RSA加密算法

#include <iostream>;#include <time.h> using namespace std;void getPrimeNumber(int &x,int &y);//生成x，y两个素数(小的)bool checkIsPrime(int x);//检查是否为素数int gcd(int x, int y);//最大公约数函数  int ectgcd(int c, int d);//乘法逆元函数，求模反元素 int Power(int a, int m, int n);//求幂bool conPrime(int x,int y);int main() {srand((unsigned)time(NULL));int p, q;//得到两个getPrimeNumber(p,q);cout << "素数p:" << p << "  素数q:" << q << endl;//计算p和q的乘积nint n = p*q;cout << "乘积n:" << n  << endl;//计算n的欧拉函数φ(n)int phi = (p-1)*(q-1);//随机选择一个整数e，条件是1< e < φ(n)，且e与φ(n) 互质。cout << "欧拉函数phi:" << phi << endl;int e;e = rand()*phi;while (!conPrime(e, phi)) {e = rand()%phi;}cout << "公钥e:" << e << endl;//计算e对于φ(n)的模反元素d。int d = ectgcd(e,phi);cout << "模反元素d,也就是密钥:" << d << endl;//将n和e封装成公钥，n和d封装成私钥//公钥负责加密，私钥负责解密;私钥负责签名，公钥负责验证cout << "公钥n=" << n << ",e=" << e << endl;cout << "私钥n=" << n << ",d=" << d << endl;int clearText = 99;int result;cout << "加密前" << clearText << endl;int cipher;//加密cipher = Power(clearText,e,n);cout << "加密后" << cipher << endl;//解密result= Power(cipher, d, n);cout << "解密后：" << result << endl;}void getPrimeNumber(int & x, int & y){x = rand() % 1000;y =rand() % 1000;while (!checkIsPrime(x)) {x = rand() % 1000;}while (!checkIsPrime(y)) {y = rand() % 1000;while (y == x) {y = rand() % 1000;}}}bool checkIsPrime(int x){int i, j;for (i = 2, j = int(sqrt(x)); i <= j; i++)if (x%i == 0)  return false;return true;}int ectgcd(int c, int d){int r0, r1, y, s, t, s0, s1, t0, t1, q, r;r0 = d;r1 = c%d;if (r1 == 1){y = 1;}else{s0 = 1;s1 = 0;t0 = 0;t1 = 1;while (r0%r1 != 0){q = r0 / r1;r = r0%r1;r0 = r1;r1 = r;s = s0 - q*s1;s0 = s1;s1 = s;t = t0 - q*t1;t0 = t1;t1 = t;if (r == 1){if (t>0){y = t;}else if (t<0){y = t + d;}}}}return y;}int Power(int a, int m, int n){if (m == 1) return a%n;if (m == 2) return a*a%n;if (m % 2 == 1) {int temp = Power(a, m / 2, n) % n;temp = temp*temp%n;temp = temp*a%n;return temp;}else {int temp = Power(a, m / 2, n) % n;temp = temp*temp%n;return temp;}}bool conPrime(int x, int y){//判断互为质数只需要检查最大公约数是否为1即可。if (gcd(x, y) == 1)return true;else return false;}int gcd(int x, int y){int m;while (y != 0){m = x%y;x = y;y = m;}return (x);}