Erba Aitbayev &#39;KZ&#39; - 1 year ago 211
Python Question

# RSA Python & Extended Euclidean algorithm to generate the private key. Variable is None

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.

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)

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

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.