test_paillier

test_paillier.py

from useless.math import *
from Crypto.Util.number import *
import random

def gen_key(bits):
    p = getPrime(bits); q = getPrime(bits)
    n = p*q
    k = random.randint(2, n)
    g = (1 + k*n) % (n**2)

    print("[+] (p, q) :", (p, q))
    print("[+] g :", g)

    return p, q, n, k, g

def L(u):
    return (u-1)//n

def LMD(p, q): # p and q are respectively prime
    g = gcd(p-1, q-1)
    return (p-1)*(q-1)//g

def enc(m):
    r = random.randint(2, n**2)
    s = pow(g, m, n**2)
    t = pow(r, n, n**2)
    return s*t % (n**2)

def dec(c):
    s = L(pow(c, LMD(p, q), n**2))
    t = L(pow(g, LMD(p, q), n**2))
    return s * modinv(t, n) % n

p, q, n, k, g = gen_key(1024)
assert gcd(L(pow(g, LMD(p, q), n**2)), n) == 1

m1 = 114
m2 = 514

assert dec(enc(m1)) == m1
assert dec(enc(m2)) == m2

c1 = enc(m1)
c2 = enc(m2)
print(dec(c1*c2) == m1+m2)