DH秘钥交换协议

实现思路

参考：这里

具体步骤

• 这个协议使用一个质数p的整数模n乘法群以及其原根g
• Alice与Bob协定使用 p以及base g
• Alice选择一个秘密整数a, 计算A = g**a mod p并发送给Bob。
• Bob选择一个秘密整数b, 计算B = g**b mod p并发送给Alice。
• Alice计算alice_key = B a mod p
• Bob计算bob_key = A b mod p

下面贴出代码

import random
import math
from random import choice

def getRandomPrime(Nmax):
    isPrime = [0]*(Nmax+1)
    primeList = []
    isPrime[2] = 1
    for i in range(3,Nmax,2):
        isPrime[i] = 1
    for i in range(3,int(math.sqrt((Nmax+1)))+1,2):
        if(isPrime[i] == 1):
            for j in range(i*i,Nmax+1,2*i):
                isPrime[j] = 0
    for i in range(2,Nmax+1):
        if (isPrime[i]==1):
            primeList.append(i)
    p , q  = random.sample(primeList,2)
    return p

#根据原根的性质求质数de原根
def getPrimaryRoot(p):
    a = 2
    while True:
        mark = 0
        if a ** (p - 1) % p == 1:
            num = 2
            while num < p - 1:
                if a ** num % p == 1:
                    mark = 1
                num += 1
            if mark == 0:
                return a
        a += 1

def getA_B(g,a,p):
    return (g ** a) % p

def getKey(A_B,a_b,p):
    return (A_B**a_b) % p

if __name__ == "__main__":
    p = getRandomPrime(200)
    g = getPrimaryRoot(p)
    rand_a = random.randint(0, p - 1)
    A = getA_B(g, rand_a, p)
    rand_b = random.randint(0, p - 1)
    B = getA_B(g, rand_b, p)
    alice_key = getKey(B,rand_a,p)
    bob_key = getKey(A,rand_b,p)

    print("step1: ","a:",rand_a," ","g:",g," ","p:",p)
    print("step2: ", "A:", A)
    print("step3: ", "B:", B)
    print("step4: ", "Alice_key:", alice_key)
    print("step5: ", "Bob_key:", bob_key)

下面贴出运行截图