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Hacl.Poly1305.Field32xN.Lemmas0.smul_add_felem5_eval_lemma_i",
"Lib.Sequence.lseq",
"Prims.l_Forall",
"Prims.l_imp",
"Lib.Sequence.index",
"Lib.Sequence.map2",
"Prims.op_Multiply"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_add_felem5_eval_lemma | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
u1: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 u1 m1} ->
f2: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Spec.Poly1305.Field32xN.felem_fits5 f2 m2} ->
acc1:
Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
{Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5 acc1 m3}
-> FStar.Pervasives.Lemma
(ensures
Hacl.Spec.Poly1305.Field32xN.fas_nat5 (Hacl.Spec.Poly1305.Field32xN.smul_add_felem5 u1 f2 acc1
) ==
Lib.Sequence.map2 (fun a b -> a + b)
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 acc1)
(Lib.Sequence.map2 (fun a b -> a * b)
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v u1)
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 f2))) | {
"end_col": 57,
"end_line": 359,
"start_col": 58,
"start_line": 354
} |
FStar.Pervasives.Lemma | val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i]) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i]) | val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i = | false | null | true | let o = smul_felem5 #w u1 f2 in
let m20, m21, m22, m23, m24 = m2 in
let vu1 = (uint64xN_v u1).[ i ] in
let tf20, tf21, tf22, tf23, tf24 = as_tup64_i f2 i in
let to0, to1, to2, to3, to4 = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[ i ] ==
vu1 * v tf20 + (vu1 * v tf21) * pow26 + (vu1 * v tf22) * pow52 + (vu1 * v tf23) * pow78 +
(vu1 * v tf24) * pow104);
calc ( == ) {
vu1 * (fas_nat5 f2).[ i ];
( == ) { () }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
( == ) { lemma_mul5_distr_l vu1
(v tf20)
(v tf21 * pow26)
(v tf22 * pow52)
(v tf23 * pow78)
(v tf24 * pow104) }
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) +
vu1 * (v tf24 * pow104);
( == ) { (FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104) }
vu1 * v tf20 + (vu1 * v tf21) * pow26 + (vu1 * v tf22) * pow52 + (vu1 * v tf23) * pow78 +
(vu1 * v tf24) * pow104;
};
assert (vu1 * (fas_nat5 f2).[ i ] == (fas_nat5 o).[ i ]) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.scale32_5",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"FStar.Mul.op_Star",
"Lib.Sequence.op_String_Access",
"Hacl.Spec.Poly1305.Field32xN.fas_nat5",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_mul5_distr_l",
"FStar.Math.Lemmas.paren_mul_right",
"Hacl.Poly1305.Field32xN.Lemmas0.smul_mod_lemma",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.smul_felem5"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i]) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i]) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_felem5_eval_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
u1: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 u1 m1} ->
f2: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Spec.Poly1305.Field32xN.felem_fits5 f2 m2} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 (Hacl.Spec.Poly1305.Field32xN.smul_felem5 u1 f2)).[ i ] ==
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v u1).[ i ] *
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 f2).[ i ]) | {
"end_col": 54,
"end_line": 157,
"start_col": 49,
"start_line": 128
} |
FStar.Pervasives.Lemma | val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26) | val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i = | false | null | true | let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[ i ] (uint64xN_v f2).[ i ] (uint64xN_v acc1).[ i ];
assert ((uint64xN_v o).[ i ] ==
(uint64xN_v acc1).[ i ] + (uint64xN_v u1).[ i ] * (uint64xN_v f2).[ i ]);
lemma_mult_le (uint64xN_v u1).[ i ] (m1 * max26) (uint64xN_v f2).[ i ] (m2 * max26);
assert ((uint64xN_v o).[ i ] <= (m3 * max26) * max26 + ((m1 * m2) * max26) * max26) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.scale64",
"Prims.b2t",
"Prims.op_LessThanOrEqual",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1",
"Prims.nat",
"Prims.op_LessThan",
"Prims._assert",
"Lib.Sequence.op_String_Access",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Hacl.Spec.Poly1305.Field32xN.max26",
"Prims.unit",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_mult_le",
"Prims.eq2",
"Prims.int",
"Hacl.Poly1305.Field32xN.Lemmas0.smul_add_mod_lemma",
"Lib.IntVector.vec_t",
"Lib.IntTypes.U64",
"Lib.IntVector.vec_add_mod",
"Lib.IntVector.vec_mul_mod"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 200,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_add_felem5_fits_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
u1: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 u1 m1} ->
f2: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 f2 m2} ->
acc1:
Hacl.Spec.Poly1305.Field32xN.uint64xN w
{Hacl.Spec.Poly1305.Field32xN.felem_wide_fits1 acc1 m3} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v (Lib.IntVector.vec_add_mod acc1
(Lib.IntVector.vec_mul_mod f2 u1))).[ i ] <=
((m3 + m1 * m2) * Hacl.Spec.Poly1305.Field32xN.max26) * Hacl.Spec.Poly1305.Field32xN.max26) | {
"end_col": 77,
"end_line": 232,
"start_col": 62,
"start_line": 227
} |
FStar.Pervasives.Lemma | val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i]) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime | val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i = | false | null | true | let o = fadd5 f1 f2 in
let f10, f11, f12, f13, f14 = as_tup64_i f1 i in
let f20, f21, f22, f23, f24 = as_tup64_i f2 i in
let o0, o1, o2, o3, o4 = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l (as_nat5 (f10, f11, f12, f13, f14))
(as_nat5 (f20, f21, f22, f23, f24))
prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r (as_nat5 (f10, f11, f12, f13, f14) % prime)
(as_nat5 (f20, f21, f22, f23, f24))
prime | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Lib.IntTypes.uint64",
"FStar.Math.Lemmas.lemma_mod_plus_distr_r",
"Prims.op_Modulus",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.unit",
"FStar.Math.Lemmas.lemma_mod_plus_distr_l",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Addition",
"Hacl.Poly1305.Field32xN.Lemmas0.add5_lemma1",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"Hacl.Spec.Poly1305.Field32xN.fadd5"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i]) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i]) | [] | Hacl.Poly1305.Field32xN.Lemmas0.fadd5_eval_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f1:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 f1 (2, 2, 2, 2, 2)} ->
f2:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 f2 (1, 1, 1, 1, 1)} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(Hacl.Spec.Poly1305.Field32xN.feval5 (Hacl.Spec.Poly1305.Field32xN.fadd5 f1 f2)).[ i ] ==
Hacl.Spec.Poly1305.Vec.pfadd (Hacl.Spec.Poly1305.Field32xN.feval5 f1).[ i ]
(Hacl.Spec.Poly1305.Field32xN.feval5 f2).[ i ]) | {
"end_col": 89,
"end_line": 100,
"start_col": 35,
"start_line": 84
} |
FStar.Pervasives.Lemma | val mul_felem5_eval_as_tup64:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (3, 3, 3, 3, 3)}
-> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}
-> r5:felem5 w{felem_fits5 r5 (10, 10, 10, 10, 10) /\ r5 == precomp_r5 r}
-> i:nat{i < w} ->
Lemma
(let (r0, r1, r2, r3, r4) = r in
let (f10, f11, f12, f13, f14) = f1 in
let (r50, r51, r52, r53, r54) = r5 in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
let (tf10, tf11, tf12, tf13, tf14) = as_tup64_i f1 i in
(uint64xN_v f10).[i] * (fas_nat5 (r0,r1,r2,r3,r4)).[i] +
(uint64xN_v f11).[i] * (fas_nat5 (r54,r0,r1,r2,r3)).[i] +
(uint64xN_v f12).[i] * (fas_nat5 (r53,r54,r0,r1,r2)).[i] +
(uint64xN_v f13).[i] * (fas_nat5 (r52,r53,r54,r0,r1)).[i] +
(uint64xN_v f14).[i] * (fas_nat5 (r51,r52,r53,r54,r0)).[i] ==
(v tf10 * as_nat5 (tr0, tr1, tr2, tr3, tr4) +
v tf11 * as_nat5 (tr4 *! u64 5, tr0, tr1, tr2, tr3) +
v tf12 * as_nat5 (tr3 *! u64 5, tr4 *! u64 5, tr0, tr1, tr2) +
v tf13 * as_nat5 (tr2 *! u64 5, tr3 *! u64 5, tr4 *! u64 5, tr0, tr1) +
v tf14 * as_nat5 (tr1 *! u64 5, tr2 *! u64 5, tr3 *! u64 5, tr4 *! u64 5, tr0))) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let mul_felem5_eval_as_tup64 #w f1 r r5 i =
let (r0, r1, r2, r3, r4) = r in
let (f10, f11, f12, f13, f14) = f1 in
let (r50, r51, r52, r53, r54) = r5 in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
let (tf10, tf11, tf12, tf13, tf14) = as_tup64_i f1 i in
let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in
assert (
(uint64xN_v f10).[i] * (fas_nat5 (r0,r1,r2,r3,r4)).[i] +
(uint64xN_v f11).[i] * (fas_nat5 (r54,r0,r1,r2,r3)).[i] +
(uint64xN_v f12).[i] * (fas_nat5 (r53,r54,r0,r1,r2)).[i] +
(uint64xN_v f13).[i] * (fas_nat5 (r52,r53,r54,r0,r1)).[i] +
(uint64xN_v f14).[i] * (fas_nat5 (r51,r52,r53,r54,r0)).[i] ==
v tf10 * as_nat5 (tr0,tr1,tr2,tr3,tr4) +
v tf11 * as_nat5 (tr54,tr0,tr1,tr2,tr3) +
v tf12 * as_nat5 (tr53,tr54,tr0,tr1,tr2) +
v tf13 * as_nat5 (tr52,tr53,tr54,tr0,tr1) +
v tf14 * as_nat5 (tr51,tr52,tr53,tr54,tr0));
precomp_r5_as_tup64 #w r i | val mul_felem5_eval_as_tup64:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (3, 3, 3, 3, 3)}
-> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}
-> r5:felem5 w{felem_fits5 r5 (10, 10, 10, 10, 10) /\ r5 == precomp_r5 r}
-> i:nat{i < w} ->
Lemma
(let (r0, r1, r2, r3, r4) = r in
let (f10, f11, f12, f13, f14) = f1 in
let (r50, r51, r52, r53, r54) = r5 in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
let (tf10, tf11, tf12, tf13, tf14) = as_tup64_i f1 i in
(uint64xN_v f10).[i] * (fas_nat5 (r0,r1,r2,r3,r4)).[i] +
(uint64xN_v f11).[i] * (fas_nat5 (r54,r0,r1,r2,r3)).[i] +
(uint64xN_v f12).[i] * (fas_nat5 (r53,r54,r0,r1,r2)).[i] +
(uint64xN_v f13).[i] * (fas_nat5 (r52,r53,r54,r0,r1)).[i] +
(uint64xN_v f14).[i] * (fas_nat5 (r51,r52,r53,r54,r0)).[i] ==
(v tf10 * as_nat5 (tr0, tr1, tr2, tr3, tr4) +
v tf11 * as_nat5 (tr4 *! u64 5, tr0, tr1, tr2, tr3) +
v tf12 * as_nat5 (tr3 *! u64 5, tr4 *! u64 5, tr0, tr1, tr2) +
v tf13 * as_nat5 (tr2 *! u64 5, tr3 *! u64 5, tr4 *! u64 5, tr0, tr1) +
v tf14 * as_nat5 (tr1 *! u64 5, tr2 *! u64 5, tr3 *! u64 5, tr4 *! u64 5, tr0)))
let mul_felem5_eval_as_tup64 #w f1 r r5 i = | false | null | true | let r0, r1, r2, r3, r4 = r in
let f10, f11, f12, f13, f14 = f1 in
let r50, r51, r52, r53, r54 = r5 in
let tr0, tr1, tr2, tr3, tr4 = as_tup64_i r i in
let tf10, tf11, tf12, tf13, tf14 = as_tup64_i f1 i in
let tr50, tr51, tr52, tr53, tr54 = as_tup64_i r5 i in
assert ((uint64xN_v f10).[ i ] * (fas_nat5 (r0, r1, r2, r3, r4)).[ i ] +
(uint64xN_v f11).[ i ] * (fas_nat5 (r54, r0, r1, r2, r3)).[ i ] +
(uint64xN_v f12).[ i ] * (fas_nat5 (r53, r54, r0, r1, r2)).[ i ] +
(uint64xN_v f13).[ i ] * (fas_nat5 (r52, r53, r54, r0, r1)).[ i ] +
(uint64xN_v f14).[ i ] * (fas_nat5 (r51, r52, r53, r54, r0)).[ i ] ==
v tf10 * as_nat5 (tr0, tr1, tr2, tr3, tr4) + v tf11 * as_nat5 (tr54, tr0, tr1, tr2, tr3) +
v tf12 * as_nat5 (tr53, tr54, tr0, tr1, tr2) +
v tf13 * as_nat5 (tr52, tr53, tr54, tr0, tr1) +
v tf14 * as_nat5 (tr51, tr52, tr53, tr54, tr0));
precomp_r5_as_tup64 #w r i | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Prims.l_and",
"Prims.eq2",
"Hacl.Spec.Poly1305.Field32xN.precomp_r5",
"Prims.b2t",
"Prims.op_LessThan",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Lib.IntTypes.uint64",
"Hacl.Poly1305.Field32xN.Lemmas0.precomp_r5_as_tup64",
"Prims.unit",
"Prims._assert",
"Prims.int",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Lib.Sequence.op_String_Access",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Hacl.Spec.Poly1305.Field32xN.fas_nat5",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime)
val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime))
let lemma_fmul5_pow52 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow52 * as_nat5 r) % prime;
(==) { assert_norm (pow52 == pow26 * pow26) }
(pow26 * pow26 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
(==) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)
val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime))
let lemma_fmul5_pow78 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow78 * as_nat5 r) % prime;
(==) { assert_norm (pow78 == pow26 * pow52) }
(pow26 * pow52 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow52 * as_nat5 r) prime }
(pow26 * (pow52 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow52 r }
(pow26 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(pow26 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
(==) { lemma_fmul5_pow26 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) }
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime;
};
assert ((pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)
val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime))
let lemma_fmul5_pow104 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow104 * as_nat5 r) % prime;
(==) { assert_norm (pow104 == pow26 * pow78) }
(pow26 * pow78 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow78 * as_nat5 r) prime }
(pow26 * (pow78 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow78 r }
(pow26 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(pow26 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
(==) { lemma_fmul5_pow26 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) }
as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime;
};
assert ((pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime)
val mul_felem5_lemma_1:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_1 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp = v f10 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { }
(v f10 + v f11 * pow26 + v f12 * pow52 + v f13 * pow78 + v f14 * pow104) * as_nat5 r % prime;
(==) { lemma_mul5_distr_r (v f10) (v f11 * pow26) (v f12 * pow52) (v f13 * pow78) (v f14 * pow104) (as_nat5 r) }
(v f10 * as_nat5 r + v f11 * pow26 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * pow26 * as_nat5 r) prime }
(tmp + (v f11 * pow26 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f11) pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow26 * as_nat5 r) prime }
(tmp + v f11 * (pow26 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow26 r }
(tmp + v f11 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime)
val mul_felem5_lemma_2:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_2 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_1 f1 r }
(tmp + v f12 * pow52 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * pow52 * as_nat5 r) prime }
(tmp + (v f12 * pow52 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f12) pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (pow52 * as_nat5 r) prime }
(tmp + v f12 * (pow52 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow52 r }
(tmp + v f12 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime)
val mul_felem5_lemma_3:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_3 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_2 f1 r }
(tmp + v f13 * pow78 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f13 * pow78 * as_nat5 r) prime }
(tmp + (v f13 * pow78 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f13) pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (pow78 * as_nat5 r) prime }
(tmp + v f13 * (pow78 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow78 r }
(tmp + v f13 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime)
val mul_felem5_lemma_4:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)
let mul_felem5_lemma_4 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_3 f1 r }
(tmp + v f14 * pow104 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f14 * pow104 * as_nat5 r) prime }
(tmp + (v f14 * pow104 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f14) pow104 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (pow104 * as_nat5 r) prime }
(tmp + v f14 * (pow104 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow104 r }
(tmp + v f14 * (as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) prime }
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) prime }
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)
val mul_felem5_lemma:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_pfelem5 f1) `pfmul` (as_pfelem5 r) ==
(v f10 * as_nat5 (r0, r1, r2, r3, r4) +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)
let mul_felem5_lemma f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
mul_felem5_lemma_4 f1 r;
FStar.Math.Lemmas.lemma_mod_mul_distr_l (as_nat5 f1) (as_nat5 r) prime;
FStar.Math.Lemmas.lemma_mod_mul_distr_r (as_nat5 f1 % prime) (as_nat5 r) prime
val precomp_r5_as_tup64:
#w:lanes
-> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}
-> i:nat{i < w} ->
Lemma
(let r5 = precomp_r5 r in
let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
tr50 == tr0 *! u64 5 /\
tr51 == tr1 *! u64 5 /\
tr52 == tr2 *! u64 5 /\
tr53 == tr3 *! u64 5 /\
tr54 == tr4 *! u64 5)
let precomp_r5_as_tup64 #w r i =
let r5 = precomp_r5 r in
let (r50, r51, r52, r53, r54) = r5 in
let (r0, r1, r2, r3, r4) = r in
let (tr50, tr51, tr52, tr53, tr54) = as_tup64_i r5 i in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
assert_norm (max26 = pow2 26 - 1);
FStar.Math.Lemmas.modulo_lemma (5 * v tr0) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr1) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr2) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr3) (pow2 64);
FStar.Math.Lemmas.modulo_lemma (5 * v tr4) (pow2 64);
assert (v tr50 == v (tr0 *! u64 5));
assert (v tr51 == v (tr1 *! u64 5));
assert (v tr52 == v (tr2 *! u64 5));
assert (v tr53 == v (tr3 *! u64 5));
assert (v tr54 == v (tr4 *! u64 5))
val mul_felem5_eval_as_tup64:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (3, 3, 3, 3, 3)}
-> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}
-> r5:felem5 w{felem_fits5 r5 (10, 10, 10, 10, 10) /\ r5 == precomp_r5 r}
-> i:nat{i < w} ->
Lemma
(let (r0, r1, r2, r3, r4) = r in
let (f10, f11, f12, f13, f14) = f1 in
let (r50, r51, r52, r53, r54) = r5 in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
let (tf10, tf11, tf12, tf13, tf14) = as_tup64_i f1 i in
(uint64xN_v f10).[i] * (fas_nat5 (r0,r1,r2,r3,r4)).[i] +
(uint64xN_v f11).[i] * (fas_nat5 (r54,r0,r1,r2,r3)).[i] +
(uint64xN_v f12).[i] * (fas_nat5 (r53,r54,r0,r1,r2)).[i] +
(uint64xN_v f13).[i] * (fas_nat5 (r52,r53,r54,r0,r1)).[i] +
(uint64xN_v f14).[i] * (fas_nat5 (r51,r52,r53,r54,r0)).[i] ==
(v tf10 * as_nat5 (tr0, tr1, tr2, tr3, tr4) +
v tf11 * as_nat5 (tr4 *! u64 5, tr0, tr1, tr2, tr3) +
v tf12 * as_nat5 (tr3 *! u64 5, tr4 *! u64 5, tr0, tr1, tr2) +
v tf13 * as_nat5 (tr2 *! u64 5, tr3 *! u64 5, tr4 *! u64 5, tr0, tr1) +
v tf14 * as_nat5 (tr1 *! u64 5, tr2 *! u64 5, tr3 *! u64 5, tr4 *! u64 5, tr0))) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val mul_felem5_eval_as_tup64:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (3, 3, 3, 3, 3)}
-> r:felem5 w{felem_fits5 r (2, 2, 2, 2, 2)}
-> r5:felem5 w{felem_fits5 r5 (10, 10, 10, 10, 10) /\ r5 == precomp_r5 r}
-> i:nat{i < w} ->
Lemma
(let (r0, r1, r2, r3, r4) = r in
let (f10, f11, f12, f13, f14) = f1 in
let (r50, r51, r52, r53, r54) = r5 in
let (tr0, tr1, tr2, tr3, tr4) = as_tup64_i r i in
let (tf10, tf11, tf12, tf13, tf14) = as_tup64_i f1 i in
(uint64xN_v f10).[i] * (fas_nat5 (r0,r1,r2,r3,r4)).[i] +
(uint64xN_v f11).[i] * (fas_nat5 (r54,r0,r1,r2,r3)).[i] +
(uint64xN_v f12).[i] * (fas_nat5 (r53,r54,r0,r1,r2)).[i] +
(uint64xN_v f13).[i] * (fas_nat5 (r52,r53,r54,r0,r1)).[i] +
(uint64xN_v f14).[i] * (fas_nat5 (r51,r52,r53,r54,r0)).[i] ==
(v tf10 * as_nat5 (tr0, tr1, tr2, tr3, tr4) +
v tf11 * as_nat5 (tr4 *! u64 5, tr0, tr1, tr2, tr3) +
v tf12 * as_nat5 (tr3 *! u64 5, tr4 *! u64 5, tr0, tr1, tr2) +
v tf13 * as_nat5 (tr2 *! u64 5, tr3 *! u64 5, tr4 *! u64 5, tr0, tr1) +
v tf14 * as_nat5 (tr1 *! u64 5, tr2 *! u64 5, tr3 *! u64 5, tr4 *! u64 5, tr0))) | [] | Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_eval_as_tup64 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f1:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 f1 (3, 3, 3, 3, 3)} ->
r:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{Hacl.Spec.Poly1305.Field32xN.felem_fits5 r (2, 2, 2, 2, 2)} ->
r5:
Hacl.Spec.Poly1305.Field32xN.felem5 w
{ Hacl.Spec.Poly1305.Field32xN.felem_fits5 r5 (10, 10, 10, 10, 10) /\
r5 == Hacl.Spec.Poly1305.Field32xN.precomp_r5 r } ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in
let _ = f1 in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in
let _ = r5 in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ _ r51 r52 r53 r54 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.as_tup64_i r i in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ tr0 tr1 tr2 tr3 tr4 = _ in
let _ = Hacl.Spec.Poly1305.Field32xN.as_tup64_i f1 i in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ tf10 tf11 tf12 tf13 tf14 = _ in
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v f10).[ i ] *
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 (r0, r1, r2, r3, r4)).[ i ] +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v f11).[ i ] *
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 (r54, r0, r1, r2, r3)).[ i ] +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v f12).[ i ] *
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 (r53, r54, r0, r1, r2)).[ i ] +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v f13).[ i ] *
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 (r52, r53, r54, r0, r1)).[ i ] +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v f14).[ i ] *
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 (r51, r52, r53, r54, r0)).[ i ] ==
Lib.IntTypes.v tf10 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (tr0, tr1, tr2, tr3, tr4) +
Lib.IntTypes.v tf11 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (tr4 *! Lib.IntTypes.u64 5,
tr0,
tr1,
tr2,
tr3) +
Lib.IntTypes.v tf12 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (tr3 *! Lib.IntTypes.u64 5,
tr4 *! Lib.IntTypes.u64 5,
tr0,
tr1,
tr2) +
Lib.IntTypes.v tf13 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (tr2 *! Lib.IntTypes.u64 5,
tr3 *! Lib.IntTypes.u64 5,
tr4 *! Lib.IntTypes.u64 5,
tr0,
tr1) +
Lib.IntTypes.v tf14 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (tr1 *! Lib.IntTypes.u64 5,
tr2 *! Lib.IntTypes.u64 5,
tr3 *! Lib.IntTypes.u64 5,
tr4 *! Lib.IntTypes.u64 5,
tr0))
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)
<:
Type0)) | {
"end_col": 28,
"end_line": 730,
"start_col": 43,
"start_line": 712
} |
FStar.Pervasives.Lemma | val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i]) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i]) | val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i = | false | null | true | let o = smul_add_felem5 #w u1 f2 acc1 in
let m20, m21, m22, m23, m24 = m2 in
let m30, m31, m32, m33, m34 = m3 in
let vu1 = (uint64xN_v u1).[ i ] in
let tf20, tf21, tf22, tf23, tf24 = as_tup64_i f2 i in
let ta0, ta1, ta2, ta3, ta4 = as_tup64_i acc1 i in
let to0, to1, to2, to3, to4 = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc ( == ) {
(fas_nat5 o).[ i ];
( == ) { () }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 +
(v ta4 + vu1 * v tf24) * pow104;
( == ) { (FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104) }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 + vu1 * v tf20 +
(vu1 * v tf21) * pow26 +
(vu1 * v tf22) * pow52 +
(vu1 * v tf23) * pow78 +
(vu1 * v tf24) * pow104;
( == ) { () }
(fas_nat5 acc1).[ i ] + vu1 * v tf20 + (vu1 * v tf21) * pow26 + (vu1 * v tf22) * pow52 +
(vu1 * v tf23) * pow78 +
(vu1 * v tf24) * pow104;
};
assert ((fas_nat5 o).[ i ] ==
(fas_nat5 acc1).[ i ] + vu1 * v tf20 + (vu1 * v tf21) * pow26 + (vu1 * v tf22) * pow52 +
(vu1 * v tf23) * pow78 +
(vu1 * v tf24) * pow104);
calc ( == ) {
vu1 * (fas_nat5 f2).[ i ];
( == ) { () }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
( == ) { lemma_mul5_distr_l vu1
(v tf20)
(v tf21 * pow26)
(v tf22 * pow52)
(v tf23 * pow78)
(v tf24 * pow104) }
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) +
vu1 * (v tf24 * pow104);
( == ) { (FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104) }
vu1 * v tf20 + (vu1 * v tf21) * pow26 + (vu1 * v tf22) * pow52 + (vu1 * v tf23) * pow78 +
(vu1 * v tf24) * pow104;
};
assert ((fas_nat5 o).[ i ] == (fas_nat5 acc1).[ i ] + vu1 * (fas_nat5 f2).[ i ]) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.lanes",
"Hacl.Spec.Poly1305.Field32xN.scale32",
"Hacl.Spec.Poly1305.Field32xN.scale32_5",
"Hacl.Spec.Poly1305.Field32xN.scale64_5",
"Hacl.Spec.Poly1305.Field32xN.op_Less_Equals_Star",
"Hacl.Spec.Poly1305.Field32xN.op_Plus_Star",
"Hacl.Spec.Poly1305.Field32xN.op_Star_Hat",
"Hacl.Spec.Poly1305.Field32xN.s64x5",
"Hacl.Spec.Poly1305.Field32xN.uint64xN",
"Hacl.Spec.Poly1305.Field32xN.felem_fits1",
"Hacl.Spec.Poly1305.Field32xN.felem5",
"Hacl.Spec.Poly1305.Field32xN.felem_fits5",
"Hacl.Spec.Poly1305.Field32xN.felem_wide5",
"Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5",
"Prims.nat",
"Prims.b2t",
"Prims.op_LessThan",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Lib.Sequence.op_String_Access",
"Hacl.Spec.Poly1305.Field32xN.fas_nat5",
"Prims.op_Addition",
"FStar.Mul.op_Star",
"Prims.unit",
"FStar.Calc.calc_finish",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_mul5_distr_l",
"FStar.Math.Lemmas.paren_mul_right",
"FStar.Seq.Base.index",
"Lib.Sequence.to_seq",
"FStar.Math.Lemmas.distributivity_add_left",
"Hacl.Poly1305.Field32xN.Lemmas0.smul_add_mod_lemma",
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.as_tup64_i",
"Hacl.Spec.Poly1305.Field32xN.uint64xN_v",
"Hacl.Spec.Poly1305.Field32xN.smul_add_felem5"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i]) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i]) | [] | Hacl.Poly1305.Field32xN.Lemmas0.smul_add_felem5_eval_lemma_i | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
u1: Hacl.Spec.Poly1305.Field32xN.uint64xN w {Hacl.Spec.Poly1305.Field32xN.felem_fits1 u1 m1} ->
f2: Hacl.Spec.Poly1305.Field32xN.felem5 w {Hacl.Spec.Poly1305.Field32xN.felem_fits5 f2 m2} ->
acc1:
Hacl.Spec.Poly1305.Field32xN.felem_wide5 w
{Hacl.Spec.Poly1305.Field32xN.felem_wide_fits5 acc1 m3} ->
i: Prims.nat{i < w}
-> FStar.Pervasives.Lemma
(ensures
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 (Hacl.Spec.Poly1305.Field32xN.smul_add_felem5 u1
f2
acc1)).[ i ] ==
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 acc1).[ i ] +
(Hacl.Spec.Poly1305.Field32xN.uint64xN_v u1).[ i ] *
(Hacl.Spec.Poly1305.Field32xN.fas_nat5 f2).[ i ]) | {
"end_col": 76,
"end_line": 293,
"start_col": 62,
"start_line": 247
} |
FStar.Pervasives.Lemma | val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_fmul5_pow78 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow78 * as_nat5 r) % prime;
(==) { assert_norm (pow78 == pow26 * pow52) }
(pow26 * pow52 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow52 * as_nat5 r) prime }
(pow26 * (pow52 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow52 r }
(pow26 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(pow26 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
(==) { lemma_fmul5_pow26 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) }
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime;
};
assert ((pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) | val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime))
let lemma_fmul5_pow78 r = | false | null | true | let r0, r1, r2, r3, r4 = r in
calc ( == ) {
(pow78 * as_nat5 r) % prime;
( == ) { assert_norm (pow78 == pow26 * pow52) }
((pow26 * pow52) * as_nat5 r) % prime;
( == ) { (FStar.Math.Lemmas.paren_mul_right pow26 pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow52 * as_nat5 r) prime) }
(pow26 * (pow52 * as_nat5 r % prime)) % prime;
( == ) { lemma_fmul5_pow52 r }
(pow26 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26
(as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2))
prime }
(pow26 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
( == ) { lemma_fmul5_pow26 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) }
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime;
};
assert ((pow78 * as_nat5 r) % prime ==
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"FStar.Pervasives.Native.Mktuple5",
"Lib.IntTypes.op_Star_Bang",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.u64",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Pervasives.assert_norm",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"FStar.Math.Lemmas.paren_mul_right",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow52",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow26"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime)
val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime))
let lemma_fmul5_pow52 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow52 * as_nat5 r) % prime;
(==) { assert_norm (pow52 == pow26 * pow26) }
(pow26 * pow26 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
(==) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)
val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) | [] | Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow78 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | r: Hacl.Spec.Poly1305.Field32xN.tup64_5
-> FStar.Pervasives.Lemma
(requires
(let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ _ _ r2 r3 r4 = _ in
Lib.IntTypes.v r4 * 5 <= 10 * Hacl.Spec.Poly1305.Field32xN.pow26 /\
Lib.IntTypes.v r3 * 5 <= 10 * Hacl.Spec.Poly1305.Field32xN.pow26 /\
Lib.IntTypes.v r2 * 5 <= 10 * Hacl.Spec.Poly1305.Field32xN.pow26)
<:
Type0))
(ensures
(let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in
Hacl.Spec.Poly1305.Field32xN.pow78 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r %
Hacl.Spec.Poly1305.Vec.prime ==
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r2 *! Lib.IntTypes.u64 5,
r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0,
r1) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)) | {
"end_col": 105,
"end_line": 447,
"start_col": 25,
"start_line": 430
} |
FStar.Pervasives.Lemma | val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_fmul5_pow52 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow52 * as_nat5 r) % prime;
(==) { assert_norm (pow52 == pow26 * pow26) }
(pow26 * pow26 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
(==) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) | val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime))
let lemma_fmul5_pow52 r = | false | null | true | let r0, r1, r2, r3, r4 = r in
calc ( == ) {
(pow52 * as_nat5 r) % prime;
( == ) { assert_norm (pow52 == pow26 * pow26) }
((pow26 * pow26) * as_nat5 r) % prime;
( == ) { (FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime) }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
( == ) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26
(as_nat5 (r4 *! u64 5, r0, r1, r2, r3))
prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
( == ) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"FStar.Pervasives.Native.Mktuple5",
"Lib.IntTypes.op_Star_Bang",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.u64",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Pervasives.assert_norm",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"FStar.Math.Lemmas.paren_mul_right",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow26"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime)
val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) | [] | Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow52 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | r: Hacl.Spec.Poly1305.Field32xN.tup64_5
-> FStar.Pervasives.Lemma
(requires
(let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ _ _ _ r3 r4 = _ in
Lib.IntTypes.v r4 * 5 <= 10 * Hacl.Spec.Poly1305.Field32xN.pow26 /\
Lib.IntTypes.v r3 * 5 <= 10 * Hacl.Spec.Poly1305.Field32xN.pow26)
<:
Type0))
(ensures
(let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in
Hacl.Spec.Poly1305.Field32xN.pow52 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r %
Hacl.Spec.Poly1305.Vec.prime ==
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0,
r1,
r2) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)) | {
"end_col": 96,
"end_line": 421,
"start_col": 25,
"start_line": 404
} |
FStar.Pervasives.Lemma | val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_fmul5_pow104 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow104 * as_nat5 r) % prime;
(==) { assert_norm (pow104 == pow26 * pow78) }
(pow26 * pow78 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow78 * as_nat5 r) prime }
(pow26 * (pow78 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow78 r }
(pow26 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(pow26 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
(==) { lemma_fmul5_pow26 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) }
as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime;
};
assert ((pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) | val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime))
let lemma_fmul5_pow104 r = | false | null | true | let r0, r1, r2, r3, r4 = r in
calc ( == ) {
(pow104 * as_nat5 r) % prime;
( == ) { assert_norm (pow104 == pow26 * pow78) }
((pow26 * pow78) * as_nat5 r) % prime;
( == ) { (FStar.Math.Lemmas.paren_mul_right pow26 pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow78 * as_nat5 r) prime) }
(pow26 * (pow78 * as_nat5 r % prime)) % prime;
( == ) { lemma_fmul5_pow78 r }
(pow26 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26
(as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1))
prime }
(pow26 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
( == ) { lemma_fmul5_pow26 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) }
as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime;
};
assert ((pow104 * as_nat5 r) % prime ==
as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"FStar.Pervasives.Native.Mktuple5",
"Lib.IntTypes.op_Star_Bang",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.u64",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"FStar.Pervasives.assert_norm",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"FStar.Math.Lemmas.paren_mul_right",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow78",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow26"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime)
val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime))
let lemma_fmul5_pow52 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow52 * as_nat5 r) % prime;
(==) { assert_norm (pow52 == pow26 * pow26) }
(pow26 * pow26 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
(==) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)
val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime))
let lemma_fmul5_pow78 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow78 * as_nat5 r) % prime;
(==) { assert_norm (pow78 == pow26 * pow52) }
(pow26 * pow52 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow52 * as_nat5 r) prime }
(pow26 * (pow52 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow52 r }
(pow26 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(pow26 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
(==) { lemma_fmul5_pow26 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) }
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime;
};
assert ((pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)
val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime)) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime)) | [] | Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow104 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | r: Hacl.Spec.Poly1305.Field32xN.tup64_5
-> FStar.Pervasives.Lemma
(requires
(let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ _ r1 r2 r3 r4 = _ in
Lib.IntTypes.v r4 * 5 <= 10 * Hacl.Spec.Poly1305.Field32xN.pow26 /\
Lib.IntTypes.v r3 * 5 <= 10 * Hacl.Spec.Poly1305.Field32xN.pow26 /\
Lib.IntTypes.v r2 * 5 <= 10 * Hacl.Spec.Poly1305.Field32xN.pow26 /\
Lib.IntTypes.v r1 * 5 <= 10 * Hacl.Spec.Poly1305.Field32xN.pow26)
<:
Type0))
(ensures
(let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in
Hacl.Spec.Poly1305.Field32xN.pow104 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r %
Hacl.Spec.Poly1305.Vec.prime ==
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r1 *! Lib.IntTypes.u64 5,
r2 *! Lib.IntTypes.u64 5,
r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)) | {
"end_col": 115,
"end_line": 474,
"start_col": 26,
"start_line": 457
} |
FStar.Pervasives.Lemma | val mul_felem5_lemma_2:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let mul_felem5_lemma_2 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_1 f1 r }
(tmp + v f12 * pow52 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * pow52 * as_nat5 r) prime }
(tmp + (v f12 * pow52 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f12) pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (pow52 * as_nat5 r) prime }
(tmp + v f12 * (pow52 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow52 r }
(tmp + v f12 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime) | val mul_felem5_lemma_2:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_2 f1 r = | false | null | true | let f10, f11, f12, f13, f14 = f1 in
let r0, r1, r2, r3, r4 = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) + (v f13 * pow78) * as_nat5 r +
(v f14 * pow104) * as_nat5 r
in
calc ( == ) {
(as_nat5 f1 * as_nat5 r) % prime;
( == ) { mul_felem5_lemma_1 f1 r }
(tmp + (v f12 * pow52) * as_nat5 r) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp ((v f12 * pow52) * as_nat5 r) prime }
(tmp + ((v f12 * pow52) * as_nat5 r) % prime) % prime;
( == ) { (FStar.Math.Lemmas.paren_mul_right (v f12) pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (pow52 * as_nat5 r) prime) }
(tmp + v f12 * (pow52 * as_nat5 r % prime) % prime) % prime;
( == ) { lemma_fmul5_pow52 r }
(tmp + v f12 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12)
(as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2))
prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp
(v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2))
prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime ==
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Star_Bang",
"Lib.IntTypes.u64",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_lemma_1",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mod_plus_distr_r",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"FStar.Math.Lemmas.paren_mul_right",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime)
val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime))
let lemma_fmul5_pow52 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow52 * as_nat5 r) % prime;
(==) { assert_norm (pow52 == pow26 * pow26) }
(pow26 * pow26 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
(==) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)
val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime))
let lemma_fmul5_pow78 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow78 * as_nat5 r) % prime;
(==) { assert_norm (pow78 == pow26 * pow52) }
(pow26 * pow52 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow52 * as_nat5 r) prime }
(pow26 * (pow52 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow52 r }
(pow26 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(pow26 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
(==) { lemma_fmul5_pow26 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) }
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime;
};
assert ((pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)
val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime))
let lemma_fmul5_pow104 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow104 * as_nat5 r) % prime;
(==) { assert_norm (pow104 == pow26 * pow78) }
(pow26 * pow78 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow78 * as_nat5 r) prime }
(pow26 * (pow78 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow78 r }
(pow26 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(pow26 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
(==) { lemma_fmul5_pow26 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) }
as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime;
};
assert ((pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime)
val mul_felem5_lemma_1:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_1 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp = v f10 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { }
(v f10 + v f11 * pow26 + v f12 * pow52 + v f13 * pow78 + v f14 * pow104) * as_nat5 r % prime;
(==) { lemma_mul5_distr_r (v f10) (v f11 * pow26) (v f12 * pow52) (v f13 * pow78) (v f14 * pow104) (as_nat5 r) }
(v f10 * as_nat5 r + v f11 * pow26 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * pow26 * as_nat5 r) prime }
(tmp + (v f11 * pow26 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f11) pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow26 * as_nat5 r) prime }
(tmp + v f11 * (pow26 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow26 r }
(tmp + v f11 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime)
val mul_felem5_lemma_2:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val mul_felem5_lemma_2:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_lemma_2 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f1:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 f1 (3, 3, 3, 3, 3)} ->
r:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 r (2, 2, 2, 2, 2)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = f1 in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in
let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in
Hacl.Spec.Poly1305.Field32xN.as_nat5 f1 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r %
Hacl.Spec.Poly1305.Vec.prime ==
(Lib.IntTypes.v f10 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r +
Lib.IntTypes.v f11 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r4 *! Lib.IntTypes.u64 5, r0, r1, r2, r3) +
Lib.IntTypes.v f12 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0,
r1,
r2) +
(Lib.IntTypes.v f13 * Hacl.Spec.Poly1305.Field32xN.pow78) *
Hacl.Spec.Poly1305.Field32xN.as_nat5 r +
(Lib.IntTypes.v f14 * Hacl.Spec.Poly1305.Field32xN.pow104) *
Hacl.Spec.Poly1305.Field32xN.as_nat5 r) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)
<:
Type0)) | {
"end_col": 117,
"end_line": 552,
"start_col": 29,
"start_line": 528
} |
FStar.Pervasives.Lemma | val mul_felem5_lemma_3:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * pow104 * as_nat5 r) % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let mul_felem5_lemma_3 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_2 f1 r }
(tmp + v f13 * pow78 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f13 * pow78 * as_nat5 r) prime }
(tmp + (v f13 * pow78 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f13) pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (pow78 * as_nat5 r) prime }
(tmp + v f13 * (pow78 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow78 r }
(tmp + v f13 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime) | val mul_felem5_lemma_3:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_3 f1 r = | false | null | true | let f10, f11, f12, f13, f14 = f1 in
let r0, r1, r2, r3, r4 = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
(v f14 * pow104) * as_nat5 r
in
calc ( == ) {
(as_nat5 f1 * as_nat5 r) % prime;
( == ) { mul_felem5_lemma_2 f1 r }
(tmp + (v f13 * pow78) * as_nat5 r) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp ((v f13 * pow78) * as_nat5 r) prime }
(tmp + ((v f13 * pow78) * as_nat5 r) % prime) % prime;
( == ) { (FStar.Math.Lemmas.paren_mul_right (v f13) pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (pow78 * as_nat5 r) prime) }
(tmp + v f13 * (pow78 * as_nat5 r % prime) % prime) % prime;
( == ) { lemma_fmul5_pow78 r }
(tmp + v f13 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13)
(as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1))
prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp
(v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1))
prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime ==
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Star_Bang",
"Lib.IntTypes.u64",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_lemma_2",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mod_plus_distr_r",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"FStar.Math.Lemmas.paren_mul_right",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime)
val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime))
let lemma_fmul5_pow52 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow52 * as_nat5 r) % prime;
(==) { assert_norm (pow52 == pow26 * pow26) }
(pow26 * pow26 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
(==) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)
val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime))
let lemma_fmul5_pow78 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow78 * as_nat5 r) % prime;
(==) { assert_norm (pow78 == pow26 * pow52) }
(pow26 * pow52 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow52 * as_nat5 r) prime }
(pow26 * (pow52 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow52 r }
(pow26 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(pow26 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
(==) { lemma_fmul5_pow26 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) }
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime;
};
assert ((pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)
val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime))
let lemma_fmul5_pow104 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow104 * as_nat5 r) % prime;
(==) { assert_norm (pow104 == pow26 * pow78) }
(pow26 * pow78 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow78 * as_nat5 r) prime }
(pow26 * (pow78 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow78 r }
(pow26 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(pow26 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
(==) { lemma_fmul5_pow26 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) }
as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime;
};
assert ((pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime)
val mul_felem5_lemma_1:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_1 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp = v f10 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { }
(v f10 + v f11 * pow26 + v f12 * pow52 + v f13 * pow78 + v f14 * pow104) * as_nat5 r % prime;
(==) { lemma_mul5_distr_r (v f10) (v f11 * pow26) (v f12 * pow52) (v f13 * pow78) (v f14 * pow104) (as_nat5 r) }
(v f10 * as_nat5 r + v f11 * pow26 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * pow26 * as_nat5 r) prime }
(tmp + (v f11 * pow26 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f11) pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow26 * as_nat5 r) prime }
(tmp + v f11 * (pow26 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow26 r }
(tmp + v f11 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime)
val mul_felem5_lemma_2:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_2 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_1 f1 r }
(tmp + v f12 * pow52 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * pow52 * as_nat5 r) prime }
(tmp + (v f12 * pow52 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f12) pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (pow52 * as_nat5 r) prime }
(tmp + v f12 * (pow52 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow52 r }
(tmp + v f12 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime)
val mul_felem5_lemma_3:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * pow104 * as_nat5 r) % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val mul_felem5_lemma_3:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * pow104 * as_nat5 r) % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_lemma_3 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f1:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 f1 (3, 3, 3, 3, 3)} ->
r:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 r (2, 2, 2, 2, 2)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = f1 in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in
let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in
Hacl.Spec.Poly1305.Field32xN.as_nat5 f1 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r %
Hacl.Spec.Poly1305.Vec.prime ==
(Lib.IntTypes.v f10 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r +
Lib.IntTypes.v f11 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r4 *! Lib.IntTypes.u64 5, r0, r1, r2, r3) +
Lib.IntTypes.v f12 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0,
r1,
r2) +
Lib.IntTypes.v f13 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r2 *! Lib.IntTypes.u64 5,
r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0,
r1) +
(Lib.IntTypes.v f14 * Hacl.Spec.Poly1305.Field32xN.pow104) *
Hacl.Spec.Poly1305.Field32xN.as_nat5 r) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)
<:
Type0)) | {
"end_col": 126,
"end_line": 592,
"start_col": 29,
"start_line": 568
} |
FStar.Pervasives.Lemma | val mul_felem5_lemma_1:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let mul_felem5_lemma_1 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp = v f10 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { }
(v f10 + v f11 * pow26 + v f12 * pow52 + v f13 * pow78 + v f14 * pow104) * as_nat5 r % prime;
(==) { lemma_mul5_distr_r (v f10) (v f11 * pow26) (v f12 * pow52) (v f13 * pow78) (v f14 * pow104) (as_nat5 r) }
(v f10 * as_nat5 r + v f11 * pow26 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * pow26 * as_nat5 r) prime }
(tmp + (v f11 * pow26 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f11) pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow26 * as_nat5 r) prime }
(tmp + v f11 * (pow26 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow26 r }
(tmp + v f11 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime) | val mul_felem5_lemma_1:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_1 f1 r = | false | null | true | let f10, f11, f12, f13, f14 = f1 in
let r0, r1, r2, r3, r4 = r in
let tmp =
v f10 * as_nat5 r + (v f12 * pow52) * as_nat5 r + (v f13 * pow78) * as_nat5 r +
(v f14 * pow104) * as_nat5 r
in
calc ( == ) {
(as_nat5 f1 * as_nat5 r) % prime;
( == ) { () }
(v f10 + v f11 * pow26 + v f12 * pow52 + v f13 * pow78 + v f14 * pow104) * as_nat5 r % prime;
( == ) { lemma_mul5_distr_r (v f10)
(v f11 * pow26)
(v f12 * pow52)
(v f13 * pow78)
(v f14 * pow104)
(as_nat5 r) }
(v f10 * as_nat5 r + (v f11 * pow26) * as_nat5 r + (v f12 * pow52) * as_nat5 r +
(v f13 * pow78) * as_nat5 r +
(v f14 * pow104) * as_nat5 r) %
prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp ((v f11 * pow26) * as_nat5 r) prime }
(tmp + ((v f11 * pow26) * as_nat5 r) % prime) % prime;
( == ) { (FStar.Math.Lemmas.paren_mul_right (v f11) pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow26 * as_nat5 r) prime) }
(tmp + v f11 * (pow26 * as_nat5 r % prime) % prime) % prime;
( == ) { lemma_fmul5_pow26 r }
(tmp + v f11 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11)
(as_nat5 (r4 *! u64 5, r0, r1, r2, r3))
prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp
(v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3))
prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime ==
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Star_Bang",
"Lib.IntTypes.u64",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_mul5_distr_r",
"FStar.Math.Lemmas.lemma_mod_plus_distr_r",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"FStar.Math.Lemmas.paren_mul_right",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow26"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime)
val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime))
let lemma_fmul5_pow52 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow52 * as_nat5 r) % prime;
(==) { assert_norm (pow52 == pow26 * pow26) }
(pow26 * pow26 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
(==) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)
val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime))
let lemma_fmul5_pow78 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow78 * as_nat5 r) % prime;
(==) { assert_norm (pow78 == pow26 * pow52) }
(pow26 * pow52 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow52 * as_nat5 r) prime }
(pow26 * (pow52 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow52 r }
(pow26 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(pow26 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
(==) { lemma_fmul5_pow26 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) }
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime;
};
assert ((pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)
val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime))
let lemma_fmul5_pow104 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow104 * as_nat5 r) % prime;
(==) { assert_norm (pow104 == pow26 * pow78) }
(pow26 * pow78 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow78 * as_nat5 r) prime }
(pow26 * (pow78 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow78 r }
(pow26 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(pow26 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
(==) { lemma_fmul5_pow26 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) }
as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime;
};
assert ((pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime)
val mul_felem5_lemma_1:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val mul_felem5_lemma_1:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_lemma_1 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f1:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 f1 (3, 3, 3, 3, 3)} ->
r:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 r (2, 2, 2, 2, 2)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = f1 in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in
let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in
Hacl.Spec.Poly1305.Field32xN.as_nat5 f1 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r %
Hacl.Spec.Poly1305.Vec.prime ==
(Lib.IntTypes.v f10 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r +
Lib.IntTypes.v f11 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r4 *! Lib.IntTypes.u64 5, r0, r1, r2, r3) +
(Lib.IntTypes.v f12 * Hacl.Spec.Poly1305.Field32xN.pow52) *
Hacl.Spec.Poly1305.Field32xN.as_nat5 r +
(Lib.IntTypes.v f13 * Hacl.Spec.Poly1305.Field32xN.pow78) *
Hacl.Spec.Poly1305.Field32xN.as_nat5 r +
(Lib.IntTypes.v f14 * Hacl.Spec.Poly1305.Field32xN.pow104) *
Hacl.Spec.Poly1305.Field32xN.as_nat5 r) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)
<:
Type0)) | {
"end_col": 108,
"end_line": 513,
"start_col": 29,
"start_line": 488
} |
FStar.Pervasives.Lemma | val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime) | val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r = | false | null | true | let r0, r1, r2, r3, r4 = r in
calc ( == ) {
(pow26 * as_nat5 r) % prime;
( == ) { () }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
( == ) { lemma_mul5_distr_l pow26
(v r0)
(v r1 * pow26)
(v r2 * pow52)
(v r3 * pow78)
(v r4 * pow104) }
(v r0 * pow26 + (pow26 * v r1) * pow26 + (pow26 * v r2) * pow52 + (pow26 * v r3) * pow78 +
(pow26 * v r4) * pow104) %
prime;
( == ) { () }
(v r0 * pow26 + (v r1 * pow26) * pow26 + (v r2 * pow26) * pow52 + (v r3 * pow26) * pow78 +
(v r4 * pow26) * pow104) %
prime;
( == ) { (assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130)) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r (v r0 * pow26 + v r1 * pow52 + v r2 * pow78 +
v r3 * pow104)
(v r4 * pow2 130)
prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) %
prime;
( == ) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r (v r0 * pow26 + v r1 * pow52 + v r2 * pow78 +
v r3 * pow104)
(v r4 * 5)
prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.pow26",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Hacl.Spec.Poly1305.Field32xN.pow52",
"Hacl.Spec.Poly1305.Field32xN.pow78",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Prims.pow2",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Prims.squash",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_mul5_distr_l",
"FStar.Pervasives.assert_norm",
"Prims.b2t",
"Prims.op_Equality",
"FStar.Math.Lemmas.lemma_mod_plus_distr_r",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_prime"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) | [] | Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow26 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} | r: Hacl.Spec.Poly1305.Field32xN.tup64_5
-> FStar.Pervasives.Lemma
(requires
(let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ _ _ _ _ r4 = _ in
Lib.IntTypes.v r4 * 5 <= 10 * Hacl.Spec.Poly1305.Field32xN.pow26)
<:
Type0))
(ensures
(let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in
Hacl.Spec.Poly1305.Field32xN.pow26 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r %
Hacl.Spec.Poly1305.Vec.prime ==
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r4 *! Lib.IntTypes.u64 5, r0, r1, r2, r3) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)) | {
"end_col": 84,
"end_line": 395,
"start_col": 25,
"start_line": 367
} |
FStar.Pervasives.Lemma | val mul_felem5_lemma_4:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime) | [
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Spec.Poly1305.Vec",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Calc",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.Sequence",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntVector",
"short_module": null
},
{
"abbrev": false,
"full_module": "Lib.IntTypes",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "Hacl.Poly1305.Field32xN",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let mul_felem5_lemma_4 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_3 f1 r }
(tmp + v f14 * pow104 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f14 * pow104 * as_nat5 r) prime }
(tmp + (v f14 * pow104 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f14) pow104 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (pow104 * as_nat5 r) prime }
(tmp + v f14 * (pow104 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow104 r }
(tmp + v f14 * (as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) prime }
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) prime }
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime) | val mul_felem5_lemma_4:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime)
let mul_felem5_lemma_4 f1 r = | false | null | true | let f10, f11, f12, f13, f14 = f1 in
let r0, r1, r2, r3, r4 = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)
in
calc ( == ) {
(as_nat5 f1 * as_nat5 r) % prime;
( == ) { mul_felem5_lemma_3 f1 r }
(tmp + (v f14 * pow104) * as_nat5 r) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp ((v f14 * pow104) * as_nat5 r) prime }
(tmp + ((v f14 * pow104) * as_nat5 r) % prime) % prime;
( == ) { (FStar.Math.Lemmas.paren_mul_right (v f14) pow104 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14) (pow104 * as_nat5 r) prime) }
(tmp + v f14 * (pow104 * as_nat5 r % prime) % prime) % prime;
( == ) { lemma_fmul5_pow104 r }
(tmp + v f14 * (as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) % prime) %
prime;
( == ) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f14)
(as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0))
prime }
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime) % prime;
( == ) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp
(v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0))
prime }
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime ==
(tmp + v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime) | {
"checked_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst.checked",
"dependencies": [
"prims.fst.checked",
"Lib.Sequence.fsti.checked",
"Lib.IntVector.fsti.checked",
"Lib.IntTypes.fsti.checked",
"Hacl.Spec.Poly1305.Vec.fst.checked",
"Hacl.Spec.Poly1305.Field32xN.fst.checked",
"FStar.Pervasives.Native.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked",
"FStar.Classical.fsti.checked",
"FStar.Calc.fsti.checked"
],
"interface_file": false,
"source_file": "Hacl.Poly1305.Field32xN.Lemmas0.fst"
} | [
"lemma"
] | [
"Hacl.Spec.Poly1305.Field32xN.tup64_5",
"Hacl.Spec.Poly1305.Field32xN.tup64_fits5",
"FStar.Pervasives.Native.Mktuple5",
"Prims.nat",
"Lib.IntTypes.uint64",
"Prims._assert",
"Prims.eq2",
"Prims.int",
"Prims.op_Modulus",
"FStar.Mul.op_Star",
"Hacl.Spec.Poly1305.Field32xN.as_nat5",
"Hacl.Spec.Poly1305.Vec.prime",
"Prims.op_Addition",
"Lib.IntTypes.v",
"Lib.IntTypes.U64",
"Lib.IntTypes.SEC",
"Lib.IntTypes.op_Star_Bang",
"Lib.IntTypes.u64",
"Prims.unit",
"FStar.Calc.calc_finish",
"Prims.Cons",
"FStar.Preorder.relation",
"Prims.Nil",
"FStar.Calc.calc_step",
"Hacl.Spec.Poly1305.Field32xN.pow104",
"FStar.Calc.calc_init",
"FStar.Calc.calc_pack",
"Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_lemma_3",
"Prims.squash",
"FStar.Math.Lemmas.lemma_mod_plus_distr_r",
"FStar.Math.Lemmas.lemma_mod_mul_distr_r",
"FStar.Math.Lemmas.paren_mul_right",
"Hacl.Poly1305.Field32xN.Lemmas0.lemma_fmul5_pow104"
] | [] | module Hacl.Poly1305.Field32xN.Lemmas0
open Lib.IntTypes
open Lib.IntVector
open Lib.Sequence
open FStar.Mul
open FStar.Calc
open Hacl.Spec.Poly1305.Vec
include Hacl.Spec.Poly1305.Field32xN
#reset-options "--z3rlimit 50 --using_facts_from '* -FStar.Seq' --max_fuel 0 --max_ifuel 0"
val lemma_prime: unit -> Lemma (pow2 130 % prime = 5)
let lemma_prime () =
assert_norm (pow2 130 % prime = 5 % prime);
assert_norm (5 < prime);
FStar.Math.Lemmas.modulo_lemma 5 prime
val lemma_mult_le: a:nat -> b:nat -> c:nat -> d:nat -> Lemma
(requires a <= b /\ c <= d)
(ensures a * c <= b * d)
let lemma_mult_le a b c d = ()
val lemma_mul5_distr_l: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
(a * (b + c + d + e + f) == a * b + a * c + a * d + a * e + a * f)
let lemma_mul5_distr_l a b c d e f = ()
val lemma_mul5_distr_r: a:nat -> b:nat -> c:nat -> d:nat -> e:nat -> f:nat -> Lemma
((a + b + c + d + e) * f == a * f + b * f + c * f + d * f + e * f)
let lemma_mul5_distr_r a b c d e f = ()
val smul_mod_lemma:
#m1:scale32
-> #m2:scale32
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26} ->
Lemma (a * b % pow2 64 == a * b)
let smul_mod_lemma #m1 #m2 a b =
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (a * b <= m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (a * b) (pow2 64)
val smul_add_mod_lemma:
#m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> a:nat{a <= m1 * max26}
-> b:nat{b <= m2 * max26}
-> c:nat{c <= m3 * max26 * max26} ->
Lemma ((c + a * b % pow2 64) % pow2 64 == c + a * b)
let smul_add_mod_lemma #m1 #m2 #m3 a b c =
assert_norm ((m3 + m1 * m2) * max26 * max26 < pow2 64);
lemma_mult_le a (m1 * max26) b (m2 * max26);
assert (c + a * b <= m3 * max26 * max26 + m1 * m2 * max26 * max26);
FStar.Math.Lemmas.modulo_lemma (c + a * b) (pow2 64)
val add5_lemma1: ma:scale64 -> mb:scale64 -> a:uint64 -> b:uint64 -> Lemma
(requires v a <= ma * max26 /\ v b <= mb * max26 /\ ma + mb <= 64)
(ensures v (a +. b) == v a + v b /\ v (a +. b) <= (ma + mb) * max26)
let add5_lemma1 ma mb a b =
assert (v a + v b <= (ma + mb) * max26);
Math.Lemmas.lemma_mult_le_right max26 (ma + mb) 64;
assert (v a + v b <= 64 * max26);
assert_norm (64 * max26 < pow2 32);
Math.Lemmas.small_mod (v a + v b) (pow2 32)
#set-options "--ifuel 1"
val fadd5_eval_lemma_i:
#w:lanes
-> f1:felem5 w{felem_fits5 f1 (2,2,2,2,2)}
-> f2:felem5 w{felem_fits5 f2 (1,1,1,1,1)}
-> i:nat{i < w} ->
Lemma ((feval5 (fadd5 f1 f2)).[i] == pfadd (feval5 f1).[i] (feval5 f2).[i])
let fadd5_eval_lemma_i #w f1 f2 i =
let o = fadd5 f1 f2 in
let (f10, f11, f12, f13, f14) = as_tup64_i f1 i in
let (f20, f21, f22, f23, f24) = as_tup64_i f2 i in
let (o0, o1, o2, o3, o4) = as_tup64_i o i in
add5_lemma1 2 1 f10 f20;
add5_lemma1 2 1 f11 f21;
add5_lemma1 2 1 f12 f22;
add5_lemma1 2 1 f13 f23;
add5_lemma1 2 1 f14 f24;
assert (as_nat5 (o0, o1, o2, o3, o4) ==
as_nat5 (f10, f11, f12, f13, f14) + as_nat5 (f20, f21, f22, f23, f24));
FStar.Math.Lemmas.lemma_mod_plus_distr_l
(as_nat5 (f10, f11, f12, f13, f14)) (as_nat5 (f20, f21, f22, f23, f24)) prime;
FStar.Math.Lemmas.lemma_mod_plus_distr_r
(as_nat5 (f10, f11, f12, f13, f14) % prime) (as_nat5 (f20, f21, f22, f23, f24)) prime
val smul_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_mul_mod f2 u1)).[i] <= m1 * m2 * max26 * max26)
let smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 i =
let o = vec_mul_mod f2 u1 in
smul_mod_lemma #m1 #m2 (uint64xN_v u1).[i] (uint64xN_v f2).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26)
val smul_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_felem5 #w u1 f2)).[i] == (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2 i =
let o = smul_felem5 #w u1 f2 in
let (m20, m21, m22, m23, m24) = m2 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_mod_lemma #m1 #m20 vu1 (v tf20);
smul_mod_lemma #m1 #m21 vu1 (v tf21);
smul_mod_lemma #m1 #m22 vu1 (v tf22);
smul_mod_lemma #m1 #m23 vu1 (v tf23);
smul_mod_lemma #m1 #m24 vu1 (v tf24);
assert ((fas_nat5 o).[i] == vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 +
vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert (vu1 * (fas_nat5 f2).[i] == (fas_nat5 o).[i])
val smul_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2} ->
Lemma (felem_wide_fits1 (vec_mul_mod f2 u1) (m1 * m2))
let smul_felem5_fits_lemma1 #w #m1 #m2 u1 f2 =
match w with
| 1 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0
| 2 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1
| 4 ->
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 0;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 1;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 2;
smul_felem5_fits_lemma_i #w #m1 #m2 u1 f2 3
val smul_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (felem_wide_fits5 (smul_felem5 #w u1 f2) (m1 *^ m2))
let smul_felem5_fits_lemma #w #m1 #m2 u1 f2 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
smul_felem5_fits_lemma1 #w #m1 #m20 u1 f20;
smul_felem5_fits_lemma1 #w #m1 #m21 u1 f21;
smul_felem5_fits_lemma1 #w #m1 #m22 u1 f22;
smul_felem5_fits_lemma1 #w #m1 #m23 u1 f23;
smul_felem5_fits_lemma1 #w #m1 #m24 u1 f24
val smul_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2} ->
Lemma (fas_nat5 (smul_felem5 #w u1 f2) ==
map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
let smul_felem5_eval_lemma #w #m1 #m2 u1 f2 =
FStar.Classical.forall_intro (smul_felem5_eval_lemma_i #w #m1 #m2 u1 f2);
eq_intro (fas_nat5 (smul_felem5 #w u1 f2))
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2))
val smul_add_felem5_fits_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3}
-> i:nat{i < w} ->
Lemma ((uint64xN_v (vec_add_mod acc1 (vec_mul_mod f2 u1))).[i] <= (m3 + m1 * m2) * max26 * max26)
#push-options "--z3rlimit 200"
let smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = vec_add_mod acc1 (vec_mul_mod f2 u1) in
smul_add_mod_lemma #m1 #m2 #m3 (uint64xN_v u1).[i] (uint64xN_v f2).[i] (uint64xN_v acc1).[i];
assert ((uint64xN_v o).[i] == (uint64xN_v acc1).[i] + (uint64xN_v u1).[i] * (uint64xN_v f2).[i]);
lemma_mult_le (uint64xN_v u1).[i] (m1 * max26) (uint64xN_v f2).[i] (m2 * max26);
assert ((uint64xN_v o).[i] <= m3 * max26 * max26 + m1 * m2 * max26 * max26)
#pop-options
val smul_add_felem5_eval_lemma_i:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3}
-> i:nat{i < w} ->
Lemma ((fas_nat5 (smul_add_felem5 #w u1 f2 acc1)).[i] ==
(fas_nat5 acc1).[i] + (uint64xN_v u1).[i] * (fas_nat5 f2).[i])
let smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 i =
let o = smul_add_felem5 #w u1 f2 acc1 in
let (m20, m21, m22, m23, m24) = m2 in
let (m30, m31, m32, m33, m34) = m3 in
let vu1 = (uint64xN_v u1).[i] in
let (tf20, tf21, tf22, tf23, tf24) = as_tup64_i f2 i in
let (ta0, ta1, ta2, ta3, ta4) = as_tup64_i acc1 i in
let (to0, to1, to2, to3, to4) = as_tup64_i o i in
smul_add_mod_lemma #m1 #m20 #m30 vu1 (v tf20) (v ta0);
smul_add_mod_lemma #m1 #m21 #m31 vu1 (v tf21) (v ta1);
smul_add_mod_lemma #m1 #m22 #m32 vu1 (v tf22) (v ta2);
smul_add_mod_lemma #m1 #m23 #m33 vu1 (v tf23) (v ta3);
smul_add_mod_lemma #m1 #m24 #m34 vu1 (v tf24) (v ta4);
calc (==) {
(fas_nat5 o).[i];
(==) { }
v ta0 + vu1 * v tf20 + (v ta1 + vu1 * v tf21) * pow26 + (v ta2 + vu1 * v tf22) * pow52 +
(v ta3 + vu1 * v tf23) * pow78 + (v ta4 + vu1 * v tf24) * pow104;
(==) {
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf21) pow26;
FStar.Math.Lemmas.distributivity_add_left (v ta2) (vu1 * v tf22) pow52;
FStar.Math.Lemmas.distributivity_add_left (v ta3) (vu1 * v tf23) pow78;
FStar.Math.Lemmas.distributivity_add_left (v ta1) (vu1 * v tf24) pow104 }
v ta0 + v ta1 * pow26 + v ta2 * pow52 + v ta3 * pow78 + v ta4 * pow104 +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
(==) { }
(fas_nat5 acc1).[i] + vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] +
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104);
calc (==) {
vu1 * (fas_nat5 f2).[i];
(==) { }
vu1 * (v tf20 + v tf21 * pow26 + v tf22 * pow52 + v tf23 * pow78 + v tf24 * pow104);
(==) { lemma_mul5_distr_l vu1 (v tf20) (v tf21 * pow26) (v tf22 * pow52) (v tf23 * pow78) (v tf24 * pow104)}
vu1 * v tf20 + vu1 * (v tf21 * pow26) + vu1 * (v tf22 * pow52) + vu1 * (v tf23 * pow78) + vu1 * (v tf24 * pow104);
(==) {
FStar.Math.Lemmas.paren_mul_right vu1 (v tf21) pow26;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf22) pow52;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf23) pow78;
FStar.Math.Lemmas.paren_mul_right vu1 (v tf24) pow104}
vu1 * v tf20 + vu1 * v tf21 * pow26 + vu1 * v tf22 * pow52 + vu1 * v tf23 * pow78 + vu1 * v tf24 * pow104;
};
assert ((fas_nat5 o).[i] == (fas_nat5 acc1).[i] + vu1 * (fas_nat5 f2).[i])
val smul_add_felem5_fits_lemma1:
#w:lanes
-> #m1:scale32
-> #m2:scale32
-> #m3:scale64{m3 + m1 * m2 <= 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:uint64xN w{felem_fits1 f2 m2}
-> acc1:uint64xN w{felem_wide_fits1 acc1 m3} ->
Lemma (felem_wide_fits1 (vec_add_mod acc1 (vec_mul_mod f2 u1)) (m3 + m1 * m2))
let smul_add_felem5_fits_lemma1 #w #m1 #m2 #m3 u1 f2 acc1 =
match w with
| 1 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0
| 2 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1
| 4 ->
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 0;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 1;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 2;
smul_add_felem5_fits_lemma_i #w #m1 #m2 #m3 u1 f2 acc1 3
val smul_add_felem5_fits_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (felem_wide_fits5 (smul_add_felem5 #w u1 f2 acc1) (m3 +* m1 *^ m2))
let smul_add_felem5_fits_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let (f20, f21, f22, f23, f24) = f2 in
let (m20, m21, m22, m23, m24) = m2 in
let (a0, a1, a2, a3, a4) = acc1 in
let (m30, m31, m32, m33, m34) = m3 in
smul_add_felem5_fits_lemma1 #w #m1 #m20 #m30 u1 f20 a0;
smul_add_felem5_fits_lemma1 #w #m1 #m21 #m31 u1 f21 a1;
smul_add_felem5_fits_lemma1 #w #m1 #m22 #m32 u1 f22 a2;
smul_add_felem5_fits_lemma1 #w #m1 #m23 #m33 u1 f23 a3;
smul_add_felem5_fits_lemma1 #w #m1 #m24 #m34 u1 f24 a4
val smul_add_felem5_eval_lemma:
#w:lanes
-> #m1:scale32
-> #m2:scale32_5
-> #m3:scale64_5{m3 +* m1 *^ m2 <=* s64x5 4096}
-> u1:uint64xN w{felem_fits1 u1 m1}
-> f2:felem5 w{felem_fits5 f2 m2}
-> acc1:felem_wide5 w{felem_wide_fits5 acc1 m3} ->
Lemma (fas_nat5 (smul_add_felem5 #w u1 f2 acc1) ==
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)))
let smul_add_felem5_eval_lemma #w #m1 #m2 #m3 u1 f2 acc1 =
let tmp =
map2 #nat #nat #nat (fun a b -> a + b) (fas_nat5 acc1)
(map2 #nat #nat #nat (fun a b -> a * b) (uint64xN_v u1) (fas_nat5 f2)) in
FStar.Classical.forall_intro (smul_add_felem5_eval_lemma_i #w #m1 #m2 #m3 u1 f2 acc1);
eq_intro (fas_nat5 (smul_add_felem5 #w u1 f2 acc1)) tmp
val lemma_fmul5_pow26: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in v r4 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow26 * as_nat5 r) % prime == as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime))
let lemma_fmul5_pow26 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow26 * as_nat5 r) % prime;
(==) { }
(pow26 * (v r0 + v r1 * pow26 + v r2 * pow52 + v r3 * pow78 + v r4 * pow104)) % prime;
(==) { lemma_mul5_distr_l pow26 (v r0) (v r1 * pow26) (v r2 * pow52) (v r3 * pow78) (v r4 * pow104) }
(v r0 * pow26 + pow26 * v r1 * pow26 + pow26 * v r2 * pow52 + pow26 * v r3 * pow78 + pow26 * v r4 * pow104) % prime;
(==) { }
(v r0 * pow26 + v r1 * pow26 * pow26 + v r2 * pow26 * pow52 + v r3 * pow26 * pow78 + v r4 * pow26 * pow104) % prime;
(==) {
assert_norm (pow26 * pow26 = pow52);
assert_norm (pow26 * pow52 = pow78);
assert_norm (pow26 * pow78 = pow104);
assert_norm (pow26 * pow104 = pow2 130) }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * pow2 130) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * pow2 130) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v r4) (pow2 130) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * (pow2 130 % prime)) % prime) % prime;
(==) { lemma_prime () }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + (v r4 * 5) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104) (v r4 * 5) prime }
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime;
};
assert ((pow26 * as_nat5 r) % prime ==
(v r0 * pow26 + v r1 * pow52 + v r2 * pow78 + v r3 * pow104 + v r4 * 5) % prime)
val lemma_fmul5_pow52: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime))
let lemma_fmul5_pow52 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow52 * as_nat5 r) % prime;
(==) { assert_norm (pow52 == pow26 * pow26) }
(pow26 * pow26 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow26 * as_nat5 r) prime }
(pow26 * (pow26 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow26 r }
(pow26 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(pow26 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
(==) { lemma_fmul5_pow26 (r4 *! u64 5, r0, r1, r2, r3) }
as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime;
};
assert ((pow52 * as_nat5 r) % prime == as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)
val lemma_fmul5_pow78: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\ v r2 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime))
let lemma_fmul5_pow78 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow78 * as_nat5 r) % prime;
(==) { assert_norm (pow78 == pow26 * pow52) }
(pow26 * pow52 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow52 * as_nat5 r) prime }
(pow26 * (pow52 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow52 r }
(pow26 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(pow26 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
(==) { lemma_fmul5_pow26 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) }
as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime;
};
assert ((pow78 * as_nat5 r) % prime == as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)
val lemma_fmul5_pow104: r:tup64_5 -> Lemma
(requires (let (r0, r1, r2, r3, r4) = r in
v r4 * 5 <= 10 * pow26 /\ v r3 * 5 <= 10 * pow26 /\
v r2 * 5 <= 10 * pow26 /\ v r1 * 5 <= 10 * pow26))
(ensures (let (r0, r1, r2, r3, r4) = r in
(pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime))
let lemma_fmul5_pow104 r =
let (r0, r1, r2, r3, r4) = r in
calc (==) {
(pow104 * as_nat5 r) % prime;
(==) { assert_norm (pow104 == pow26 * pow78) }
(pow26 * pow78 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right pow26 pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (pow78 * as_nat5 r) prime }
(pow26 * (pow78 * as_nat5 r % prime)) % prime;
(==) { lemma_fmul5_pow78 r }
(pow26 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime)) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r pow26 (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(pow26 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
(==) { lemma_fmul5_pow26 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) }
as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime;
};
assert ((pow104 * as_nat5 r) % prime == as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0) % prime)
val mul_felem5_lemma_1:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_1 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp = v f10 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { }
(v f10 + v f11 * pow26 + v f12 * pow52 + v f13 * pow78 + v f14 * pow104) * as_nat5 r % prime;
(==) { lemma_mul5_distr_r (v f10) (v f11 * pow26) (v f12 * pow52) (v f13 * pow78) (v f14 * pow104) (as_nat5 r) }
(v f10 * as_nat5 r + v f11 * pow26 * as_nat5 r + v f12 * pow52 * as_nat5 r + v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime;
(==) {
FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * pow26 * as_nat5 r) prime }
(tmp + (v f11 * pow26 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f11) pow26 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (pow26 * as_nat5 r) prime }
(tmp + v f11 * (pow26 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow26 r }
(tmp + v f11 * (as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f11) (as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) prime }
(tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3)) % prime)
val mul_felem5_lemma_2:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_2 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f13 * pow78 * as_nat5 r + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_1 f1 r }
(tmp + v f12 * pow52 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * pow52 * as_nat5 r) prime }
(tmp + (v f12 * pow52 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f12) pow52 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (pow52 * as_nat5 r) prime }
(tmp + v f12 * (pow52 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow52 r }
(tmp + v f12 * (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f12) (as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) prime }
(tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2)) % prime)
val mul_felem5_lemma_3:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * pow104 * as_nat5 r) % prime)
let mul_felem5_lemma_3 f1 r =
let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
let tmp =
v f10 * as_nat5 r + v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) + v f14 * pow104 * as_nat5 r in
calc (==) {
(as_nat5 f1 * as_nat5 r) % prime;
(==) { mul_felem5_lemma_2 f1 r }
(tmp + v f13 * pow78 * as_nat5 r) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f13 * pow78 * as_nat5 r) prime }
(tmp + (v f13 * pow78 * as_nat5 r) % prime) % prime;
(==) {
FStar.Math.Lemmas.paren_mul_right (v f13) pow78 (as_nat5 r);
FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (pow78 * as_nat5 r) prime }
(tmp + v f13 * (pow78 * as_nat5 r % prime) % prime) % prime;
(==) { lemma_fmul5_pow78 r }
(tmp + v f13 * (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_mul_distr_r (v f13) (as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) % prime) % prime;
(==) { FStar.Math.Lemmas.lemma_mod_plus_distr_r tmp (v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) prime }
(tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime;
};
assert ((as_nat5 f1 * as_nat5 r) % prime == (tmp + v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1)) % prime)
val mul_felem5_lemma_4:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime) | false | false | Hacl.Poly1305.Field32xN.Lemmas0.fst | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 0,
"max_ifuel": 1,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": false,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 50,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val mul_felem5_lemma_4:
f1:tup64_5{tup64_fits5 f1 (3, 3, 3, 3, 3)}
-> r:tup64_5{tup64_fits5 r (2, 2, 2, 2, 2)} ->
Lemma
(let (f10, f11, f12, f13, f14) = f1 in
let (r0, r1, r2, r3, r4) = r in
(as_nat5 f1 * as_nat5 r) % prime ==
(v f10 * as_nat5 r +
v f11 * as_nat5 (r4 *! u64 5, r0, r1, r2, r3) +
v f12 * as_nat5 (r3 *! u64 5, r4 *! u64 5, r0, r1, r2) +
v f13 * as_nat5 (r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0, r1) +
v f14 * as_nat5 (r1 *! u64 5, r2 *! u64 5, r3 *! u64 5, r4 *! u64 5, r0)) % prime) | [] | Hacl.Poly1305.Field32xN.Lemmas0.mul_felem5_lemma_4 | {
"file_name": "code/poly1305/Hacl.Poly1305.Field32xN.Lemmas0.fst",
"git_rev": "12c5e9539c7e3c366c26409d3b86493548c4483e",
"git_url": "https://github.com/hacl-star/hacl-star.git",
"project_name": "hacl-star"
} |
f1:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 f1 (3, 3, 3, 3, 3)} ->
r:
Hacl.Spec.Poly1305.Field32xN.tup64_5
{Hacl.Spec.Poly1305.Field32xN.tup64_fits5 r (2, 2, 2, 2, 2)}
-> FStar.Pervasives.Lemma
(ensures
(let _ = f1 in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ f10 f11 f12 f13 f14 = _ in
let _ = r in
(let FStar.Pervasives.Native.Mktuple5 #_ #_ #_ #_ #_ r0 r1 r2 r3 r4 = _ in
Hacl.Spec.Poly1305.Field32xN.as_nat5 f1 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r %
Hacl.Spec.Poly1305.Vec.prime ==
(Lib.IntTypes.v f10 * Hacl.Spec.Poly1305.Field32xN.as_nat5 r +
Lib.IntTypes.v f11 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r4 *! Lib.IntTypes.u64 5, r0, r1, r2, r3) +
Lib.IntTypes.v f12 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0,
r1,
r2) +
Lib.IntTypes.v f13 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r2 *! Lib.IntTypes.u64 5,
r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0,
r1) +
Lib.IntTypes.v f14 *
Hacl.Spec.Poly1305.Field32xN.as_nat5 (r1 *! Lib.IntTypes.u64 5,
r2 *! Lib.IntTypes.u64 5,
r3 *! Lib.IntTypes.u64 5,
r4 *! Lib.IntTypes.u64 5,
r0)) %
Hacl.Spec.Poly1305.Vec.prime)
<:
Type0)
<:
Type0)) | {
"end_col": 135,
"end_line": 632,
"start_col": 29,
"start_line": 608
} |
Prims.Tot | val le_of_uint32 (x: UInt32.t) : b: bytes{S.length b = 4} | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let le_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_le 4 (UInt32.v x) | val le_of_uint32 (x: UInt32.t) : b: bytes{S.length b = 4}
let le_of_uint32 (x: UInt32.t) : b: bytes{S.length b = 4} = | false | null | false | n_to_le 4 (UInt32.v x) | {
"checked_file": "FStar.Endianness.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked"
],
"interface_file": false,
"source_file": "FStar.Endianness.fsti"
} | [
"total"
] | [
"FStar.UInt32.t",
"FStar.Endianness.n_to_le",
"FStar.UInt32.v",
"FStar.Endianness.bytes",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.UInt8.t"
] | [] | module FStar.Endianness
/// A library of lemmas for reasoning about sequences of machine integers and
/// their (little|big)-endian representation as a sequence of bytes.
///
/// The functions in this module aim to be as generic as possible, in order to
/// facilitate compatibility with:
/// - Vale's model of machine integers (nat64 et al.), which does not rely on
/// FStar's machine integers
/// - HACL*'s Lib.IntTypes module, which exposes a universal indexed integer
/// type but uses F* machine integers under the hood.
///
/// To achieve maximum compatibility, we try to state most lemmas using nat
/// rather than UIntX.
///
/// To limit context pollution, the definitions of the recursive functions are
/// abstract; please add lemmas as you see fit. In extreme cases, ``friend``'ing
/// might be de rigueur.
///
/// .. note::
///
/// This module supersedes the poorly-named ``FStar.Krml.Endianness``.
module U8 = FStar.UInt8
module U32 = FStar.UInt32
module U64 = FStar.UInt64
module Math = FStar.Math.Lemmas
module S = FStar.Seq
[@@ noextract_to "krml"]
type bytes = S.seq U8.t
open FStar.Mul
/// Definition of little and big-endianness
/// ---------------------------------------
///
/// This is our spec, to be audited. From bytes to nat.
/// lt_to_n interprets a byte sequence as a little-endian natural number
val le_to_n : b:bytes -> Tot nat
/// be_to_n interprets a byte sequence as a big-endian natural number
val be_to_n : b:bytes -> Tot nat
/// Induction for le_to_n and be_to_n
val reveal_le_to_n (b:bytes)
: Lemma
(le_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.head b) + pow2 8 * le_to_n (S.tail b)))
val reveal_be_to_n (b:bytes)
: Lemma
(be_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))))
val lemma_le_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (le_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
val lemma_be_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (be_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
/// Inverse operations
/// ------------------
///
/// From nat to bytes, and their functional correctness.
/// n_to_le encodes a number as a little-endian byte sequence of a fixed,
/// sufficiently large length.
val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == le_to_n b})
(decreases len)
/// n_to_be encodes a numbers as a big-endian byte sequence of a fixed,
/// sufficiently large length
val n_to_be:
len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == be_to_n b})
(decreases len)
/// Injectivity
/// -----------
val n_to_le_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})):
Lemma (requires (n_to_le len n1 == n_to_le len n2))
(ensures (n1 == n2))
val n_to_be_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})) :
Lemma (requires (n_to_be len n1 == n_to_be len n2))
(ensures (n1 == n2))
val be_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ be_to_n b1 == be_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
val le_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ le_to_n b1 == le_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
/// Roundtripping
/// -------------
val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
be_to_n s < pow2 (8 * len) /\
n_to_be len (be_to_n s) == s
))
[SMTPat (n_to_be len (be_to_n s))]
val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
le_to_n s < pow2 (8 * len) /\
n_to_le len (le_to_n s) == s
))
[SMTPat (n_to_le len (le_to_n s))]
/// Specializations for F* machine integers
/// ---------------------------------------
///
/// These are useful because they take care of calling the right ``*_is_bounded`` lemmas.
let uint32_of_le (b: bytes { S.length b = 4 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n | false | false | FStar.Endianness.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val le_of_uint32 (x: UInt32.t) : b: bytes{S.length b = 4} | [] | FStar.Endianness.le_of_uint32 | {
"file_name": "ulib/FStar.Endianness.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | x: FStar.UInt32.t -> b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 4} | {
"end_col": 24,
"end_line": 148,
"start_col": 2,
"start_line": 148
} |
Prims.Tot | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let uint64_of_be (b: bytes { S.length b = 8 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt64.uint_to_t n | let uint64_of_be (b: bytes{S.length b = 8}) = | false | null | false | let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt64.uint_to_t n | {
"checked_file": "FStar.Endianness.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked"
],
"interface_file": false,
"source_file": "FStar.Endianness.fsti"
} | [
"total"
] | [
"FStar.Endianness.bytes",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.UInt8.t",
"FStar.UInt64.uint_to_t",
"Prims.unit",
"FStar.Endianness.lemma_be_to_n_is_bounded",
"Prims.nat",
"FStar.Endianness.be_to_n",
"FStar.UInt64.t"
] | [] | module FStar.Endianness
/// A library of lemmas for reasoning about sequences of machine integers and
/// their (little|big)-endian representation as a sequence of bytes.
///
/// The functions in this module aim to be as generic as possible, in order to
/// facilitate compatibility with:
/// - Vale's model of machine integers (nat64 et al.), which does not rely on
/// FStar's machine integers
/// - HACL*'s Lib.IntTypes module, which exposes a universal indexed integer
/// type but uses F* machine integers under the hood.
///
/// To achieve maximum compatibility, we try to state most lemmas using nat
/// rather than UIntX.
///
/// To limit context pollution, the definitions of the recursive functions are
/// abstract; please add lemmas as you see fit. In extreme cases, ``friend``'ing
/// might be de rigueur.
///
/// .. note::
///
/// This module supersedes the poorly-named ``FStar.Krml.Endianness``.
module U8 = FStar.UInt8
module U32 = FStar.UInt32
module U64 = FStar.UInt64
module Math = FStar.Math.Lemmas
module S = FStar.Seq
[@@ noextract_to "krml"]
type bytes = S.seq U8.t
open FStar.Mul
/// Definition of little and big-endianness
/// ---------------------------------------
///
/// This is our spec, to be audited. From bytes to nat.
/// lt_to_n interprets a byte sequence as a little-endian natural number
val le_to_n : b:bytes -> Tot nat
/// be_to_n interprets a byte sequence as a big-endian natural number
val be_to_n : b:bytes -> Tot nat
/// Induction for le_to_n and be_to_n
val reveal_le_to_n (b:bytes)
: Lemma
(le_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.head b) + pow2 8 * le_to_n (S.tail b)))
val reveal_be_to_n (b:bytes)
: Lemma
(be_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))))
val lemma_le_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (le_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
val lemma_be_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (be_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
/// Inverse operations
/// ------------------
///
/// From nat to bytes, and their functional correctness.
/// n_to_le encodes a number as a little-endian byte sequence of a fixed,
/// sufficiently large length.
val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == le_to_n b})
(decreases len)
/// n_to_be encodes a numbers as a big-endian byte sequence of a fixed,
/// sufficiently large length
val n_to_be:
len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == be_to_n b})
(decreases len)
/// Injectivity
/// -----------
val n_to_le_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})):
Lemma (requires (n_to_le len n1 == n_to_le len n2))
(ensures (n1 == n2))
val n_to_be_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})) :
Lemma (requires (n_to_be len n1 == n_to_be len n2))
(ensures (n1 == n2))
val be_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ be_to_n b1 == be_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
val le_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ le_to_n b1 == le_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
/// Roundtripping
/// -------------
val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
be_to_n s < pow2 (8 * len) /\
n_to_be len (be_to_n s) == s
))
[SMTPat (n_to_be len (be_to_n s))]
val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
le_to_n s < pow2 (8 * len) /\
n_to_le len (le_to_n s) == s
))
[SMTPat (n_to_le len (le_to_n s))]
/// Specializations for F* machine integers
/// ---------------------------------------
///
/// These are useful because they take care of calling the right ``*_is_bounded`` lemmas.
let uint32_of_le (b: bytes { S.length b = 4 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n
let le_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_le 4 (UInt32.v x)
let uint32_of_be (b: bytes { S.length b = 4 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt32.uint_to_t n
let be_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_be 4 (UInt32.v x)
let uint64_of_le (b: bytes { S.length b = 8 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt64.uint_to_t n
let le_of_uint64 (x: UInt64.t): b:bytes{ S.length b = 8 } =
n_to_le 8 (UInt64.v x) | false | false | FStar.Endianness.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val uint64_of_be : b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 8} -> FStar.UInt64.t | [] | FStar.Endianness.uint64_of_be | {
"file_name": "ulib/FStar.Endianness.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 8} -> FStar.UInt64.t | {
"end_col": 20,
"end_line": 169,
"start_col": 48,
"start_line": 166
} |
|
Prims.Tot | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let uint64_of_le (b: bytes { S.length b = 8 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt64.uint_to_t n | let uint64_of_le (b: bytes{S.length b = 8}) = | false | null | false | let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt64.uint_to_t n | {
"checked_file": "FStar.Endianness.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked"
],
"interface_file": false,
"source_file": "FStar.Endianness.fsti"
} | [
"total"
] | [
"FStar.Endianness.bytes",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.UInt8.t",
"FStar.UInt64.uint_to_t",
"Prims.unit",
"FStar.Endianness.lemma_le_to_n_is_bounded",
"Prims.nat",
"FStar.Endianness.le_to_n",
"FStar.UInt64.t"
] | [] | module FStar.Endianness
/// A library of lemmas for reasoning about sequences of machine integers and
/// their (little|big)-endian representation as a sequence of bytes.
///
/// The functions in this module aim to be as generic as possible, in order to
/// facilitate compatibility with:
/// - Vale's model of machine integers (nat64 et al.), which does not rely on
/// FStar's machine integers
/// - HACL*'s Lib.IntTypes module, which exposes a universal indexed integer
/// type but uses F* machine integers under the hood.
///
/// To achieve maximum compatibility, we try to state most lemmas using nat
/// rather than UIntX.
///
/// To limit context pollution, the definitions of the recursive functions are
/// abstract; please add lemmas as you see fit. In extreme cases, ``friend``'ing
/// might be de rigueur.
///
/// .. note::
///
/// This module supersedes the poorly-named ``FStar.Krml.Endianness``.
module U8 = FStar.UInt8
module U32 = FStar.UInt32
module U64 = FStar.UInt64
module Math = FStar.Math.Lemmas
module S = FStar.Seq
[@@ noextract_to "krml"]
type bytes = S.seq U8.t
open FStar.Mul
/// Definition of little and big-endianness
/// ---------------------------------------
///
/// This is our spec, to be audited. From bytes to nat.
/// lt_to_n interprets a byte sequence as a little-endian natural number
val le_to_n : b:bytes -> Tot nat
/// be_to_n interprets a byte sequence as a big-endian natural number
val be_to_n : b:bytes -> Tot nat
/// Induction for le_to_n and be_to_n
val reveal_le_to_n (b:bytes)
: Lemma
(le_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.head b) + pow2 8 * le_to_n (S.tail b)))
val reveal_be_to_n (b:bytes)
: Lemma
(be_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))))
val lemma_le_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (le_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
val lemma_be_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (be_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
/// Inverse operations
/// ------------------
///
/// From nat to bytes, and their functional correctness.
/// n_to_le encodes a number as a little-endian byte sequence of a fixed,
/// sufficiently large length.
val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == le_to_n b})
(decreases len)
/// n_to_be encodes a numbers as a big-endian byte sequence of a fixed,
/// sufficiently large length
val n_to_be:
len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == be_to_n b})
(decreases len)
/// Injectivity
/// -----------
val n_to_le_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})):
Lemma (requires (n_to_le len n1 == n_to_le len n2))
(ensures (n1 == n2))
val n_to_be_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})) :
Lemma (requires (n_to_be len n1 == n_to_be len n2))
(ensures (n1 == n2))
val be_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ be_to_n b1 == be_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
val le_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ le_to_n b1 == le_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
/// Roundtripping
/// -------------
val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
be_to_n s < pow2 (8 * len) /\
n_to_be len (be_to_n s) == s
))
[SMTPat (n_to_be len (be_to_n s))]
val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
le_to_n s < pow2 (8 * len) /\
n_to_le len (le_to_n s) == s
))
[SMTPat (n_to_le len (le_to_n s))]
/// Specializations for F* machine integers
/// ---------------------------------------
///
/// These are useful because they take care of calling the right ``*_is_bounded`` lemmas.
let uint32_of_le (b: bytes { S.length b = 4 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n
let le_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_le 4 (UInt32.v x)
let uint32_of_be (b: bytes { S.length b = 4 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt32.uint_to_t n
let be_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_be 4 (UInt32.v x) | false | false | FStar.Endianness.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val uint64_of_le : b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 8} -> FStar.UInt64.t | [] | FStar.Endianness.uint64_of_le | {
"file_name": "ulib/FStar.Endianness.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 8} -> FStar.UInt64.t | {
"end_col": 20,
"end_line": 161,
"start_col": 48,
"start_line": 158
} |
|
Prims.Tot | val be_of_uint64 (x: UInt64.t) : b: bytes{S.length b = 8} | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let be_of_uint64 (x: UInt64.t): b:bytes{ S.length b = 8 } =
n_to_be 8 (UInt64.v x) | val be_of_uint64 (x: UInt64.t) : b: bytes{S.length b = 8}
let be_of_uint64 (x: UInt64.t) : b: bytes{S.length b = 8} = | false | null | false | n_to_be 8 (UInt64.v x) | {
"checked_file": "FStar.Endianness.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked"
],
"interface_file": false,
"source_file": "FStar.Endianness.fsti"
} | [
"total"
] | [
"FStar.UInt64.t",
"FStar.Endianness.n_to_be",
"FStar.UInt64.v",
"FStar.Endianness.bytes",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.UInt8.t"
] | [] | module FStar.Endianness
/// A library of lemmas for reasoning about sequences of machine integers and
/// their (little|big)-endian representation as a sequence of bytes.
///
/// The functions in this module aim to be as generic as possible, in order to
/// facilitate compatibility with:
/// - Vale's model of machine integers (nat64 et al.), which does not rely on
/// FStar's machine integers
/// - HACL*'s Lib.IntTypes module, which exposes a universal indexed integer
/// type but uses F* machine integers under the hood.
///
/// To achieve maximum compatibility, we try to state most lemmas using nat
/// rather than UIntX.
///
/// To limit context pollution, the definitions of the recursive functions are
/// abstract; please add lemmas as you see fit. In extreme cases, ``friend``'ing
/// might be de rigueur.
///
/// .. note::
///
/// This module supersedes the poorly-named ``FStar.Krml.Endianness``.
module U8 = FStar.UInt8
module U32 = FStar.UInt32
module U64 = FStar.UInt64
module Math = FStar.Math.Lemmas
module S = FStar.Seq
[@@ noextract_to "krml"]
type bytes = S.seq U8.t
open FStar.Mul
/// Definition of little and big-endianness
/// ---------------------------------------
///
/// This is our spec, to be audited. From bytes to nat.
/// lt_to_n interprets a byte sequence as a little-endian natural number
val le_to_n : b:bytes -> Tot nat
/// be_to_n interprets a byte sequence as a big-endian natural number
val be_to_n : b:bytes -> Tot nat
/// Induction for le_to_n and be_to_n
val reveal_le_to_n (b:bytes)
: Lemma
(le_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.head b) + pow2 8 * le_to_n (S.tail b)))
val reveal_be_to_n (b:bytes)
: Lemma
(be_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))))
val lemma_le_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (le_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
val lemma_be_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (be_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
/// Inverse operations
/// ------------------
///
/// From nat to bytes, and their functional correctness.
/// n_to_le encodes a number as a little-endian byte sequence of a fixed,
/// sufficiently large length.
val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == le_to_n b})
(decreases len)
/// n_to_be encodes a numbers as a big-endian byte sequence of a fixed,
/// sufficiently large length
val n_to_be:
len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == be_to_n b})
(decreases len)
/// Injectivity
/// -----------
val n_to_le_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})):
Lemma (requires (n_to_le len n1 == n_to_le len n2))
(ensures (n1 == n2))
val n_to_be_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})) :
Lemma (requires (n_to_be len n1 == n_to_be len n2))
(ensures (n1 == n2))
val be_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ be_to_n b1 == be_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
val le_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ le_to_n b1 == le_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
/// Roundtripping
/// -------------
val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
be_to_n s < pow2 (8 * len) /\
n_to_be len (be_to_n s) == s
))
[SMTPat (n_to_be len (be_to_n s))]
val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
le_to_n s < pow2 (8 * len) /\
n_to_le len (le_to_n s) == s
))
[SMTPat (n_to_le len (le_to_n s))]
/// Specializations for F* machine integers
/// ---------------------------------------
///
/// These are useful because they take care of calling the right ``*_is_bounded`` lemmas.
let uint32_of_le (b: bytes { S.length b = 4 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n
let le_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_le 4 (UInt32.v x)
let uint32_of_be (b: bytes { S.length b = 4 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt32.uint_to_t n
let be_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_be 4 (UInt32.v x)
let uint64_of_le (b: bytes { S.length b = 8 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt64.uint_to_t n
let le_of_uint64 (x: UInt64.t): b:bytes{ S.length b = 8 } =
n_to_le 8 (UInt64.v x)
let uint64_of_be (b: bytes { S.length b = 8 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt64.uint_to_t n | false | false | FStar.Endianness.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val be_of_uint64 (x: UInt64.t) : b: bytes{S.length b = 8} | [] | FStar.Endianness.be_of_uint64 | {
"file_name": "ulib/FStar.Endianness.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | x: FStar.UInt64.t -> b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 8} | {
"end_col": 24,
"end_line": 172,
"start_col": 2,
"start_line": 172
} |
Prims.Tot | val le_of_uint64 (x: UInt64.t) : b: bytes{S.length b = 8} | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let le_of_uint64 (x: UInt64.t): b:bytes{ S.length b = 8 } =
n_to_le 8 (UInt64.v x) | val le_of_uint64 (x: UInt64.t) : b: bytes{S.length b = 8}
let le_of_uint64 (x: UInt64.t) : b: bytes{S.length b = 8} = | false | null | false | n_to_le 8 (UInt64.v x) | {
"checked_file": "FStar.Endianness.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked"
],
"interface_file": false,
"source_file": "FStar.Endianness.fsti"
} | [
"total"
] | [
"FStar.UInt64.t",
"FStar.Endianness.n_to_le",
"FStar.UInt64.v",
"FStar.Endianness.bytes",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.UInt8.t"
] | [] | module FStar.Endianness
/// A library of lemmas for reasoning about sequences of machine integers and
/// their (little|big)-endian representation as a sequence of bytes.
///
/// The functions in this module aim to be as generic as possible, in order to
/// facilitate compatibility with:
/// - Vale's model of machine integers (nat64 et al.), which does not rely on
/// FStar's machine integers
/// - HACL*'s Lib.IntTypes module, which exposes a universal indexed integer
/// type but uses F* machine integers under the hood.
///
/// To achieve maximum compatibility, we try to state most lemmas using nat
/// rather than UIntX.
///
/// To limit context pollution, the definitions of the recursive functions are
/// abstract; please add lemmas as you see fit. In extreme cases, ``friend``'ing
/// might be de rigueur.
///
/// .. note::
///
/// This module supersedes the poorly-named ``FStar.Krml.Endianness``.
module U8 = FStar.UInt8
module U32 = FStar.UInt32
module U64 = FStar.UInt64
module Math = FStar.Math.Lemmas
module S = FStar.Seq
[@@ noextract_to "krml"]
type bytes = S.seq U8.t
open FStar.Mul
/// Definition of little and big-endianness
/// ---------------------------------------
///
/// This is our spec, to be audited. From bytes to nat.
/// lt_to_n interprets a byte sequence as a little-endian natural number
val le_to_n : b:bytes -> Tot nat
/// be_to_n interprets a byte sequence as a big-endian natural number
val be_to_n : b:bytes -> Tot nat
/// Induction for le_to_n and be_to_n
val reveal_le_to_n (b:bytes)
: Lemma
(le_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.head b) + pow2 8 * le_to_n (S.tail b)))
val reveal_be_to_n (b:bytes)
: Lemma
(be_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))))
val lemma_le_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (le_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
val lemma_be_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (be_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
/// Inverse operations
/// ------------------
///
/// From nat to bytes, and their functional correctness.
/// n_to_le encodes a number as a little-endian byte sequence of a fixed,
/// sufficiently large length.
val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == le_to_n b})
(decreases len)
/// n_to_be encodes a numbers as a big-endian byte sequence of a fixed,
/// sufficiently large length
val n_to_be:
len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == be_to_n b})
(decreases len)
/// Injectivity
/// -----------
val n_to_le_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})):
Lemma (requires (n_to_le len n1 == n_to_le len n2))
(ensures (n1 == n2))
val n_to_be_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})) :
Lemma (requires (n_to_be len n1 == n_to_be len n2))
(ensures (n1 == n2))
val be_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ be_to_n b1 == be_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
val le_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ le_to_n b1 == le_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
/// Roundtripping
/// -------------
val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
be_to_n s < pow2 (8 * len) /\
n_to_be len (be_to_n s) == s
))
[SMTPat (n_to_be len (be_to_n s))]
val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
le_to_n s < pow2 (8 * len) /\
n_to_le len (le_to_n s) == s
))
[SMTPat (n_to_le len (le_to_n s))]
/// Specializations for F* machine integers
/// ---------------------------------------
///
/// These are useful because they take care of calling the right ``*_is_bounded`` lemmas.
let uint32_of_le (b: bytes { S.length b = 4 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n
let le_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_le 4 (UInt32.v x)
let uint32_of_be (b: bytes { S.length b = 4 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt32.uint_to_t n
let be_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_be 4 (UInt32.v x)
let uint64_of_le (b: bytes { S.length b = 8 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt64.uint_to_t n | false | false | FStar.Endianness.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val le_of_uint64 (x: UInt64.t) : b: bytes{S.length b = 8} | [] | FStar.Endianness.le_of_uint64 | {
"file_name": "ulib/FStar.Endianness.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | x: FStar.UInt64.t -> b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 8} | {
"end_col": 24,
"end_line": 164,
"start_col": 2,
"start_line": 164
} |
Prims.Tot | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let uint32_of_be (b: bytes { S.length b = 4 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt32.uint_to_t n | let uint32_of_be (b: bytes{S.length b = 4}) = | false | null | false | let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt32.uint_to_t n | {
"checked_file": "FStar.Endianness.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked"
],
"interface_file": false,
"source_file": "FStar.Endianness.fsti"
} | [
"total"
] | [
"FStar.Endianness.bytes",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.UInt8.t",
"FStar.UInt32.uint_to_t",
"Prims.unit",
"FStar.Endianness.lemma_be_to_n_is_bounded",
"Prims.nat",
"FStar.Endianness.be_to_n",
"FStar.UInt32.t"
] | [] | module FStar.Endianness
/// A library of lemmas for reasoning about sequences of machine integers and
/// their (little|big)-endian representation as a sequence of bytes.
///
/// The functions in this module aim to be as generic as possible, in order to
/// facilitate compatibility with:
/// - Vale's model of machine integers (nat64 et al.), which does not rely on
/// FStar's machine integers
/// - HACL*'s Lib.IntTypes module, which exposes a universal indexed integer
/// type but uses F* machine integers under the hood.
///
/// To achieve maximum compatibility, we try to state most lemmas using nat
/// rather than UIntX.
///
/// To limit context pollution, the definitions of the recursive functions are
/// abstract; please add lemmas as you see fit. In extreme cases, ``friend``'ing
/// might be de rigueur.
///
/// .. note::
///
/// This module supersedes the poorly-named ``FStar.Krml.Endianness``.
module U8 = FStar.UInt8
module U32 = FStar.UInt32
module U64 = FStar.UInt64
module Math = FStar.Math.Lemmas
module S = FStar.Seq
[@@ noextract_to "krml"]
type bytes = S.seq U8.t
open FStar.Mul
/// Definition of little and big-endianness
/// ---------------------------------------
///
/// This is our spec, to be audited. From bytes to nat.
/// lt_to_n interprets a byte sequence as a little-endian natural number
val le_to_n : b:bytes -> Tot nat
/// be_to_n interprets a byte sequence as a big-endian natural number
val be_to_n : b:bytes -> Tot nat
/// Induction for le_to_n and be_to_n
val reveal_le_to_n (b:bytes)
: Lemma
(le_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.head b) + pow2 8 * le_to_n (S.tail b)))
val reveal_be_to_n (b:bytes)
: Lemma
(be_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))))
val lemma_le_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (le_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
val lemma_be_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (be_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
/// Inverse operations
/// ------------------
///
/// From nat to bytes, and their functional correctness.
/// n_to_le encodes a number as a little-endian byte sequence of a fixed,
/// sufficiently large length.
val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == le_to_n b})
(decreases len)
/// n_to_be encodes a numbers as a big-endian byte sequence of a fixed,
/// sufficiently large length
val n_to_be:
len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == be_to_n b})
(decreases len)
/// Injectivity
/// -----------
val n_to_le_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})):
Lemma (requires (n_to_le len n1 == n_to_le len n2))
(ensures (n1 == n2))
val n_to_be_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})) :
Lemma (requires (n_to_be len n1 == n_to_be len n2))
(ensures (n1 == n2))
val be_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ be_to_n b1 == be_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
val le_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ le_to_n b1 == le_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
/// Roundtripping
/// -------------
val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
be_to_n s < pow2 (8 * len) /\
n_to_be len (be_to_n s) == s
))
[SMTPat (n_to_be len (be_to_n s))]
val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
le_to_n s < pow2 (8 * len) /\
n_to_le len (le_to_n s) == s
))
[SMTPat (n_to_le len (le_to_n s))]
/// Specializations for F* machine integers
/// ---------------------------------------
///
/// These are useful because they take care of calling the right ``*_is_bounded`` lemmas.
let uint32_of_le (b: bytes { S.length b = 4 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n
let le_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_le 4 (UInt32.v x) | false | false | FStar.Endianness.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val uint32_of_be : b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 4} -> FStar.UInt32.t | [] | FStar.Endianness.uint32_of_be | {
"file_name": "ulib/FStar.Endianness.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 4} -> FStar.UInt32.t | {
"end_col": 20,
"end_line": 153,
"start_col": 48,
"start_line": 150
} |
|
Prims.Tot | val be_of_uint32 (x: UInt32.t) : b: bytes{S.length b = 4} | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let be_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_be 4 (UInt32.v x) | val be_of_uint32 (x: UInt32.t) : b: bytes{S.length b = 4}
let be_of_uint32 (x: UInt32.t) : b: bytes{S.length b = 4} = | false | null | false | n_to_be 4 (UInt32.v x) | {
"checked_file": "FStar.Endianness.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked"
],
"interface_file": false,
"source_file": "FStar.Endianness.fsti"
} | [
"total"
] | [
"FStar.UInt32.t",
"FStar.Endianness.n_to_be",
"FStar.UInt32.v",
"FStar.Endianness.bytes",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.UInt8.t"
] | [] | module FStar.Endianness
/// A library of lemmas for reasoning about sequences of machine integers and
/// their (little|big)-endian representation as a sequence of bytes.
///
/// The functions in this module aim to be as generic as possible, in order to
/// facilitate compatibility with:
/// - Vale's model of machine integers (nat64 et al.), which does not rely on
/// FStar's machine integers
/// - HACL*'s Lib.IntTypes module, which exposes a universal indexed integer
/// type but uses F* machine integers under the hood.
///
/// To achieve maximum compatibility, we try to state most lemmas using nat
/// rather than UIntX.
///
/// To limit context pollution, the definitions of the recursive functions are
/// abstract; please add lemmas as you see fit. In extreme cases, ``friend``'ing
/// might be de rigueur.
///
/// .. note::
///
/// This module supersedes the poorly-named ``FStar.Krml.Endianness``.
module U8 = FStar.UInt8
module U32 = FStar.UInt32
module U64 = FStar.UInt64
module Math = FStar.Math.Lemmas
module S = FStar.Seq
[@@ noextract_to "krml"]
type bytes = S.seq U8.t
open FStar.Mul
/// Definition of little and big-endianness
/// ---------------------------------------
///
/// This is our spec, to be audited. From bytes to nat.
/// lt_to_n interprets a byte sequence as a little-endian natural number
val le_to_n : b:bytes -> Tot nat
/// be_to_n interprets a byte sequence as a big-endian natural number
val be_to_n : b:bytes -> Tot nat
/// Induction for le_to_n and be_to_n
val reveal_le_to_n (b:bytes)
: Lemma
(le_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.head b) + pow2 8 * le_to_n (S.tail b)))
val reveal_be_to_n (b:bytes)
: Lemma
(be_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))))
val lemma_le_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (le_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
val lemma_be_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (be_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
/// Inverse operations
/// ------------------
///
/// From nat to bytes, and their functional correctness.
/// n_to_le encodes a number as a little-endian byte sequence of a fixed,
/// sufficiently large length.
val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == le_to_n b})
(decreases len)
/// n_to_be encodes a numbers as a big-endian byte sequence of a fixed,
/// sufficiently large length
val n_to_be:
len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == be_to_n b})
(decreases len)
/// Injectivity
/// -----------
val n_to_le_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})):
Lemma (requires (n_to_le len n1 == n_to_le len n2))
(ensures (n1 == n2))
val n_to_be_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})) :
Lemma (requires (n_to_be len n1 == n_to_be len n2))
(ensures (n1 == n2))
val be_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ be_to_n b1 == be_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
val le_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ le_to_n b1 == le_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
/// Roundtripping
/// -------------
val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
be_to_n s < pow2 (8 * len) /\
n_to_be len (be_to_n s) == s
))
[SMTPat (n_to_be len (be_to_n s))]
val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
le_to_n s < pow2 (8 * len) /\
n_to_le len (le_to_n s) == s
))
[SMTPat (n_to_le len (le_to_n s))]
/// Specializations for F* machine integers
/// ---------------------------------------
///
/// These are useful because they take care of calling the right ``*_is_bounded`` lemmas.
let uint32_of_le (b: bytes { S.length b = 4 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n
let le_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_le 4 (UInt32.v x)
let uint32_of_be (b: bytes { S.length b = 4 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt32.uint_to_t n | false | false | FStar.Endianness.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val be_of_uint32 (x: UInt32.t) : b: bytes{S.length b = 4} | [] | FStar.Endianness.be_of_uint32 | {
"file_name": "ulib/FStar.Endianness.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | x: FStar.UInt32.t -> b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 4} | {
"end_col": 24,
"end_line": 156,
"start_col": 2,
"start_line": 156
} |
Prims.Tot | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let uint32_of_le (b: bytes { S.length b = 4 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n | let uint32_of_le (b: bytes{S.length b = 4}) = | false | null | false | let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n | {
"checked_file": "FStar.Endianness.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked"
],
"interface_file": false,
"source_file": "FStar.Endianness.fsti"
} | [
"total"
] | [
"FStar.Endianness.bytes",
"Prims.b2t",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.UInt8.t",
"FStar.UInt32.uint_to_t",
"Prims.unit",
"FStar.Endianness.lemma_le_to_n_is_bounded",
"Prims.nat",
"FStar.Endianness.le_to_n",
"FStar.UInt32.t"
] | [] | module FStar.Endianness
/// A library of lemmas for reasoning about sequences of machine integers and
/// their (little|big)-endian representation as a sequence of bytes.
///
/// The functions in this module aim to be as generic as possible, in order to
/// facilitate compatibility with:
/// - Vale's model of machine integers (nat64 et al.), which does not rely on
/// FStar's machine integers
/// - HACL*'s Lib.IntTypes module, which exposes a universal indexed integer
/// type but uses F* machine integers under the hood.
///
/// To achieve maximum compatibility, we try to state most lemmas using nat
/// rather than UIntX.
///
/// To limit context pollution, the definitions of the recursive functions are
/// abstract; please add lemmas as you see fit. In extreme cases, ``friend``'ing
/// might be de rigueur.
///
/// .. note::
///
/// This module supersedes the poorly-named ``FStar.Krml.Endianness``.
module U8 = FStar.UInt8
module U32 = FStar.UInt32
module U64 = FStar.UInt64
module Math = FStar.Math.Lemmas
module S = FStar.Seq
[@@ noextract_to "krml"]
type bytes = S.seq U8.t
open FStar.Mul
/// Definition of little and big-endianness
/// ---------------------------------------
///
/// This is our spec, to be audited. From bytes to nat.
/// lt_to_n interprets a byte sequence as a little-endian natural number
val le_to_n : b:bytes -> Tot nat
/// be_to_n interprets a byte sequence as a big-endian natural number
val be_to_n : b:bytes -> Tot nat
/// Induction for le_to_n and be_to_n
val reveal_le_to_n (b:bytes)
: Lemma
(le_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.head b) + pow2 8 * le_to_n (S.tail b)))
val reveal_be_to_n (b:bytes)
: Lemma
(be_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))))
val lemma_le_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (le_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
val lemma_be_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (be_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
/// Inverse operations
/// ------------------
///
/// From nat to bytes, and their functional correctness.
/// n_to_le encodes a number as a little-endian byte sequence of a fixed,
/// sufficiently large length.
val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == le_to_n b})
(decreases len)
/// n_to_be encodes a numbers as a big-endian byte sequence of a fixed,
/// sufficiently large length
val n_to_be:
len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == be_to_n b})
(decreases len)
/// Injectivity
/// -----------
val n_to_le_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})):
Lemma (requires (n_to_le len n1 == n_to_le len n2))
(ensures (n1 == n2))
val n_to_be_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})) :
Lemma (requires (n_to_be len n1 == n_to_be len n2))
(ensures (n1 == n2))
val be_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ be_to_n b1 == be_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
val le_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ le_to_n b1 == le_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
/// Roundtripping
/// -------------
val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
be_to_n s < pow2 (8 * len) /\
n_to_be len (be_to_n s) == s
))
[SMTPat (n_to_be len (be_to_n s))]
val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
le_to_n s < pow2 (8 * len) /\
n_to_le len (le_to_n s) == s
))
[SMTPat (n_to_le len (le_to_n s))]
/// Specializations for F* machine integers
/// ---------------------------------------
///
/// These are useful because they take care of calling the right ``*_is_bounded`` lemmas. | false | false | FStar.Endianness.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val uint32_of_le : b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 4} -> FStar.UInt32.t | [] | FStar.Endianness.uint32_of_le | {
"file_name": "ulib/FStar.Endianness.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | b: FStar.Endianness.bytes{FStar.Seq.Base.length b = 4} -> FStar.UInt32.t | {
"end_col": 20,
"end_line": 145,
"start_col": 48,
"start_line": 142
} |
|
FStar.Pervasives.Lemma | val be_to_n_zeros (s: bytes)
: Lemma (requires forall (i: nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures be_to_n s == 0)
(decreases (Seq.length s)) | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec be_to_n_zeros (s:bytes)
: Lemma
(requires
forall (i:nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures be_to_n s == 0)
(decreases (Seq.length s))
= reveal_be_to_n s;
if Seq.length s = 0 then ()
else be_to_n_zeros (Seq.slice s 0 (Seq.length s - 1)) | val be_to_n_zeros (s: bytes)
: Lemma (requires forall (i: nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures be_to_n s == 0)
(decreases (Seq.length s))
let rec be_to_n_zeros (s: bytes)
: Lemma (requires forall (i: nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures be_to_n s == 0)
(decreases (Seq.length s)) = | false | null | true | reveal_be_to_n s;
if Seq.length s = 0 then () else be_to_n_zeros (Seq.slice s 0 (Seq.length s - 1)) | {
"checked_file": "FStar.Endianness.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked"
],
"interface_file": false,
"source_file": "FStar.Endianness.fsti"
} | [
"lemma",
""
] | [
"FStar.Endianness.bytes",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.UInt8.t",
"Prims.bool",
"FStar.Endianness.be_to_n_zeros",
"FStar.Seq.Base.slice",
"Prims.op_Subtraction",
"Prims.unit",
"FStar.Endianness.reveal_be_to_n",
"Prims.l_Forall",
"Prims.nat",
"Prims.l_imp",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.eq2",
"FStar.Seq.Base.index",
"FStar.UInt8.__uint_to_t",
"Prims.squash",
"FStar.Endianness.be_to_n",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | module FStar.Endianness
/// A library of lemmas for reasoning about sequences of machine integers and
/// their (little|big)-endian representation as a sequence of bytes.
///
/// The functions in this module aim to be as generic as possible, in order to
/// facilitate compatibility with:
/// - Vale's model of machine integers (nat64 et al.), which does not rely on
/// FStar's machine integers
/// - HACL*'s Lib.IntTypes module, which exposes a universal indexed integer
/// type but uses F* machine integers under the hood.
///
/// To achieve maximum compatibility, we try to state most lemmas using nat
/// rather than UIntX.
///
/// To limit context pollution, the definitions of the recursive functions are
/// abstract; please add lemmas as you see fit. In extreme cases, ``friend``'ing
/// might be de rigueur.
///
/// .. note::
///
/// This module supersedes the poorly-named ``FStar.Krml.Endianness``.
module U8 = FStar.UInt8
module U32 = FStar.UInt32
module U64 = FStar.UInt64
module Math = FStar.Math.Lemmas
module S = FStar.Seq
[@@ noextract_to "krml"]
type bytes = S.seq U8.t
open FStar.Mul
/// Definition of little and big-endianness
/// ---------------------------------------
///
/// This is our spec, to be audited. From bytes to nat.
/// lt_to_n interprets a byte sequence as a little-endian natural number
val le_to_n : b:bytes -> Tot nat
/// be_to_n interprets a byte sequence as a big-endian natural number
val be_to_n : b:bytes -> Tot nat
/// Induction for le_to_n and be_to_n
val reveal_le_to_n (b:bytes)
: Lemma
(le_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.head b) + pow2 8 * le_to_n (S.tail b)))
val reveal_be_to_n (b:bytes)
: Lemma
(be_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))))
val lemma_le_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (le_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
val lemma_be_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (be_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
/// Inverse operations
/// ------------------
///
/// From nat to bytes, and their functional correctness.
/// n_to_le encodes a number as a little-endian byte sequence of a fixed,
/// sufficiently large length.
val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == le_to_n b})
(decreases len)
/// n_to_be encodes a numbers as a big-endian byte sequence of a fixed,
/// sufficiently large length
val n_to_be:
len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == be_to_n b})
(decreases len)
/// Injectivity
/// -----------
val n_to_le_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})):
Lemma (requires (n_to_le len n1 == n_to_le len n2))
(ensures (n1 == n2))
val n_to_be_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})) :
Lemma (requires (n_to_be len n1 == n_to_be len n2))
(ensures (n1 == n2))
val be_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ be_to_n b1 == be_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
val le_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ le_to_n b1 == le_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
/// Roundtripping
/// -------------
val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
be_to_n s < pow2 (8 * len) /\
n_to_be len (be_to_n s) == s
))
[SMTPat (n_to_be len (be_to_n s))]
val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
le_to_n s < pow2 (8 * len) /\
n_to_le len (le_to_n s) == s
))
[SMTPat (n_to_le len (le_to_n s))]
/// Specializations for F* machine integers
/// ---------------------------------------
///
/// These are useful because they take care of calling the right ``*_is_bounded`` lemmas.
let uint32_of_le (b: bytes { S.length b = 4 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n
let le_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_le 4 (UInt32.v x)
let uint32_of_be (b: bytes { S.length b = 4 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt32.uint_to_t n
let be_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_be 4 (UInt32.v x)
let uint64_of_le (b: bytes { S.length b = 8 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt64.uint_to_t n
let le_of_uint64 (x: UInt64.t): b:bytes{ S.length b = 8 } =
n_to_le 8 (UInt64.v x)
let uint64_of_be (b: bytes { S.length b = 8 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt64.uint_to_t n
let be_of_uint64 (x: UInt64.t): b:bytes{ S.length b = 8 } =
n_to_be 8 (UInt64.v x)
/// Lifting {le,be}_to_n / n_to_{le,be} to sequences
/// ------------------------------------------------
///
/// TODO: 16-bit (but is it really needed?)
/// TODO: should these be specializations of generic functions that chop on
/// N-byte boundaries, and operate on bounded nats instead of uints?
val seq_uint32_of_le (l: nat) (b: bytes{ S.length b = 4 * l }):
s:S.seq UInt32.t { S.length s = l }
val le_of_seq_uint32 (s: S.seq UInt32.t):
Tot (b:bytes { S.length b = 4 * S.length s })
(decreases (S.length s))
val seq_uint32_of_be (l: nat) (b: bytes{ S.length b = 4 * l }):
s:S.seq UInt32.t { S.length s = l }
val be_of_seq_uint32 (s: S.seq UInt32.t):
Tot (b:bytes { S.length b = 4 * S.length s })
(decreases (S.length s))
val seq_uint64_of_le (l: nat) (b: bytes{ S.length b = 8 * l }):
s:S.seq UInt64.t { S.length s = l }
val le_of_seq_uint64 (s: S.seq UInt64.t):
Tot (b:bytes { S.length b = 8 * S.length s })
(decreases (S.length s))
val seq_uint64_of_be (l: nat) (b: bytes{ S.length b = 8 * l }):
s:S.seq UInt64.t { S.length s = l }
val be_of_seq_uint64 (s: S.seq UInt64.t):
Tot (b:bytes { S.length b = 8 * S.length s })
(decreases (S.length s))
/// Complete specification of the combinators above, relating them to {le,be}_to_ / n_to_{le,be}
/// --------------------------------------------------------------------------------------------
val offset_uint32_be (b: bytes) (n: nat) (i: nat):
Lemma
(requires (
S.length b = 4 * n /\
i < n))
(ensures (
S.index (seq_uint32_of_be n b) i == uint32_of_be (S.slice b (4 * i) (4 * i + 4))))
(decreases (
S.length b))
[ SMTPat (S.index (seq_uint32_of_be n b) i) ]
val offset_uint32_le (b: bytes) (n: nat) (i: nat):
Lemma
(requires (
S.length b = 4 * n /\
i < n))
(ensures (
S.index (seq_uint32_of_le n b) i == uint32_of_le (S.slice b (4 * i) (4 * i + 4))))
(decreases (
S.length b))
[ SMTPat (S.index (seq_uint32_of_le n b) i) ]
val offset_uint64_be (b: bytes) (n: nat) (i: nat):
Lemma
(requires (
S.length b = 8 * n /\
i < n))
(ensures (
S.index (seq_uint64_of_be n b) i == uint64_of_be (S.slice b (8 * i) (8 * i + 8))))
(decreases (
S.length b))
[ SMTPat (S.index (seq_uint64_of_be n b) i) ]
val offset_uint64_le (b: bytes) (n: nat) (i: nat):
Lemma
(requires (
S.length b = 8 * n /\
i < n))
(ensures (
S.index (seq_uint64_of_le n b) i == uint64_of_le (S.slice b (8 * i) (8 * i + 8))))
(decreases (
S.length b))
[ SMTPat (S.index (seq_uint64_of_le n b) i) ]
/// Reasoning about appending such sequences
/// ----------------------------------------
///
/// TODO: this is fairly incomplete
/// TODO: the *_base cases seem ad-hoc and derivable trivially from offset above; why have them?
val be_of_seq_uint32_base (s1: S.seq U32.t) (s2: S.seq U8.t): Lemma
(requires (
S.length s1 = 1 /\
S.length s2 = 4 /\
be_to_n s2 = U32.v (S.index s1 0)))
(ensures (S.equal s2 (be_of_seq_uint32 s1)))
[ SMTPat (be_to_n s2); SMTPat (U32.v (S.index s1 0)) ]
val le_of_seq_uint32_base (s1: S.seq U32.t) (s2: S.seq U8.t): Lemma
(requires (
S.length s1 = 1 /\
S.length s2 = 4 /\
le_to_n s2 = U32.v (S.index s1 0)))
(ensures (S.equal s2 (le_of_seq_uint32 s1)))
[ SMTPat (le_to_n s2); SMTPat (U32.v (S.index s1 0)) ]
val be_of_seq_uint64_base (s1: S.seq U64.t) (s2: S.seq U8.t): Lemma
(requires (
S.length s1 = 1 /\
S.length s2 = 8 /\
be_to_n s2 = U64.v (S.index s1 0)))
(ensures (S.equal s2 (be_of_seq_uint64 s1)))
[ SMTPat (be_to_n s2); SMTPat (U64.v (S.index s1 0)) ]
val be_of_seq_uint32_append (s1 s2: S.seq U32.t): Lemma
(ensures (
S.equal (be_of_seq_uint32 (S.append s1 s2))
(S.append (be_of_seq_uint32 s1) (be_of_seq_uint32 s2))))
(decreases (
S.length s1))
[ SMTPat (S.append (be_of_seq_uint32 s1) (be_of_seq_uint32 s2)) ]
val le_of_seq_uint32_append (s1 s2: S.seq U32.t): Lemma
(ensures (
S.equal (le_of_seq_uint32 (S.append s1 s2))
(S.append (le_of_seq_uint32 s1) (le_of_seq_uint32 s2))))
(decreases (
S.length s1))
[ SMTPat (S.append (le_of_seq_uint32 s1) (le_of_seq_uint32 s2)) ]
val be_of_seq_uint64_append (s1 s2: S.seq U64.t): Lemma
(ensures (
S.equal (be_of_seq_uint64 (S.append s1 s2))
(S.append (be_of_seq_uint64 s1) (be_of_seq_uint64 s2))))
(decreases (
S.length s1))
[ SMTPat (S.append (be_of_seq_uint64 s1) (be_of_seq_uint64 s2)) ]
/// Roundtripping
/// -------------
///
/// TODO: also incomplete
val seq_uint32_of_be_be_of_seq_uint32 (n: nat) (s: S.seq U32.t) : Lemma
(requires (n == S.length s))
(ensures (seq_uint32_of_be n (be_of_seq_uint32 s) `S.equal` s))
(decreases n)
[SMTPat (seq_uint32_of_be n (be_of_seq_uint32 s))]
val be_of_seq_uint32_seq_uint32_of_be (n: nat) (s: S.seq U8.t) : Lemma
(requires (4 * n == S.length s))
(ensures (be_of_seq_uint32 (seq_uint32_of_be n s) `S.equal` s))
(decreases n)
[SMTPat (be_of_seq_uint32 (seq_uint32_of_be n s))]
/// Reasoning about slicing such sequences
/// --------------------------------------
///
/// (Needs SMTPats above for roundtripping in their proof, hence why they're at the end.)
val slice_seq_uint32_of_be (n: nat) (s: S.seq U8.t) (lo: nat) (hi: nat) : Lemma
(requires (4 * n == S.length s /\ lo <= hi /\ hi <= n))
(ensures (S.slice (seq_uint32_of_be n s) lo hi) `S.equal` seq_uint32_of_be (hi - lo) (S.slice s (4 * lo) (4 * hi)))
val be_of_seq_uint32_slice (s: S.seq U32.t) (lo: nat) (hi: nat) : Lemma
(requires (lo <= hi /\ hi <= S.length s))
(ensures (be_of_seq_uint32 (S.slice s lo hi) `S.equal` S.slice (be_of_seq_uint32 s) (4 * lo) (4 * hi)))
/// Some reasoning about zero bytes
let rec le_to_n_zeros (s:bytes)
: Lemma
(requires
forall (i:nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures le_to_n s == 0)
(decreases (Seq.length s))
= reveal_le_to_n s;
if Seq.length s = 0 then ()
else le_to_n_zeros (Seq.tail s)
let rec be_to_n_zeros (s:bytes)
: Lemma
(requires
forall (i:nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures be_to_n s == 0) | false | false | FStar.Endianness.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val be_to_n_zeros (s: bytes)
: Lemma (requires forall (i: nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures be_to_n s == 0)
(decreases (Seq.length s)) | [
"recursion"
] | FStar.Endianness.be_to_n_zeros | {
"file_name": "ulib/FStar.Endianness.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Endianness.bytes
-> FStar.Pervasives.Lemma
(requires
forall (i: Prims.nat). i < FStar.Seq.Base.length s ==> FStar.Seq.Base.index s i == 0uy)
(ensures FStar.Endianness.be_to_n s == 0)
(decreases FStar.Seq.Base.length s) | {
"end_col": 57,
"end_line": 364,
"start_col": 4,
"start_line": 362
} |
FStar.Pervasives.Lemma | val le_to_n_zeros (s: bytes)
: Lemma (requires forall (i: nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures le_to_n s == 0)
(decreases (Seq.length s)) | [
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.Seq",
"short_module": "S"
},
{
"abbrev": true,
"full_module": "FStar.Math.Lemmas",
"short_module": "Math"
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt8",
"short_module": "U8"
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let rec le_to_n_zeros (s:bytes)
: Lemma
(requires
forall (i:nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures le_to_n s == 0)
(decreases (Seq.length s))
= reveal_le_to_n s;
if Seq.length s = 0 then ()
else le_to_n_zeros (Seq.tail s) | val le_to_n_zeros (s: bytes)
: Lemma (requires forall (i: nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures le_to_n s == 0)
(decreases (Seq.length s))
let rec le_to_n_zeros (s: bytes)
: Lemma (requires forall (i: nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures le_to_n s == 0)
(decreases (Seq.length s)) = | false | null | true | reveal_le_to_n s;
if Seq.length s = 0 then () else le_to_n_zeros (Seq.tail s) | {
"checked_file": "FStar.Endianness.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt8.fsti.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.Seq.fst.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked",
"FStar.Math.Lemmas.fst.checked"
],
"interface_file": false,
"source_file": "FStar.Endianness.fsti"
} | [
"lemma",
""
] | [
"FStar.Endianness.bytes",
"Prims.op_Equality",
"Prims.int",
"FStar.Seq.Base.length",
"FStar.UInt8.t",
"Prims.bool",
"FStar.Endianness.le_to_n_zeros",
"FStar.Seq.Properties.tail",
"Prims.unit",
"FStar.Endianness.reveal_le_to_n",
"Prims.l_Forall",
"Prims.nat",
"Prims.l_imp",
"Prims.b2t",
"Prims.op_LessThan",
"Prims.eq2",
"FStar.Seq.Base.index",
"FStar.UInt8.__uint_to_t",
"Prims.squash",
"FStar.Endianness.le_to_n",
"Prims.Nil",
"FStar.Pervasives.pattern"
] | [] | module FStar.Endianness
/// A library of lemmas for reasoning about sequences of machine integers and
/// their (little|big)-endian representation as a sequence of bytes.
///
/// The functions in this module aim to be as generic as possible, in order to
/// facilitate compatibility with:
/// - Vale's model of machine integers (nat64 et al.), which does not rely on
/// FStar's machine integers
/// - HACL*'s Lib.IntTypes module, which exposes a universal indexed integer
/// type but uses F* machine integers under the hood.
///
/// To achieve maximum compatibility, we try to state most lemmas using nat
/// rather than UIntX.
///
/// To limit context pollution, the definitions of the recursive functions are
/// abstract; please add lemmas as you see fit. In extreme cases, ``friend``'ing
/// might be de rigueur.
///
/// .. note::
///
/// This module supersedes the poorly-named ``FStar.Krml.Endianness``.
module U8 = FStar.UInt8
module U32 = FStar.UInt32
module U64 = FStar.UInt64
module Math = FStar.Math.Lemmas
module S = FStar.Seq
[@@ noextract_to "krml"]
type bytes = S.seq U8.t
open FStar.Mul
/// Definition of little and big-endianness
/// ---------------------------------------
///
/// This is our spec, to be audited. From bytes to nat.
/// lt_to_n interprets a byte sequence as a little-endian natural number
val le_to_n : b:bytes -> Tot nat
/// be_to_n interprets a byte sequence as a big-endian natural number
val be_to_n : b:bytes -> Tot nat
/// Induction for le_to_n and be_to_n
val reveal_le_to_n (b:bytes)
: Lemma
(le_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.head b) + pow2 8 * le_to_n (S.tail b)))
val reveal_be_to_n (b:bytes)
: Lemma
(be_to_n b ==
(match Seq.length b with
| 0 -> 0
| _ -> U8.v (S.last b) + pow2 8 * be_to_n (S.slice b 0 (S.length b - 1))))
val lemma_le_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (le_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
val lemma_be_to_n_is_bounded: b:bytes -> Lemma
(requires True)
(ensures (be_to_n b < pow2 (8 * Seq.length b)))
(decreases (Seq.length b))
/// Inverse operations
/// ------------------
///
/// From nat to bytes, and their functional correctness.
/// n_to_le encodes a number as a little-endian byte sequence of a fixed,
/// sufficiently large length.
val n_to_le : len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == le_to_n b})
(decreases len)
/// n_to_be encodes a numbers as a big-endian byte sequence of a fixed,
/// sufficiently large length
val n_to_be:
len:nat -> n:nat{n < pow2 (8 * len)} ->
Tot (b:bytes{S.length b == len /\ n == be_to_n b})
(decreases len)
/// Injectivity
/// -----------
val n_to_le_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})):
Lemma (requires (n_to_le len n1 == n_to_le len n2))
(ensures (n1 == n2))
val n_to_be_inj (len: nat) (n1 n2: (n:nat{n < pow2 (8 * len)})) :
Lemma (requires (n_to_be len n1 == n_to_be len n2))
(ensures (n1 == n2))
val be_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ be_to_n b1 == be_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
val le_to_n_inj
(b1 b2: Seq.seq U8.t)
: Lemma
(requires (Seq.length b1 == Seq.length b2 /\ le_to_n b1 == le_to_n b2))
(ensures (Seq.equal b1 b2))
(decreases (Seq.length b1))
/// Roundtripping
/// -------------
val n_to_be_be_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
be_to_n s < pow2 (8 * len) /\
n_to_be len (be_to_n s) == s
))
[SMTPat (n_to_be len (be_to_n s))]
val n_to_le_le_to_n (len: nat) (s: Seq.seq U8.t) : Lemma
(requires (Seq.length s == len))
(ensures (
le_to_n s < pow2 (8 * len) /\
n_to_le len (le_to_n s) == s
))
[SMTPat (n_to_le len (le_to_n s))]
/// Specializations for F* machine integers
/// ---------------------------------------
///
/// These are useful because they take care of calling the right ``*_is_bounded`` lemmas.
let uint32_of_le (b: bytes { S.length b = 4 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt32.uint_to_t n
let le_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_le 4 (UInt32.v x)
let uint32_of_be (b: bytes { S.length b = 4 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt32.uint_to_t n
let be_of_uint32 (x: UInt32.t): b:bytes{ S.length b = 4 } =
n_to_be 4 (UInt32.v x)
let uint64_of_le (b: bytes { S.length b = 8 }) =
let n = le_to_n b in
lemma_le_to_n_is_bounded b;
UInt64.uint_to_t n
let le_of_uint64 (x: UInt64.t): b:bytes{ S.length b = 8 } =
n_to_le 8 (UInt64.v x)
let uint64_of_be (b: bytes { S.length b = 8 }) =
let n = be_to_n b in
lemma_be_to_n_is_bounded b;
UInt64.uint_to_t n
let be_of_uint64 (x: UInt64.t): b:bytes{ S.length b = 8 } =
n_to_be 8 (UInt64.v x)
/// Lifting {le,be}_to_n / n_to_{le,be} to sequences
/// ------------------------------------------------
///
/// TODO: 16-bit (but is it really needed?)
/// TODO: should these be specializations of generic functions that chop on
/// N-byte boundaries, and operate on bounded nats instead of uints?
val seq_uint32_of_le (l: nat) (b: bytes{ S.length b = 4 * l }):
s:S.seq UInt32.t { S.length s = l }
val le_of_seq_uint32 (s: S.seq UInt32.t):
Tot (b:bytes { S.length b = 4 * S.length s })
(decreases (S.length s))
val seq_uint32_of_be (l: nat) (b: bytes{ S.length b = 4 * l }):
s:S.seq UInt32.t { S.length s = l }
val be_of_seq_uint32 (s: S.seq UInt32.t):
Tot (b:bytes { S.length b = 4 * S.length s })
(decreases (S.length s))
val seq_uint64_of_le (l: nat) (b: bytes{ S.length b = 8 * l }):
s:S.seq UInt64.t { S.length s = l }
val le_of_seq_uint64 (s: S.seq UInt64.t):
Tot (b:bytes { S.length b = 8 * S.length s })
(decreases (S.length s))
val seq_uint64_of_be (l: nat) (b: bytes{ S.length b = 8 * l }):
s:S.seq UInt64.t { S.length s = l }
val be_of_seq_uint64 (s: S.seq UInt64.t):
Tot (b:bytes { S.length b = 8 * S.length s })
(decreases (S.length s))
/// Complete specification of the combinators above, relating them to {le,be}_to_ / n_to_{le,be}
/// --------------------------------------------------------------------------------------------
val offset_uint32_be (b: bytes) (n: nat) (i: nat):
Lemma
(requires (
S.length b = 4 * n /\
i < n))
(ensures (
S.index (seq_uint32_of_be n b) i == uint32_of_be (S.slice b (4 * i) (4 * i + 4))))
(decreases (
S.length b))
[ SMTPat (S.index (seq_uint32_of_be n b) i) ]
val offset_uint32_le (b: bytes) (n: nat) (i: nat):
Lemma
(requires (
S.length b = 4 * n /\
i < n))
(ensures (
S.index (seq_uint32_of_le n b) i == uint32_of_le (S.slice b (4 * i) (4 * i + 4))))
(decreases (
S.length b))
[ SMTPat (S.index (seq_uint32_of_le n b) i) ]
val offset_uint64_be (b: bytes) (n: nat) (i: nat):
Lemma
(requires (
S.length b = 8 * n /\
i < n))
(ensures (
S.index (seq_uint64_of_be n b) i == uint64_of_be (S.slice b (8 * i) (8 * i + 8))))
(decreases (
S.length b))
[ SMTPat (S.index (seq_uint64_of_be n b) i) ]
val offset_uint64_le (b: bytes) (n: nat) (i: nat):
Lemma
(requires (
S.length b = 8 * n /\
i < n))
(ensures (
S.index (seq_uint64_of_le n b) i == uint64_of_le (S.slice b (8 * i) (8 * i + 8))))
(decreases (
S.length b))
[ SMTPat (S.index (seq_uint64_of_le n b) i) ]
/// Reasoning about appending such sequences
/// ----------------------------------------
///
/// TODO: this is fairly incomplete
/// TODO: the *_base cases seem ad-hoc and derivable trivially from offset above; why have them?
val be_of_seq_uint32_base (s1: S.seq U32.t) (s2: S.seq U8.t): Lemma
(requires (
S.length s1 = 1 /\
S.length s2 = 4 /\
be_to_n s2 = U32.v (S.index s1 0)))
(ensures (S.equal s2 (be_of_seq_uint32 s1)))
[ SMTPat (be_to_n s2); SMTPat (U32.v (S.index s1 0)) ]
val le_of_seq_uint32_base (s1: S.seq U32.t) (s2: S.seq U8.t): Lemma
(requires (
S.length s1 = 1 /\
S.length s2 = 4 /\
le_to_n s2 = U32.v (S.index s1 0)))
(ensures (S.equal s2 (le_of_seq_uint32 s1)))
[ SMTPat (le_to_n s2); SMTPat (U32.v (S.index s1 0)) ]
val be_of_seq_uint64_base (s1: S.seq U64.t) (s2: S.seq U8.t): Lemma
(requires (
S.length s1 = 1 /\
S.length s2 = 8 /\
be_to_n s2 = U64.v (S.index s1 0)))
(ensures (S.equal s2 (be_of_seq_uint64 s1)))
[ SMTPat (be_to_n s2); SMTPat (U64.v (S.index s1 0)) ]
val be_of_seq_uint32_append (s1 s2: S.seq U32.t): Lemma
(ensures (
S.equal (be_of_seq_uint32 (S.append s1 s2))
(S.append (be_of_seq_uint32 s1) (be_of_seq_uint32 s2))))
(decreases (
S.length s1))
[ SMTPat (S.append (be_of_seq_uint32 s1) (be_of_seq_uint32 s2)) ]
val le_of_seq_uint32_append (s1 s2: S.seq U32.t): Lemma
(ensures (
S.equal (le_of_seq_uint32 (S.append s1 s2))
(S.append (le_of_seq_uint32 s1) (le_of_seq_uint32 s2))))
(decreases (
S.length s1))
[ SMTPat (S.append (le_of_seq_uint32 s1) (le_of_seq_uint32 s2)) ]
val be_of_seq_uint64_append (s1 s2: S.seq U64.t): Lemma
(ensures (
S.equal (be_of_seq_uint64 (S.append s1 s2))
(S.append (be_of_seq_uint64 s1) (be_of_seq_uint64 s2))))
(decreases (
S.length s1))
[ SMTPat (S.append (be_of_seq_uint64 s1) (be_of_seq_uint64 s2)) ]
/// Roundtripping
/// -------------
///
/// TODO: also incomplete
val seq_uint32_of_be_be_of_seq_uint32 (n: nat) (s: S.seq U32.t) : Lemma
(requires (n == S.length s))
(ensures (seq_uint32_of_be n (be_of_seq_uint32 s) `S.equal` s))
(decreases n)
[SMTPat (seq_uint32_of_be n (be_of_seq_uint32 s))]
val be_of_seq_uint32_seq_uint32_of_be (n: nat) (s: S.seq U8.t) : Lemma
(requires (4 * n == S.length s))
(ensures (be_of_seq_uint32 (seq_uint32_of_be n s) `S.equal` s))
(decreases n)
[SMTPat (be_of_seq_uint32 (seq_uint32_of_be n s))]
/// Reasoning about slicing such sequences
/// --------------------------------------
///
/// (Needs SMTPats above for roundtripping in their proof, hence why they're at the end.)
val slice_seq_uint32_of_be (n: nat) (s: S.seq U8.t) (lo: nat) (hi: nat) : Lemma
(requires (4 * n == S.length s /\ lo <= hi /\ hi <= n))
(ensures (S.slice (seq_uint32_of_be n s) lo hi) `S.equal` seq_uint32_of_be (hi - lo) (S.slice s (4 * lo) (4 * hi)))
val be_of_seq_uint32_slice (s: S.seq U32.t) (lo: nat) (hi: nat) : Lemma
(requires (lo <= hi /\ hi <= S.length s))
(ensures (be_of_seq_uint32 (S.slice s lo hi) `S.equal` S.slice (be_of_seq_uint32 s) (4 * lo) (4 * hi)))
/// Some reasoning about zero bytes
let rec le_to_n_zeros (s:bytes)
: Lemma
(requires
forall (i:nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures le_to_n s == 0) | false | false | FStar.Endianness.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val le_to_n_zeros (s: bytes)
: Lemma (requires forall (i: nat). i < Seq.length s ==> Seq.index s i == 0uy)
(ensures le_to_n s == 0)
(decreases (Seq.length s)) | [
"recursion"
] | FStar.Endianness.le_to_n_zeros | {
"file_name": "ulib/FStar.Endianness.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | s: FStar.Endianness.bytes
-> FStar.Pervasives.Lemma
(requires
forall (i: Prims.nat). i < FStar.Seq.Base.length s ==> FStar.Seq.Base.index s i == 0uy)
(ensures FStar.Endianness.le_to_n s == 0)
(decreases FStar.Seq.Base.length s) | {
"end_col": 35,
"end_line": 354,
"start_col": 4,
"start_line": 352
} |
Prims.GTot | val mod_spec (a: nat{fits a}) (b: nat{fits b /\ b <> 0}) : GTot (n: nat{fits n}) | [
{
"abbrev": true,
"full_module": "FStar.Int64",
"short_module": "I64"
},
{
"abbrev": false,
"full_module": "FStar.Ghost",
"short_module": null
},
{
"abbrev": true,
"full_module": "FStar.UInt64",
"short_module": "U64"
},
{
"abbrev": true,
"full_module": "FStar.UInt32",
"short_module": "U32"
},
{
"abbrev": true,
"full_module": "FStar.UInt16",
"short_module": "U16"
},
{
"abbrev": false,
"full_module": "FStar.Mul",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar.Pervasives",
"short_module": null
},
{
"abbrev": false,
"full_module": "Prims",
"short_module": null
},
{
"abbrev": false,
"full_module": "FStar",
"short_module": null
}
] | false | let mod_spec (a:nat{fits a}) (b:nat{fits b /\ b <> 0}) : GTot (n:nat{fits n}) =
let open FStar.Mul in
let res = a - ((a/b) * b) in
fits_lte res a;
res | val mod_spec (a: nat{fits a}) (b: nat{fits b /\ b <> 0}) : GTot (n: nat{fits n})
let mod_spec (a: nat{fits a}) (b: nat{fits b /\ b <> 0}) : GTot (n: nat{fits n}) = | false | null | false | let open FStar.Mul in
let res = a - ((a / b) * b) in
fits_lte res a;
res | {
"checked_file": "FStar.SizeT.fsti.checked",
"dependencies": [
"prims.fst.checked",
"FStar.UInt64.fsti.checked",
"FStar.UInt32.fsti.checked",
"FStar.UInt16.fsti.checked",
"FStar.Pervasives.fsti.checked",
"FStar.Mul.fst.checked"
],
"interface_file": false,
"source_file": "FStar.SizeT.fsti"
} | [
"sometrivial"
] | [
"Prims.nat",
"FStar.SizeT.fits",
"Prims.l_and",
"Prims.b2t",
"Prims.op_disEquality",
"Prims.int",
"Prims.unit",
"FStar.SizeT.fits_lte",
"Prims.op_Subtraction",
"FStar.Mul.op_Star",
"Prims.op_Division"
] | [] | module FStar.SizeT
open FStar.Mul
module U16 = FStar.UInt16
module U32 = FStar.UInt32
module U64 = FStar.UInt64
val t : eqtype
val fits (x: nat) : Tot prop
/// According to the C standard, "the bit width of t is not less than 16 since c99"
/// (https://en.cppreference.com/w/c/types/size_t)
val fits_at_least_16 (x:nat)
: Lemma
(requires x < pow2 16)
(ensures fits x)
[SMTPat (fits x)]
[@@noextract_to "krml"]
val v (x: t) : Pure nat
(requires True)
(ensures (fun y -> fits y))
/// We therefore offer two functions to create a t value.
/// Any value that fits in a uint_16 can be cast directly to t
/// Any value that might not fit in a uint_16 needs to satisfy the `fits_u32`
/// or `fits_u64` predicates. These predicates can only be introduced through a
/// stateful function (currently in Steel.ST.HigherArray), which will be extracted
/// to a static_assert by krml
val uint_to_t (x: nat) : Pure t
(requires (fits x))
(ensures (fun y -> v y == x))
/// v and uint_to_t are inverses
val size_v_inj (x: t)
: Lemma
(ensures uint_to_t (v x) == x)
[SMTPat (v x)]
val size_uint_to_t_inj (x: nat)
: Lemma
(requires fits x)
(ensures v (uint_to_t x) == x)
[SMTPat (uint_to_t x)]
val fits_u32 : prop
val fits_u64 : prop
val fits_u64_implies_fits_32 (_:unit)
: Lemma
(requires fits_u64)
(ensures fits_u32)
val fits_u32_implies_fits (x:nat)
: Lemma
(requires fits_u32 /\ x < pow2 32)
(ensures fits x)
val fits_u64_implies_fits (x:nat)
: Lemma
(requires fits_u64 /\ x < pow2 64)
(ensures fits x)
/// Creates a size_t when given a uint32 literal. Note, this will not
/// extract if [x] is not a literal (e.g., 12ul). If you want to do a
/// cast, see `uint32_to_sizet` below
noextract inline_for_extraction
val of_u32 (x: U32.t) : Pure t
(requires fits_u32)
(ensures (fun y -> v y == U32.v x))
/// Creates a size_t when given a uint64 literal. Note, this will not
/// extract if [x] is not a literal (e.g., 12uL). If you want to do a
/// cast, see `uint64_to_sizet` below
noextract inline_for_extraction
val of_u64 (x: U64.t) : Pure t
(requires fits_u64)
(ensures (fun y -> v y == U64.v x))
val uint16_to_sizet (x:U16.t) : Pure t
(requires True)
(ensures fun y -> v y == U16.v x)
val uint32_to_sizet (x:U32.t) : Pure t
(requires fits_u32)
(ensures fun y -> v y == U32.v x)
val uint64_to_sizet (x:U64.t) : Pure t
(requires fits_u64)
(ensures fun y -> v y == U64.v x)
val sizet_to_uint32 (x:t) : Pure U32.t
(requires True)
(ensures fun y -> U32.v y == v x % pow2 32)
val fits_lte (x y: nat) : Lemma
(requires (x <= y /\ fits y))
(ensures (fits x))
[SMTPat (fits x); SMTPat (fits y)]
(** Non-overflowing arithmetic operations *)
val add (x y: t) : Pure t
(requires (fits (v x + v y)))
(ensures (fun z -> v z == v x + v y))
val sub (x y: t) : Pure t
(requires (v x >= v y))
(ensures (fun z -> v z == v x - v y))
val mul (x y: t) : Pure t
(requires (fits (v x * v y)))
(ensures (fun z -> v z == v x * v y))
(** Euclidean division of [a] and [b], with [b] non-zero *)
val div (a:t) (b:t{v b <> 0}) : Pure t
(requires (True))
(ensures (fun c -> v a / v b = v c))
(** Modulo specification, similar to FStar.UInt.mod *) | false | false | FStar.SizeT.fsti | {
"detail_errors": false,
"detail_hint_replay": false,
"initial_fuel": 2,
"initial_ifuel": 1,
"max_fuel": 8,
"max_ifuel": 2,
"no_plugins": false,
"no_smt": false,
"no_tactics": false,
"quake_hi": 1,
"quake_keep": false,
"quake_lo": 1,
"retry": false,
"reuse_hint_for": null,
"smtencoding_elim_box": false,
"smtencoding_l_arith_repr": "boxwrap",
"smtencoding_nl_arith_repr": "boxwrap",
"smtencoding_valid_elim": false,
"smtencoding_valid_intro": true,
"tcnorm": true,
"trivial_pre_for_unannotated_effectful_fns": true,
"z3cliopt": [],
"z3refresh": false,
"z3rlimit": 5,
"z3rlimit_factor": 1,
"z3seed": 0,
"z3smtopt": [],
"z3version": "4.8.5"
} | null | val mod_spec (a: nat{fits a}) (b: nat{fits b /\ b <> 0}) : GTot (n: nat{fits n}) | [] | FStar.SizeT.mod_spec | {
"file_name": "ulib/FStar.SizeT.fsti",
"git_rev": "f4cbb7a38d67eeb13fbdb2f4fb8a44a65cbcdc1f",
"git_url": "https://github.com/FStarLang/FStar.git",
"project_name": "FStar"
} | a: Prims.nat{FStar.SizeT.fits a} -> b: Prims.nat{FStar.SizeT.fits b /\ b <> 0}
-> Prims.GTot (n: Prims.nat{FStar.SizeT.fits n}) | {
"end_col": 5,
"end_line": 129,
"start_col": 2,
"start_line": 126
} |
Subsets and Splits