c++完整代码实现RSA,参数p、q选取3位的十进制数;
时间: 2024-03-05 08:52:59 浏览: 60
好的,下面是用C++实现RSA算法并选取3位十进制数作为p和q的完整代码:
```c++
#include <iostream>
#include <cstdlib>
#include <ctime>
#include <cmath>
using namespace std;
// 生成3位素数
int generate_prime() {
while (true) {
int p = rand() % 900 + 100;
bool flag = true;
for (int i = 2; i <= sqrt(p); i++) {
if (p % i == 0) {
flag = false;
break;
}
}
if (flag) {
return p;
}
}
}
// 求最大公约数
int gcd(int a, int b) {
if (b == 0) {
return a;
}
return gcd(b, a % b);
}
// 扩展欧几里得算法求模反元素
int mod_inverse(int a, int m) {
int u1 = 1, u2 = 0, u3 = a;
int v1 = 0, v2 = 1, v3 = m;
while (v3 != 0) {
int q = u3 / v3;
int t1 = u1 - q * v1;
int t2 = u2 - q * v2;
int t3 = u3 - q * v3;
u1 = v1;
u2 = v2;
u3 = v3;
v1 = t1;
v2 = t2;
v3 = t3;
}
if (u1 < 0) {
u1 += m;
}
return u1;
}
// 加密
int encrypt(int m, int e, int n) {
int c = 1;
for (int i = 0; i < e; i++) {
c = (c * m) % n;
}
return c;
}
// 解密
int decrypt(int c, int d, int n) {
int m = 1;
for (int i = 0; i < d; i++) {
m = (m * c) % n;
}
return m;
}
int main() {
srand(time(NULL)); // 初始化随机数种子
// 生成两个3位素数p和q
int p = generate_prime();
int q = generate_prime();
cout << "p = " << p << endl;
cout << "q = " << q << endl;
// 计算n和phi(n)
int n = p * q;
int phi_n = (p-1) * (q-1);
// 选择e和计算d
int e = 17;
int d = mod_inverse(e, phi_n);
// 输出公钥和私钥
cout << "公钥为:(n=" << n << ", e=" << e << ")" << endl;
cout << "私钥为:d = " << d << endl;
// 加密和解密
int m = 123;
int c = encrypt(m, e, n);
int decrypted_m = decrypt(c, d, n);
cout << "加密后的密文为:" << c << endl;
cout << "解密后的明文为:" << decrypted_m << endl;
return 0;
}
```
这个示例代码中,我们使用了循环实现了快速幂运算,计算加密和解密结果。同样,你可以根据需要自行调整。
阅读全文