2018计算机安全学——第四次实践性作业

1、用Python或Sage实现RSA算法的加密、解密、签名/验证签名

2、用Python或Sage实现DH秘钥交换协议的。

请提交代码的网页链接，不要提交代码压缩包。

代码如下：

1.

import rsa

(pubkey, privkey) = rsa.newkeys(1024)
# 生成密钥

with open('public.pem','w+') as f:
f.write(pubkey.save_pkcs1().decode())

with open('private.pem','w+') as f:
    f.write(privkey.save_pkcs1().decode())
# 保存密钥

with open('public.pem','r') as f:
    pubkey = rsa.PublicKey.load_pkcs1(f.read().encode())

with open('private.pem','r') as f:
    privkey = rsa.PrivateKey.load_pkcs1(f.read().encode())
# 导入密钥

message = 'secret'

crypto = rsa.encrypt(message.encode(), pubkey)
# 公钥加密

message = rsa.decrypt(crypto, privkey).decode()print(message)
# 私钥解密

signature = rsa.sign(message.encode(), privkey, 'SHA-1')
# 私钥签名

rsa.verify(message.encode(), signature, pubkey)
# 公钥验证

2.

import random
import math

def isprime() :
#素数判断
    count = 1
    while count:
        n = int(input("请输入一个素数p："))
        for i in range(2, n):
           if n % i == 0:
                print("%d不是素数！" % n)
                break
        else:
            return n

def get_generator( p):
#获取一个原根
#素数必存在至少一个原根
#g^(p-1) = 1 (mod p)当且仅当指数为p-1的时候成立
    a=2
    while 1:
        if a**(p-1) % p == 1:
            num = 2
            mark = 0
            while num < p-1:
                if a**num % p == 1:
                    mark = 1
                num += 1
        if mark == 0:
            return a
        a += 1
def get_cal(a, p, rand):
#获得计算数
    cal = (a**rand) % p
    return cal

def get_key(cal_A,cal_B,p):
#获得密钥
    key = (cal_B ** cal_A ) % p
    return key

def Is_sameKey(S_a, S_b):
#判断密钥是否相同
    if S_a == S_b:
        print("A所得的密钥与B相同")
    else:
        print("A所得的密钥与B不相同")

if __name__ == "__main__":
    p = isprime()
    a = get_generator(p)
    print("p的一个原根为%d"%a)
    rand_A = random.randint(0, p-1)
    cal_A = get_cal(a, p, rand_A)
    print("A随机数%d得到的计算数为%d" % (rand_A, cal_A))
    rand_B = random.randint(0, p-1)
    cal_B = get_cal(a, p, rand_B)
    print("B随机数%d得到的计算数为%d" % (rand_B, cal_B))
    S_a = get_key(rand_A, cal_B, p)
    print("A的密钥为%d" % S_a)
    S_b = get_key(rand_B, cal_A, p)
    print("B的密钥为%d" % S_b)
    Is_sameKey(S_a, S_b)