RSA: Common modulus attack.py

 #!/usr/bin/python3.4
   # Written by Anirudh Anand (lucif3r) : email - anirudh@anirudhanand.com   
   # This program will help to decrypt cipher text to plain text if you have
   # more than 1 cipher text encrypted with same Modulus (N) but different
   # exponents. We use extended Euclideangm Algorithm to achieve this.
   
   __author__ = 'lucif3r'
   
   import gmpy2
   
   
   class RSAModuli:
       def __init__(self):
           self.a = 0
           self.b = 0
           self.m = 0
           self.i = 0
       def gcd(self, num1, num2):
           """
           This function os used to find the GCD of 2 numbers.
           :param num1:
           :param num2:
           :return:
           """
           if num1 < num2:
               num1, num2 = num2, num1
           while num2 != 0:
               num1, num2 = num2, num1 % num2
           return num1
       def extended_euclidean(self, e1, e2):
           """
           The value a is the modular multiplicative inverse of e1 and e2.
           b is calculated from the eqn: (e1*a) + (e2*b) = gcd(e1, e2)
           :param e1: exponent 1
           :param e2: exponent 2
           """
           self.a = gmpy2.invert(e1, e2)
           self.b = (float(self.gcd(e1, e2)-(self.a*e1)))/float(e2)
       def modular_inverse(self, c1, c2, N):
           """
           i is the modular multiplicative inverse of c2 and N.
           i^-b is equal to c2^b. So if the value of b is -ve, we
           have to find out i and then do i^-b.
           Final plain text is given by m = (c1^a) * (i^-b) %N
           :param c1: cipher text 1
           :param c2: cipher text 2
           :param N: Modulus
           """
           i = gmpy2.invert(c2, N)
           mx = pow(c1, self.a, N)
           my = pow(i, int(-self.b), N)
           self.m= mx * my % N
          def print_value(self):
           print("Plain Text: ", self.m)
   
   
   def main():
       c = RSAModuli()
       N  =
       c1 =
       c2 =
       e1 =
       e2 =
       c.extended_euclidean(e1, e2)
       c.modular_inverse(c1, c2, N)
       c.print_value()
    
   if __name__ == '__main__':
       main()