# Python RSA implementation

import lib.arithmetics as arithm
import lib.miller_rabin as miller

def get_p_and_q(n: int) -> (int, int):
    # Get two random prime numbers
    p = miller.get_random_prime(n)
    q = miller.get_random_prime(n)
    # Ensure the two numbers are differents
    while p == q:
        q = get_random_prime(n)
    return (p, q)

def get_keys(l: int) -> int:
    # Get p and q
    p, q = get_p_and_q(l // 2)
    # Compute n and phy(n)
    n = p * q 
    phy_n = (p - 1) * (q - 1)
    # Chose e = 65537
    e = 65537
    # Ensure e fits with the others numbers
    while arithm.gcd(e, phy_n) != 1:
        p, q = get_p_and_q(l // 2)
        n = p * q 
        phy_n = (p - 1) * (q - 1)
    # Compute d
    d = arithm.mod_inverse(e, phy_n)
    # Return e, d and n
    return (e, d, n)

def encrypt(m: int, e: int, n: int) -> int:
    return arithm.modpow(m, e, n)

def decrypt(c: int, d: int, n: int) -> int:
    return arithm.modpow(c, d, n)