SecCrpytoExp-2

Elgamal 密码

首先用到了几个强大的库（避免重复造轮子）

import sympy
from Crypto.Util import number

sympy用于计算原根，它是一个强大的符号计算的 python 库。不仅可以像 mathematica 一样进行符号计算，也内置了很多的 OI 实用算法，包括图论、计算几何、数论、多项式等等很多方面。

更多用法可以看这里 https://2o181o28.github.io/2019/07/14/sympy%E7%9A%84OI%E7%94%A8%E6%B3%95/

Crypto则是更加强大的密码学库
然后就是 exp 了

'''
Author: M@tr1x
Date: 2020-11-06 17:15:32
LastEditTime: 2020-11-08 12:14:15
Description: Elgamal密码加解密程序
'''


import gmpy2
from Crypto.Util import number
import random
import sympy

class Elgamal():
    def __init__(self,p_length):
        self.p = number.getPrime(p_length)#a random prime number with 2 ^ p_length
        self.x = random.randint(2,self.p-3)#private key
        self.g = sympy.primitive_root(self.p)#the smallest primitive root
        self.y = int(gmpy2.powmod(self.g,self.x,self.p))#public key y

    def encrypt(self,m):
        """crypto function

        Args:
            m (num): plain decimal message

        Returns:
            y1,y2: encrypted k&m
        """
        k = random.randint(1,self.p-2)
        while int(gmpy2.gcd(k,self.p-1))!=1:
            k = random.randint(1,self.p-2)
        y1 = gmpy2.powmod(self.g,k,self.p)
        y2  = (m%self.p)*int(gmpy2.powmod(self.y,k,self.p))%self.p
        y1 = int(y1)

        return y1,y2

    def decrypt(self,y1,y2):
        """decrypto function

        Args:
            y1 (num):
            y2 (num):

        Returns:
            m: plain message
        """
        yi = int(gmpy2.invert(y1,self.p))
        m = int(gmpy2.powmod(yi,self.x,self.p))*(y2%self.p)%self.p
        return m


if __name__ == "__main__":
    new_elgamal = Elgamal(50)
    (y1,y2) = new_elgamal.encrypt(9999999)#encrypt 9999999
    print("y1:"+str(y1))
    print("y2:"+str(y2))
    m = new_elgamal.decrypt(y1,y2)#decrypt y1&y2
    print("m:"+str(m))