def generateKeys(prime_lenght=1536):
"""
Generates Paillier Cryptosystem public and private keys.
The input is the bit size of the primes to be used.
:return tuple: (n,g) the public key
(n_lambda, n_mu) the private key
"""
p = utils.getPrime(prime_lenght)
q = utils.getPrime(prime_lenght)
n = p * q
n_squared = n**2
n_lambda = utils.computeLCM(p, q)
g = utils.getRandomInZ_N2(n)
n_mu = utils.inverseMod(
utils.Lfunction(utils.powMod(g, n_lambda, n_squared), n), n)
while n_mu == None:
g = utils.getRandomInZ_N2(n)
n_mu = utils.inverseMod(
utils.Lfunction(utils.powMod(g, n_lambda, n_squared), n), n)
public_key = PaillierPublicKey(n, g)
private_key = PaillierPrivateKey(n_lambda, n_mu, p, q, public_key)
return public_key, private_key
def encrypt(self, m):
r = utils.getRandomInZ_N(self.n)
g_m = utils.powMod(self.g, m, self.n_squared)
r_n = utils.powMod(r, self.n, self.n_squared)
cipher = (g_m * r_n) % self.n_squared
return int(cipher)
def __init__(self, Lambda, mu, p, q, public_key):
self.Lambda = Lambda
self.mu = mu
self.p = p
self.q = q
self.public_key = public_key
self.h_p = utils.inverseMod(
utils.Lfunction(
utils.powMod(self.public_key.g, (self.p - 1), (self.p**2)),
self.p), self.p)
self.h_q = utils.inverseMod(
utils.Lfunction(
utils.powMod(self.public_key.g, (self.q - 1), (self.q**2)),
self.q), self.q)
self.n_squared = self.public_key.n**2
def decryptCRT(self, c):
c_lambda1 = utils.powMod(c, self.p - 1, self.p**2)
m_p = (utils.Lfunction(c_lambda1, self.p) * self.h_p) % self.p
c_lambda2 = utils.powMod(c, self.q - 1, self.q**2)
m_q = (utils.Lfunction(c_lambda2, self.q) * self.h_q) % self.q
print('m_p: ' + str(m_p))
print()
print('m_q' + str(m_q))
print()
message = utils.crt([m_p], [m_q]) % (self.public_key.n)
return int(message)
def decrypt(self, c):
c_lambda = utils.powMod(c, self.Lambda, self.n_squared)
l = utils.Lfunction(c_lambda, self.public_key.n)
message = (l * self.mu) % self.public_key.n
return int(message)