import math
from decimal import *
def isPrime(n):#判断是否为素数
    if n <= 1:
        return False
    for i in range(2, int(math.sqrt(n) + 1)):
        if n % i == 0:
            return False
    return True
def crack(n):#质因素分解
    for p in range(2, n):
        for q in range(p+1, n):
            if p*q == n and isPrime(p) and isPrime(q):
                return (p, q)
def extGcd(a, b):#扩展欧几里得可以求出最大公约数
    if a < b:
        return extGcd(b, a)
    if b == 0:
        return a, 1, 0
    gcd, x, y = extGcd(b, a%b)
    return gcd, y, x-a/b*y
def getD(n, e):      #求解私钥d
    p, q = crack(n)
    fai = (p-1)*(q-1)
    gcd, x, y = extGcd(fai, e)
    while y < 0:
        y += fai
    return y
def decrypt(n, e, ciphertext):
    plaintext = []
    d = getD(n, e)
    for num in ciphertext:
        num = num**d % n
        plaintext.append(chr(num))
    return "".join(plaintext)
if __name__ == "__main__":
    print(getD(2449,7))
    n = 2449
    e = 7
    ciphertext = [971,922,605,1446,1704,889,2090,605,1899,
    1915,2088,1988,1235,1032,65,922,958,1988,
    2144,591,1988,2270,2088,1032,65,958,2233]
    plaintext = decrypt(n, e, ciphertext)
    print (plaintext)