RSA_functions.py

# -*- coding: utf-8 -*-
"""
Created on Fri Aug 23 22:17:47 2018

@author: Swapnil Masurekar
Functions of RSA Algorithm
"""

import random


def gcd(a, b):
# GCD by euclid algorithm
    while b != 0:
        a, b = b, a % b
    return a


def modInverse(a, m) :
# Naive metho to find multiplicative inverse
    a = a % m;
    for x in range(1, m) :
        if ((a * x) % m == 1) :
            return x
    return 1


def multiplicative_inverse(e, phi):
#Euclid's extended algorithm for finding the multiplicative inverse of two numbers
    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 is_prime(num):
# Tests to see if a number is prime.
    if num == 2:
        return True
    if num < 2 or num % 2 == 0:
        return False
    for n in range(3, int(num**0.5)+2, 2):
        if num % n == 0:
            return False
    return True

def generate_keypair(p, q):
    if not (is_prime(p) and is_prime(q)):
        raise ValueError('Both numbers must be prime.')
    elif p == q:
        raise ValueError('p and q cannot be equal')
    #n = pq
    n = p * q

    # Calculating phi
    phi = (p-1) * (q-1)

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

    # Use 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)

    # Use Extended Euclid's Algorithm to generate the private key
    d = multiplicative_inverse(e, phi)
    if (d == None): # in case above function returns None
        d = modInverse(e, phi)

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

def encrypt(pk, plaintext):
    key, n = pk
    # Convert each letter in the plaintext to numbers based on the character using a^b mod m
    cipher = [(ord(char) ** key) % n for char in plaintext]
    return cipher

def decrypt(pk, ciphertext):
    key, n = pk
    #Generate the plaintext based on the ciphertext and key using a^b mod m
    plain = [chr((char ** key) % n) for char in ciphertext]
    return ''.join(plain)