Spaces:
Running
Running
File size: 8,615 Bytes
ba2f5d6 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 |
#
# ElGamal.py : ElGamal encryption/decryption and signatures
#
# Part of the Python Cryptography Toolkit
#
# Originally written by: A.M. Kuchling
#
# ===================================================================
# The contents of this file are dedicated to the public domain. To
# the extent that dedication to the public domain is not available,
# everyone is granted a worldwide, perpetual, royalty-free,
# non-exclusive license to exercise all rights associated with the
# contents of this file for any purpose whatsoever.
# No rights are reserved.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
# BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
# ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
# ===================================================================
__all__ = ['generate', 'construct', 'ElGamalKey']
from Crypto import Random
from Crypto.Math.Primality import ( generate_probable_safe_prime,
test_probable_prime, COMPOSITE )
from Crypto.Math.Numbers import Integer
# Generate an ElGamal key with N bits
def generate(bits, randfunc):
"""Randomly generate a fresh, new ElGamal key.
The key will be safe for use for both encryption and signature
(although it should be used for **only one** purpose).
Args:
bits (int):
Key length, or size (in bits) of the modulus *p*.
The recommended value is 2048.
randfunc (callable):
Random number generation function; it should accept
a single integer *N* and return a string of random
*N* random bytes.
Return:
an :class:`ElGamalKey` object
"""
obj=ElGamalKey()
# Generate a safe prime p
# See Algorithm 4.86 in Handbook of Applied Cryptography
obj.p = generate_probable_safe_prime(exact_bits=bits, randfunc=randfunc)
q = (obj.p - 1) >> 1
# Generate generator g
while 1:
# Choose a square residue; it will generate a cyclic group of order q.
obj.g = pow(Integer.random_range(min_inclusive=2,
max_exclusive=obj.p,
randfunc=randfunc), 2, obj.p)
# We must avoid g=2 because of Bleichenbacher's attack described
# in "Generating ElGamal signatures without knowning the secret key",
# 1996
if obj.g in (1, 2):
continue
# Discard g if it divides p-1 because of the attack described
# in Note 11.67 (iii) in HAC
if (obj.p - 1) % obj.g == 0:
continue
# g^{-1} must not divide p-1 because of Khadir's attack
# described in "Conditions of the generator for forging ElGamal
# signature", 2011
ginv = obj.g.inverse(obj.p)
if (obj.p - 1) % ginv == 0:
continue
# Found
break
# Generate private key x
obj.x = Integer.random_range(min_inclusive=2,
max_exclusive=obj.p-1,
randfunc=randfunc)
# Generate public key y
obj.y = pow(obj.g, obj.x, obj.p)
return obj
def construct(tup):
r"""Construct an ElGamal key from a tuple of valid ElGamal components.
The modulus *p* must be a prime.
The following conditions must apply:
.. math::
\begin{align}
&1 < g < p-1 \\
&g^{p-1} = 1 \text{ mod } 1 \\
&1 < x < p-1 \\
&g^x = y \text{ mod } p
\end{align}
Args:
tup (tuple):
A tuple with either 3 or 4 integers,
in the following order:
1. Modulus (*p*).
2. Generator (*g*).
3. Public key (*y*).
4. Private key (*x*). Optional.
Raises:
ValueError: when the key being imported fails the most basic ElGamal validity checks.
Returns:
an :class:`ElGamalKey` object
"""
obj=ElGamalKey()
if len(tup) not in [3,4]:
raise ValueError('argument for construct() wrong length')
for i in range(len(tup)):
field = obj._keydata[i]
setattr(obj, field, Integer(tup[i]))
fmt_error = test_probable_prime(obj.p) == COMPOSITE
fmt_error |= obj.g<=1 or obj.g>=obj.p
fmt_error |= pow(obj.g, obj.p-1, obj.p)!=1
fmt_error |= obj.y<1 or obj.y>=obj.p
if len(tup)==4:
fmt_error |= obj.x<=1 or obj.x>=obj.p
fmt_error |= pow(obj.g, obj.x, obj.p)!=obj.y
if fmt_error:
raise ValueError("Invalid ElGamal key components")
return obj
class ElGamalKey(object):
r"""Class defining an ElGamal key.
Do not instantiate directly.
Use :func:`generate` or :func:`construct` instead.
:ivar p: Modulus
:vartype d: integer
:ivar g: Generator
:vartype e: integer
:ivar y: Public key component
:vartype y: integer
:ivar x: Private key component
:vartype x: integer
"""
#: Dictionary of ElGamal parameters.
#:
#: A public key will only have the following entries:
#:
#: - **y**, the public key.
#: - **g**, the generator.
#: - **p**, the modulus.
#:
#: A private key will also have:
#:
#: - **x**, the private key.
_keydata=['p', 'g', 'y', 'x']
def __init__(self, randfunc=None):
if randfunc is None:
randfunc = Random.new().read
self._randfunc = randfunc
def _encrypt(self, M, K):
a=pow(self.g, K, self.p)
b=( pow(self.y, K, self.p)*M ) % self.p
return [int(a), int(b)]
def _decrypt(self, M):
if (not hasattr(self, 'x')):
raise TypeError('Private key not available in this object')
r = Integer.random_range(min_inclusive=2,
max_exclusive=self.p-1,
randfunc=self._randfunc)
a_blind = (pow(self.g, r, self.p) * M[0]) % self.p
ax=pow(a_blind, self.x, self.p)
plaintext_blind = (ax.inverse(self.p) * M[1] ) % self.p
plaintext = (plaintext_blind * pow(self.y, r, self.p)) % self.p
return int(plaintext)
def _sign(self, M, K):
if (not hasattr(self, 'x')):
raise TypeError('Private key not available in this object')
p1=self.p-1
K = Integer(K)
if (K.gcd(p1)!=1):
raise ValueError('Bad K value: GCD(K,p-1)!=1')
a=pow(self.g, K, self.p)
t=(Integer(M)-self.x*a) % p1
while t<0: t=t+p1
b=(t*K.inverse(p1)) % p1
return [int(a), int(b)]
def _verify(self, M, sig):
sig = [Integer(x) for x in sig]
if sig[0]<1 or sig[0]>self.p-1:
return 0
v1=pow(self.y, sig[0], self.p)
v1=(v1*pow(sig[0], sig[1], self.p)) % self.p
v2=pow(self.g, M, self.p)
if v1==v2:
return 1
return 0
def has_private(self):
"""Whether this is an ElGamal private key"""
if hasattr(self, 'x'):
return 1
else:
return 0
def can_encrypt(self):
return True
def can_sign(self):
return True
def publickey(self):
"""A matching ElGamal public key.
Returns:
a new :class:`ElGamalKey` object
"""
return construct((self.p, self.g, self.y))
def __eq__(self, other):
if bool(self.has_private()) != bool(other.has_private()):
return False
result = True
for comp in self._keydata:
result = result and (getattr(self.key, comp, None) ==
getattr(other.key, comp, None))
return result
def __ne__(self, other):
return not self.__eq__(other)
def __getstate__(self):
# ElGamal key is not pickable
from pickle import PicklingError
raise PicklingError
# Methods defined in PyCrypto that we don't support anymore
def sign(self, M, K):
raise NotImplementedError
def verify(self, M, signature):
raise NotImplementedError
def encrypt(self, plaintext, K):
raise NotImplementedError
def decrypt(self, ciphertext):
raise NotImplementedError
def blind(self, M, B):
raise NotImplementedError
def unblind(self, M, B):
raise NotImplementedError
def size(self):
raise NotImplementedError
|