'''
RSA Encryption/Decryption
'''

import random


'''
Euclid's algorithm for determining the greatest common divisor
Use iteration to make it faster for larger integers
'''
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
'''

# Python program to demonstrate working of extended
# Euclidean Algorithm

# function for extended Euclidean Algorithm
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


'''
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)

    print ('n=', n, ' phi= ', phi)

    #Choose an integer e such that e and phi(n) are coprime
    e = random.randrange(2, phi)

    #Use Euclid's Algorithm to verify that e and phi(n) are comprime
    g = gcd(e, phi)
    while g != 1:
        e = random.randrange(2, 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):
    key, n = pk
    print('key=', key, ' n=', n)
    for char in plaintext:
        print (ord(char))
        print (ord(char)**key % n)
    #Unpack the key into it's components

    #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,q = 4,4
    while not (is_prime(p)) or not (is_prime(q)) or p == q:
        p = int(input("Enter a prime number (17, 19, 23, etc): "))
        q = int(input("Enter another prime number (Not one you entered above): "))
        if not is_prime(p):
            print(p, ' is not prime - Start over')
        if not is_prime(q):
            print(q, ' is not prime - Start over')
        if p == q:
            print ("you've entered equal p and q. Start over")
    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 public key: ")
    encrypted_msg = encrypt(public, message)
    print('encrypted_msg=', encrypted_msg)
    print ("Your encrypted message is: ")
    print (''.join(map(lambda x: str(x), encrypted_msg)))
    print ("Decrypting message with private key ", private ," . . .")
    print ("Your message is:")
    print (decrypt(private, encrypted_msg))