rsa加密算法C++

RSA加密算法是一种非对称加密算法，通过生成公钥和私钥，使用公钥加密信息，只有使用相应的私钥才能解密。下面是一个简单的RSA加密实现的C++代码示例：

#include <iostream>
#include <cmath>
#include <cstdlib>
#include <ctime>

using namespace std;

bool is_prime(int num) 
{
    if (num < 2) {
        return false;
    }
    for (int i = 2; i <= sqrt(num); i++) {
        if (num % i == 0) {
            return false;
        }
    }
    return true;
}

int gcd(int a, int b) 
{
    if (b == 0) {
        return a;
    }
    return gcd(b, a % b);
}

int generate_prime() 
{
    int num;
    do {
        num = rand() % 100 + 1;
    } while (!is_prime(num));
    return num;
}

int generate_coprime(int phi_n) 
{
    int e;
    do {
        e = rand() % (phi_n - 2) + 2;
    } while (gcd(e, phi_n) != 1);
    return e;
}

int extended_euclidean(int a, int b, int& x, int& y) 
{
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }
    int x1, y1;
    int d = extended_euclidean(b, a % b, x1, y1);
    x = y1;
    y = x1 - (a / b) * y1;
    return d;
}

int modular_inverse(int a, int m) 
{
    int x, y;
    extended_euclidean(a, m, x, y);
    return (x + m) % m;
}

int generate_keys(int& n, int& e, int& d) 
{
    srand(time(NULL));
    int p = generate_prime();
    int q = generate_prime();
    n = p * q;
    int phi_n = (p - 1) * (q - 1);
    e = generate_coprime(phi_n);
    d = modular_inverse(e, phi_n);
}

int encrypt(int m, int e, int n) 
{
    int c = 1;
    for (int i = 0; i < e; i++) {
        c = (c * m) % n;
    }
    return c;
}

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() 
{
    int n, e, d;
    generate_keys(n, e, d);
    cout << "Public key: (" << n << ", " << e << ")" << endl;
    cout << "Private key: (" << n << ", " << d << ")" << endl;
    int m;
    cout << "Enter a message to encrypt: ";
    cin >> m;
    int c = encrypt(m, e, n);
    cout << "Encrypted message: " << c << endl;
    int decrypted_m = decrypt(c, d, n);
    cout << "Decrypted message: " << decrypted_m << endl;
    return 0;
}

这个实现采用了随机生成素数的方式生成公钥和私钥，然后使用公钥加密和私钥解密。注意，这个实现仅仅是一个简单的示例，实际应用中还需要考虑更多的安全性问题，比如选择更大的素数、采用更复杂的生成密钥方式等等。