Wednesday, January 10, 2018


import random
from math import gcd

def egcd(a, b):
    if a == 0:
        return (b, 0, 1)
        g, y, x = egcd(b % a, a)
        return (g, x - (b // a) * y, y)

def multiplicative_inverse(a, m):
    g, x, y = egcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
        return x % m

Tests to see if a number is prime.
def is_prime(num):
    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

    #Phi is the totient of n
    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)
    #Return public and private keypair
    #Public key is (e, n) and private key is (d, n)
    return ((e, n), (d, n))

def encrypt(pk, plaintext):
    #Unpack the key into it's components
    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 the array of bytes
    return cipher

def decrypt(pk, ciphertext):
    #Unpack the key into its components
    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 the array of bytes as a string
    return ''.join(plain)

if __name__ == '__main__':
    Detect if the script is being run directly by the user
#    print "RSA Encrypter/ Decrypter"
    p = int(input("Enter a prime number (17, 19, 23, etc): "))
    q = int(input("Enter another prime number (Not one you entered above): "))
#    print "Generating your public/private keypairs now . . ."
    public, private = generate_keypair(p, q)
    print ("Your public key is ", public ," and your private key is ", private)
    message = input("Enter a message to encrypt with your private key: ")
    encrypted_msg = encrypt(private, message)
#    print "Your encrypted message is: "
    print (''.join(map(lambda x: str(x), encrypted_msg)))
    print ("Decrypting message with public key ", public ," . . .")
#    print "Your message is:"
    print (decrypt(public, encrypted_msg))

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