用c++写一个DSA加密算法

好的，以下是一个简单的DSA加密算法的C++实现：

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

using namespace std;

// 生成大素数p和q，其中q为p-1的一个质因子
void generate_pq(int &p, int &q) {
    srand((unsigned)time(NULL));
    int prime[12] = { 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61 };
    int index = rand() % 12;
    q = prime[index];
    while (true) {
        p = q * rand() % 100 + 100;
        bool flag = true;
        for (int i = 2; i <= sqrt(p); i++) {
            if (p % i == 0) {
                flag = false;
                break;
            }
        }
        if (flag) break;
    }
}

// 计算a^b mod p
int mod_pow(int a, int b, int p) {
    int res = 1;
    while (b > 0) {
        if (b & 1) res = res * a % p;
        b >>= 1;
        a = a * a % p;
    }
    return res;
}

// 求逆元
int inverse(int a, int p) {
    int x1 = 1, x2 = 0, x3 = p;
    int y1 = 0, y2 = 1, y3 = a;
    int q, t1, t2, t3;
    while (y3 != 1) {
        q = x3 / y3;
        t1 = x1 - q * y1; t2 = x2 - q * y2; t3 = x3 - q * y3;
        x1 = y1; x2 = y2; x3 = y3;
        y1 = t1; y2 = t2; y3 = t3;
    }
    return y2 > 0 ? y2 : y2 + p;
}

// 生成公钥和私钥
void generate_key(int p, int q, int &x, int &y) {
    int g = 2;
    int k = rand() % (q - 1) + 1;
    x = mod_pow(g, k, p);
    y = inverse(k, q);
}

// 加密
void encrypt(int p, int q, int x, int y, int &r, int &s, int message) {
    int g = 2;
    int k = rand() % (q - 1) + 1;
    r = mod_pow(g, k, p) % q;
    s = (message + x * r) * y % q;
}

// 解密
bool decrypt(int p, int q, int x, int r, int s, int message) {
    int w = inverse(s, q);
    int u1 = message * w % q;
    int u2 = r * w % q;
    int v = (mod_pow(x, u1, p) * mod_pow(r, u2, p)) % p % q;
    return v == r;
}

int main() {
    int p, q, x, y, r, s;
    int message = 12345;

    generate_pq(p, q);
    generate_key(p, q, x, y);
    encrypt(p, q, x, y, r, s, message);

    cout << "p = " << p << endl;
    cout << "q = " << q << endl;
    cout << "x = " << x << endl;
    cout << "y = " << y << endl;
    cout << "message = " << message << endl;
    cout << "r = " << r << endl;
    cout << "s = " << s << endl;

    if (decrypt(p, q, x, r, s, message))
        cout << "Decrypt successfully!" << endl;
    else
        cout << "Decrypt failed!" << endl;

    return 0;
}

以上代码实现了DSA加密算法，并且可以生成随机的公钥和私钥，并用公钥进行加密和私钥进行解密。