import random
import math
import sys

def rabinMiller(num):
    # Returns True if num is a prime number.

    s = num - 1
    t = 0
    while s % 2 == 0:
        # keep halving s while it is even (and use t
        # to count how many times we halve s)
        s = s // 2
        t += 1

    for trials in range(5): # try to falsify num's primality 5 times
        a = random.randrange(2, num - 1)
        v = pow(a, s, num)
        if v != 1: # this test does not apply if v is 1.
            i = 0
            while v != (num - 1):
                if i == t - 1:
                    return False
                else:
                    i = i + 1
                    v = (v ** 2) % num
    return True


def isPrime(num):
    # Return True if num is a prime number. This function does a quicker
    # prime number check before calling rabinMiller().

    if (num < 2):
        return False # 0, 1, and negative numbers are not prime

    # About 1/3 of the time we can quickly determine if num is not prime
    # by dividing by the first few dozen prime numbers. This is quicker
    # than rabinMiller(), but unlike rabinMiller() is not guaranteed to
    # prove that a number is prime.
    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 num in lowPrimes:
        return True

    # See if any of the low prime numbers can divide num
    for prime in lowPrimes:
        if (num % prime == 0):
            return False

    # If all else fails, call rabinMiller() to determine if num is a prime.
    return rabinMiller(num)


def generateLargePrime(keysize=1024):
    # Return a random prime number of keysize bits in size.
    while True:
        num = random.randrange(2**(keysize-1), 2**(keysize))
        if isPrime(num):
            return num

def inverse(totient,e):
    a=[totient,e]

    while a[-1]!=1:
        #print(a[-1])
        a.append(a[-2]%a[-1])

        # Define a sequence b
    b=[]
    for i in range(len(a)-2):
        b.append(a[i]//a[i+1])

        # Define a sequence c
    c=[0,1]
    for i in range(len(b)):
        c.append(c[-1]*b[i]+c[-2])

        # Mod if necessary
    if len(c)%2==0:
        return c[-1]
    else:
        return totient-c[-1]


def binaryExpo(a,b,mod):
    binarystring = bin(b)[2:]
    product = 1
    #print(binarystring)
    for char in binarystring[::-1]:

        if char == "1":
            product*=a
            product%=mod
        a*=a
        a%=mod
    return product

p = generateLargePrime(20)
q = generateLargePrime(20)
n = p * q
print("p,q ", p,q)
print("Public Key (N): ",p*q)

e = 131071
print("e:",e)
d = inverse((p-1)*(q-1),e)
print("Private key (d): ",d)
print("Computed using extended Euclidean Algorithm")
print("")
def texttoint(text):
    result = 0
    for char in text:
        result*=256
        result+=ord(char)
    return result

def inttohext(num):
    return hex(num)

def intotext(num):
    result = ""
    while num > 0:
        result = chr(num%256)+result
        num //= 256
    return result


textmsg = "HELLO"
print("original message in text: ",textmsg)
message = texttoint(textmsg)
print("original message numeric (m): ",message)

sentmsg = binaryExpo(message,e,p*q)
print("Sent msg (m^e):",sentmsg)
print("Sent msg to text just to show it is garbled (m^e):",intotext(sentmsg))

decodedmsg = binaryExpo(sentmsg,d,p*q)
print("Decoded msg ((m^e)^d):",decodedmsg)
print("Decoded msg to text ((m^e)^d):", intotext(decodedmsg))


