RSA加密算法简单介绍以及python实现

coding=gbk

import math
import random

平方乘算法求余数 base^n mod mod

def repeatMod(base, n, mod):

a = 1
while n:
    if n&1:
        a = (a*base)%mod
    base = (base*base)%mod
    n = n>>1
return a

判断是否为素数（Miller-Rabbin）

def IsPrime(BigNum, RoundTime):

temp = BigNum - 1
k = 0
while (temp & 0x1)==0 and temp:
    temp = temp >>1
    k = k+1
m = temp
while RoundTime:
    a = random.randint(1, BigNum- 2)
    b =  repeatMod(a, m, BigNum)
    if b == 1 or b==BigNum-1:
        return True
    for i in range(1,k):
        b = repeatMod(b, 2, BigNum) #若b^2^(k-1) mod n ==+-1,则是一个素数
        if b == 1 or b==BigNum-1:
            return True
    RoundTime = RoundTime -1
return False

生成大素数

def BuildBigPrime():

flag = False
while not flag:
    BigNum = random.randint(2**512,2**513)
    if BigNum % 2 !=0 :
        flag = IsPrime(BigNum, 10)
return BigNum

辗转相除求最大公约数

def MaxCommDivisor(m,n):

if n == 1:
    return True
if m % n == 0:
  return False
else:
    flag = MaxCommDivisor(n, m%n)
return flag

#求 b mod a b的逆元
def get_(a, b):

if b == 0:
    return 1, 0
else:
    k = a // b        
    x1, y1 = get_(b, a % b)
    x, y = y1, (x1 - k * y1)
return x,y

if name == '__main__':

print("[商品期货](https://www.gendan5.com/futures/cf.html)正在生成大素数------")
p = BuildBigPrime()
q = BuildBigPrime()
while p==q:
    q = BuildBigPrime()
print("大素数p:",p,"\n大素数q:",q)
n = p*q
fn = (p-1)*(q-1)
while True:
    key1 = random.randint(2**64,2**65)
    if  MaxCommDivisor(fn, key1):
        break
print("密钥1为:",key1)
k, key2 = get_(fn,key1)
#生成的私钥key2可能为负数，我们需要mod fn来保证其为正数
if key2<0: 
    key2 = key2 % fn
print("密钥2为:",key2)
m = input("请输入明文：")
m = int(m.encode('utf-8').hex(),16)
print('\n------加密中----')
c = repeatMod(m,key1,n)
print("明文为：",m,"\n密文为：",c)
print('\n------解密中----')
m = repeatMod(c,key2,n)
print("密文为：",c,"\n明文为：",m)