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# AntonKueltz/rsa_factor.py

Created April 1, 2017 03:02
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Factor an RSA modulus given the public and private key
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 def factor(n, e, d): """http://crypto.stackexchange.com/a/25910/17884 n - modulus e - public exponent d - private exponent returns - (p, q) such that n = p*q """ from fractions import gcd from random import randint while True: z = randint(2, n - 2) k, x = 0, e * d - 1 while not x & 1: k += 1 x /= 2 t = pow(z, x, n) if t == 1 or t == (n-1): continue bad_z = False for _ in range(k): u = pow(t, 2, n) if u == -1 % n: bad_z = True break if u == 1: p = gcd(n, t-1) q = gcd(n, t+1) assert n == p * q return p, q else: t = u if bad_z: continue

### HaoPham23 commented Mar 10, 2023 • edited

In case x is big, I think we should replace x /= 2 by x >>= 1