rsa.py

import random

def rabinMiller(n, d):
  a = random.randint(2, (n - 2) - 2)
  x = pow(a, int(d), n) # a^d%n
  if x == 1 or x == n - 1:
    return True

  while d != n - 1:
    x = pow(x, 2, n)
    d *= 2

    if x == 1:
      return False
    elif x == n - 1:
      return True

  return False

def isPrime(n):
  if n < 2:
      return False

  lowPrimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]

  if n in lowPrimes:
      return True

  for prime in lowPrimes:
    if n % prime == 0:
      return False

  c = n - 1
  while c % 2 == 0:
    c /= 2

  for i in range(128):
    if not rabinMiller(n, c):
      return False

  return True

def generateKeys(keysize=110000):
  e = d = N = 0
  p = generateLargePrime(keysize)
  q = generateLargePrime(keysize)
  N = p * q
  print(f"p {p} | q {q}")

  phiN = (p - 1) * (q - 1)
  while True:
    e = random.randrange(2 ** (keysize - 1), 2 ** keysize - 1)
    if (isCoPrime(e, phiN)):
        break
  d = modularInv(e, phiN)

  return e, d, N

def generateLargePrime(keysize):
  while True:
    num = random.randrange(2 ** (keysize - 1), 2 ** keysize - 1)
    if (isPrime(num)):
      return num

def isCoPrime(p, q):
  return gcd(p, q) == 1

def gcd(p, q):
  while q:
    p, q = q, p % q
  return p

def egcd(a, b):
  s = 0; old_s = 1
  t = 1; old_t = 0
  r = b; old_r = a
  while r != 0:
    quotient = old_r // r
    old_r, r = r, old_r - quotient * r
    old_s, s = s, old_s - quotient * s
    old_t, t = t, old_t - quotient * t
  return old_r, old_s, old_t

def modularInv(a, b):
  gcd, x, y = egcd(a, b)
  if x < 0:
    x += b
  return x

def encrypt(e, N, msg):
  cipher = ""
  for c in msg:
    m = ord(c)
    cipher += str(pow(m, e, N)) + " "
  return cipher

def decrypt(d, N, cipher):
  msg = ""
  parts = cipher.split()
  for part in parts:
    if part:
      c = int(part)
      msg += chr(pow(c, d, N))
  return msg

def main():

    keysize = 4

    print(f"size  {2**(keysize - 1)} - {2**keysize -1} ")

    e, d, N = generateKeys(keysize)

    msg = "hung nho nguyen minh"

    enc = encrypt(e, N, msg)

    print(f"Message: {msg}")
    print(f"e: {e}")
    print(f"N: {N}")
    print(f"enc: {enc}")

main()