rsa.py

import random



#Euclid's algorithm for determining the greatest common divisor

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



#Euclid's extended algorithm for finding the multiplicative inverse of two numbers
def multiplicative_inverse(a, m) : 
    a = a % m; 
    for x in range(1, m) : 
        if ((a * x) % m == 1) : 
            return x 
    return 1


#Tests to see if a number is prime.
    

def is_prime(n):
  if n == 2 or n == 3: return True
  if n < 2 or n%2 == 0: return False
  if n < 9: return True
  if n%3 == 0: return False
  r = int(n**0.5)
  f = 5
  while f <= r:
    print('\t',f)
    if n%f == 0: return False
    if n%(f+2) == 0: return False
    f +=6
  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)

    #chose a random integer e and phi and Use Euclid's Algorithm to verify that e and phi(n) are comprime
    e = random.randrange(1, phi)
    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(public_key, plaintext):
    #into components
    key, n = public_key
    #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(private_key, ciphertext):
    #key into components
    key, n = private_key
    #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(public, 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(private, encrypted_msg))