Public Key Encryption (RSA) (Python recipe) by Mohammad Taha Jahangir

Forked from Recipe 577737 (Python 3 / Unicode support / Key serializing / PEP8)

ActiveState Code (http://code.activestate.com/recipes/578797/)

# coding=utf-8
from __future__ import division, absolute_import, print_function
from base64 import b64encode
from fractions import gcd
from random import randrange
from collections import namedtuple
from math import log
from binascii import hexlify, unhexlify
import sys


PY3 = sys.version_info[0] == 3
if PY3:
    binary_type = bytes
    range_func = range
else:
    binary_type = str
    range_func = xrange


def is_prime(n, k=30):
    # http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
    if n <= 3:
        return n == 2 or n == 3
    neg_one = n - 1

    # write n-1 as 2^s*d where d is odd
    s, d = 0, neg_one
    while not d & 1:
        s, d = s + 1, d >> 1
    assert 2 ** s * d == neg_one and d & 1

    for _ in range_func(k):
        a = randrange(2, neg_one)
        x = pow(a, d, n)
        if x in (1, neg_one):
            continue
        for _ in range_func(s - 1):
            x = x ** 2 % n
            if x == 1:
                return False
            if x == neg_one:
                break
        else:
            return False
    return True


def randprime(n=10 ** 8):
    p = 1
    while not is_prime(p):
        p = randrange(n)
    return p


def multinv(modulus, value):
    """
        Multiplicative inverse in a given modulus

        >>> multinv(191, 138)
        18
        >>> multinv(191, 38)
        186
        >>> multinv(120, 23)
        47
    """
    # http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
    x, lastx = 0, 1
    a, b = modulus, value
    while b:
        a, q, b = b, a // b, a % b
        x, lastx = lastx - q * x, x
    result = (1 - lastx * modulus) // value
    if result < 0:
        result += modulus
    assert 0 <= result < modulus and value * result % modulus == 1
    return result


KeyPair = namedtuple('KeyPair', 'public private')
Key = namedtuple('Key', 'exponent modulus')


def keygen(n, public=None):
    """ Generate public and private keys from primes up to N.

    Optionally, specify the public key exponent (65537 is popular choice).

        >>> pubkey, privkey = keygen(2**64)
        >>> msg = 123456789012345
        >>> coded = pow(msg, *pubkey)
        >>> plain = pow(coded, *privkey)
        >>> assert msg == plain

    """
    # http://en.wikipedia.org/wiki/RSA
    prime1 = randprime(n)
    prime2 = randprime(n)
    composite = prime1 * prime2
    totient = (prime1 - 1) * (prime2 - 1)
    if public is None:
        private = None
        while True:
            private = randrange(totient)
            if gcd(private, totient) == 1:
                break
        public = multinv(totient, private)
    else:
        private = multinv(totient, public)
    assert public * private % totient == gcd(public, totient) == gcd(private, totient) == 1
    assert pow(pow(1234567, public, composite), private, composite) == 1234567
    return KeyPair(Key(public, composite), Key(private, composite))


def encode(msg, pubkey, verbose=False):
    chunksize = int(log(pubkey.modulus, 256))
    outchunk = chunksize + 1
    outfmt = '%%0%dx' % (outchunk * 2,)
    bmsg = msg if isinstance(msg, binary_type) else msg.encode('utf-8')
    result = []
    for start in range_func(0, len(bmsg), chunksize):
        chunk = bmsg[start:start + chunksize]
        chunk += b'\x00' * (chunksize - len(chunk))
        plain = int(hexlify(chunk), 16)
        coded = pow(plain, *pubkey)
        bcoded = unhexlify((outfmt % coded).encode())
        if verbose:
            print('Encode:', chunksize, chunk, plain, coded, bcoded)
        result.append(bcoded)
    return b''.join(result)


def decode(bcipher, privkey, verbose=False):
    chunksize = int(log(privkey.modulus, 256))
    outchunk = chunksize + 1
    outfmt = '%%0%dx' % (chunksize * 2,)
    result = []
    for start in range_func(0, len(bcipher), outchunk):
        bcoded = bcipher[start: start + outchunk]
        coded = int(hexlify(bcoded), 16)
        plain = pow(coded, *privkey)
        chunk = unhexlify((outfmt % plain).encode())
        if verbose:
            print('Decode:', chunksize, chunk, plain, coded, bcoded)
        result.append(chunk)
    return b''.join(result).rstrip(b'\x00').decode('utf-8')


def key_to_str(key):
    """
    Convert `Key` to string representation
    >>> key_to_str(Key(50476910741469568741791652650587163073, 95419691922573224706255222482923256353))
    '25f97fd801214cdc163796f8a43289c1:47c92a08bc374e96c7af66eb141d7a21'
    """
    return ':'.join((('%%0%dx' % ((int(log(number, 256)) + 1) * 2)) % number) for number in key)


def str_to_key(key_str):
    """
    Convert string representation to `Key` (assuming valid input)
    >>> (str_to_key('25f97fd801214cdc163796f8a43289c1:47c92a08bc374e96c7af66eb141d7a21') ==
    ...  Key(exponent=50476910741469568741791652650587163073, modulus=95419691922573224706255222482923256353))
    True
    """
    return Key(*(int(number, 16) for number in key_str.split(':')))


def main():
    import doctest
    print(doctest.testmod())

    pubkey, privkey = keygen(2 ** 64)
    msg = u'the quick brown fox jumped over the lazy dog ® ⌀'
    h = encode(msg, pubkey, True)
    p = decode(h, privkey, True)
    print('-' * 20)
    print('message:', msg)
    print('encoded:', b64encode(h).decode())
    print('decoded:', p)
    print('private key:', key_to_str(privkey))
    print('public key:', key_to_str(pubkey))

if __name__ == '__main__':
    main()