import random
from functools import reduce
from math import floor, log2

from params import a, b, c, d, e, f, g, h, i, j, k, m, n, o, p, q, r, u, v, w


# a < b => b
# (a // b) * c + (a % b)
def wut(a, b, c):
    def wuuuuut(z):
        if z <= b:
            return z
        x, y = divmod(z, b)
        return wuuuuut(x * c + y)

    return wuuuuut(a)


def wutwut(a, b, c, d):
    return reduce(
        lambda x, y: (
            wut(x * x, c, d) if not (b >> y) & 1 else wut(wut(x * x, c, d) * a, c, d)
        ),
        reversed(range(floor(log2(b)))),
        wut(a, c, d),
    )


def rsa_decrypt(ciphertext):
    s = wutwut(wut(ciphertext, o, p), a * b + c * d, o, p)
    t = wutwut(wut(ciphertext, q, r), f * g + h * i, q, r)

    x = s - t
    y = (x * j + x * k) * u
    x = y * r
    y = t + v + y * m
    return (y - x - w) % n


# check if the code works correctly :)
for _ in range(1000):
    # encrypt 100 random plaintexts with public key
    random_plaintext = random.randint(0, n - 1)
    print(random_plaintext)

    # verify that the decryption works correctly
    assert rsa_decrypt(pow(random_plaintext, e, n)) == random_plaintext