2014-11-03 10:49:17 -05:00

107 lines
2.6 KiB
Python

import math
import primes
def invmod(a, p, maxiter=1000000):
"""The multiplicitive inverse of a in the integers modulo p:
a * b == 1 mod p
Returns b.
(http://code.activestate.com/recipes/576737-inverse-modulo-p/)"""
if a == 0:
raise ValueError('0 has no inverse mod %d' % p)
r = a
d = 1
for i in xrange(min(p, maxiter)):
d = ((p // r + 1) * d) % p
r = (d * a) % p
if r == 1:
break
else:
raise ValueError('%d has no inverse mod %d' % (a, p))
return d
def modpow(base, exponent, modulus):
"""Modular exponent:
c = b ^ e mod m
Returns c.
(http://www.programmish.com/?p=34)"""
result = 1
while exponent > 0:
if exponent & 1 == 1:
result = (result * base) % modulus
exponent = exponent >> 1
base = (base * base) % modulus
return result
class PrivateKey(object):
def __init__(self, p, q, n):
self.l = (p-1) * (q-1)
self.m = invmod(self.l, n)
class PublicKey(object):
def __init__(self, n):
self.n = n
self.n_sq = n * n
self.g = n + 1
def generate_keypair(bits):
p = primes.generate_prime(bits / 2)
q = primes.generate_prime(bits / 2)
n = p * q
return PrivateKey(p, q, n), PublicKey(n)
def encrypt(pub, plain):
while True:
r = primes.generate_prime(long(round(math.log(pub.n, 2))))
if r > 0 and r < pub.n:
break
x = pow(r, pub.n, pub.n_sq)
cipher = (pow(pub.g, plain, pub.n_sq) * x) % pub.n_sq
return cipher
def e_add(pub, a, b):
"""Add one encrypted integer to another"""
return a * b % pub.n_sq
def e_add_const(pub, a, n):
"""Add constant n to an encrypted integer"""
return a * modpow(pub.g, n, pub.n_sq) % pub.n_sq
def e_mul_const(pub, a, n):
"""Multiplies an ancrypted integer by a constant"""
return modpow(a, n, pub.n_sq)
def decrypt(priv, pub, cipher):
x = pow(cipher, priv.l, pub.n_sq) - 1
plain = ((x // pub.n) * priv.m) % pub.n
return plain
if __name__ == '__main__':
print "Generating keypair..."
priv, pub = generate_keypair(512)
x = 3
print "x =", x
print "Encrypting x..."
cx = encrypt(pub, x)
print "cx =", cx
y = 5
print "y =", y
print "Encrypting y..."
cy = encrypt(pub, y)
print "cy =", cy
print "Computing cx + cy..."
cz = e_add(pub, cx, cy)
print "cz =", cz
print "Decrypting cz..."
z = decrypt(priv, pub, cz)
print "z =", z
print "Computing decrypt((cz + 2) * 3) ..."
print "result =", decrypt(priv, pub,
e_mul_const(pub, e_add_const(pub, cz, 2), 3))