RSA Python和扩展欧几里得算法来生成私钥。 变量为无

Question

Problem with simple RSA encryption algorithm. Extended Euclidean algorithm is used to generate the private key . The problem with multiplicative_inverse(e, phi) method. It is used for finding the multiplicative inverse of two numbers. The function does not return private key correctly. It returns None value.

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I have the following code:

import random

def gcd(a, b):
    while b != 0:
        a, b = b, a % b
    return a

#Euclidean extended algorithm for finding the multiplicative inverse of two numbers
def multiplicative_inverse(e, phi):
    d = 0
    x1 = 0
    x2 = 1
    y1 = 1
    temp_phi = phi

    while e > 0:
        temp1 = temp_phi/e
        temp2 = temp_phi - temp1 * e
        temp_phi = e
        e = temp2

        x = x2- temp1* x1
        y = d - temp1 * y1

        x2 = x1
        x1 = x
        d = y1
        y1 = y

    if temp_phi == 1:
        return d + phi

def generate_keypair(p, q):
    n = p * q

    #Phi is the totient of n
    phi = (p-1) * (q-1)

    #An integer e such that e and phi(n) are coprime
    e = random.randrange(1, phi)

    #Euclid's Algorithm to verify that e and phi(n) are comprime
    g = gcd(e, phi)
    while g != 1:
        e = random.randrange(1, phi)
        g = gcd(e, phi)

    #Extended Euclid's Algorithm to generate the private key
    d = multiplicative_inverse(e, phi)

    #Public key is (e, n) and private key is (d, n)
    return ((e, n), (d, n))


if __name__ == '__main__':
    p = 17
    q = 23

    public, private = generate_keypair(p, q)
    print("Public key is:", public ," and private key is:", private)

Since the variable d in the following line d = multiplicative_inverse(e, phi) contains None value, then during encryption I receive the following error:

TypeError: unsupported operand type(s) for pow(): 'int', 'NoneType', 'int'

Output for the code that I provided in the question:

Public key is: (269, 391) and private key is: (None, 391)

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Question: Why the variable contains None value. How to fix that?

Answer 1

Well I'm not sure about the algorithm itself, and can't tell if you if it's wrong or right, but you only return a value from multiplicative_inverse function when if temp_phi == 1 . Otherwise, the result is None. So I bet your temp_phi != 1 when you run the function. There's probably some mistake in the function's logic.

Answer 2

I think that this is a problem:

if temp_phi == 1:
   return d + phi

This function return some value only under condition that temp_phi is equal to 1, otherwise it will not return any value.

Answer 3

This looks like you are converting from python 2 to 3. In 2 temp_phi/e will be an integer, but in 3 it's a float. As the multiplative inverses method of division uses integers you need to change the line to int(temp_phi / e) or temp_phi // e