import crybas
from random import randint

# shamir

def shamir(m):
    p = crybas.prime_generate()

    if m > p:
        return "error: message too long."

    # Limits
    down_limit = 10 ** 7
    up_limit = 10 ** 9

    # Alice

    # Ca generation
    while True:
        Ca = randint(down_limit, up_limit)
        if crybas.extended_gcd(Ca, p - 1)[0] == 1:
            break
    # Da generation
    Da = crybas.extended_gcd(Ca, p - 1)[1]
    if Da < 0:
        Da += p - 1

    # Bob

    # Cb generation
    while True:
        Cb = randint(down_limit, up_limit)
        if crybas.extended_gcd(Cb, p - 1)[0] == 1:
            break
    # Db generation
    Db = crybas.extended_gcd(Cb, p - 1)[1]
    if Db < 0:
        Db += p - 1

    # Alice
    x1 = crybas.fast_pow(m, Ca, p)
    # Bob
    x2 = crybas.fast_pow(x1, Cb, p)
    # Alice
    x3 = crybas.fast_pow(x2, Da, p)
    # Bob
    x4 = crybas.fast_pow(x3, Db, p)

    return x4

# shamir



# elgamal

def elgamal(m):
    p = crybas.prime_generate()
    g = crybas.g_generate(p)

    if m > p:
        return "error: message too long."

    # Alice
    k = randint(1, p - 1)
    a = crybas.fast_pow(g, k, p)
    x = randint(1, p)
    y = crybas.fast_pow(g, x, p)
    b = crybas.fast_pow_multiplicate(y, k, p, m)

    # Bob
    m_from_alice = crybas.fast_pow_multiplicate(a, p - 1 - x, p, b)

    return m_from_alice


# elgamal



# vernam

def vernam(m):
    k = randint(1, 1000000000)
    e = m ^ k
    e_decrypt = e ^ k

    return e_decrypt

# vernam



# rsa

def rsa(m):
    p = crybas.prime_generate()
    q = crybas.prime_generate()
    n = p * q

    if m > n:
        return "Error: message too long."

    f = (p - 1) * (q - 1)
    d = randint(1, f)
    while True:
        if crybas.extended_gcd(d, f)[0] == 1:
            break
        d = randint(1, f)

    c = crybas.extended_gcd(f, d)[2]
    if c < 0:
        c += f

    e = crybas.fast_pow(m, d, n)
    m_from_alice = crybas.fast_pow(e, c, n)

    return m_from_alice

# rsa


def use_ciphers():
    m = randint(1, 1000000)
    print("message:", m)
    print("***********************")
    print("shamir:", shamir(m))
    print("elgamal:", elgamal(m))
    print("vernam:", vernam(m))
    print("rsa:", rsa(m))


use_ciphers()