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fermat.py
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fermat.py
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# -*- coding: utf-8 -*-
import math
from rsa import RSA
def factorisation_fermat(n):
if (n % 2 == 0):
return (-1, -1)
A = math.ceil(math.sqrt(n))
Bsq = A * A - n
sq = (int) (math.sqrt(Bsq))
while sq * sq != Bsq:
A = A + 1
Bsq = A * A - n
sq = (int) (math.sqrt(Bsq))
return (A - sq, A + sq)
def crack_primes(n):
p,q = factorisation_fermat(n)
if p == -1:
return None
return (p, q)
def crack_msg(msg, n):
primes = crack_primes(n)
if not primes:
print("Could not crack message with Fermat factorisation algorithm")
return None
(p, q) = primes
r = RSA.generate(p, q)
return r.decrypt(msg)
if __name__ == "__main__":
original_msg = "Hello, world! This is my very secret message."
print("Encrypting:", original_msg)
r = RSA.generate(661, 673)
encrypted_msg = r.encrypt(original_msg)
# print("Encrypted data:", encrypted_msg)
print(10 * '*', "Cracking with Fermat factorisation", 10 * '*')
cracked_msg = crack_msg(encrypted_msg, r.n)
print("Got:", cracked_msg)
print("Success!" if cracked_msg == original_msg else "Failure.")