RSA算法的加密、解密、签名/验证签名

RSA算法的加密、解密

实现思路

参考：这里，这里

具体步骤

• 在给定范围内随机选择两个不相等的质数p和q
• 计算p和q的乘积n
• 计算n的欧拉函数 φ(n)=（p-1)*(q-1)
• 遍历求模反元素d
• 得到公钥和私钥
• 分别进行加密解密操作

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)
    #使用全局变量，将while里面的取值，取出
    global a,b
    while True:
        p,q = (random.sample(primeList,2))
        if(p!=q):
            a,b = p,q
            break
    return a,b

def gcd(a,b):
    if a < b:
        a, b = b, a
        if(b == 0):
            return a
        while b != 0:
            temp = a % b
            a = b
            b = temp
        return a

def selectE(res):
    while True:
        e = choice(range(100))
        #print(e)
        x = gcd(e,res)
        if ( x == 1 ):
            break
    return e

def findD(e,res):
    for d in range(100000000):
        x = (e*d) % res
        if x==1:
            return d

def encryption(plaintext,public_key):
    ciphertext = pow(plaintext,public_key[1])%public_key[0]
    return ciphertext

def decryption(ciphertext,private_key):
    plaintext = pow(ciphertext,private_key[1])%private_key[0]
    return plaintext
if __name__ == "__main__":
    #在某个范围内随机选取两个不一样的质数
    p,q = getRandomPrime(200)
    n= p*q
    res = (p - 1) * (q - 1)
    e = selectE(res)
    d = findD(e,res)
    print("公钥：(n,e) = ","(", n,",", e,")")
    print("公钥：(n,d) = ","(", n,",", d,")")
    public_key = (n,e)
    private_key = (n,d)
    plaintext = choice(range(100))
    ciphertext = encryption(plaintext,public_key)
    verification = decryption(ciphertext,private_key)
    print("明文：",plaintext)
    print("加密后的密文：",ciphertext)
    print("解密后的明文：",verification)

下面贴出运行截图

运行截图

RSA算法的签名和验证签名#

直接贴出代码

import rsa

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

# 明文
message = 'goodmorning'

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

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