C语言实现大数版本的RSA算法

以下是C语言实现大数版本的RSA算法的代码示例：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <gmp.h>

// 生成指定位数的大质数
void generate_prime(mpz_t prime, int bits) {
    gmp_randstate_t state;
    gmp_randinit_mt(state);
    while (1) {
        mpz_urandomb(prime, state, bits);
        if (mpz_probab_prime_p(prime, 25) > 0) {
            break;
        }
    }
    gmp_randclear(state);
}

// 计算最大公约数
void gcd(mpz_t result, mpz_t a, mpz_t b) {
    mpz_t temp;
    mpz_init(temp);
    while (mpz_cmp_ui(b, 0) != 0) {
        mpz_mod(temp, a, b);
        mpz_set(a, b);
        mpz_set(b, temp);
    }
    mpz_set(result, a);
    mpz_clear(temp);
}

// 计算模反元素
void mod_inverse(mpz_t result, mpz_t a, mpz_t m) {
    mpz_t x1, x2, y1, y2, q, r, temp;
    mpz_inits(x1, x2, y1, y2, q, r, temp, NULL);
    mpz_set_ui(x1, 0);
    mpz_set_ui(y2, 0);
    mpz_set_ui(x2, 1);
    mpz_set_ui(y1, 1);
    while (mpz_cmp_ui(m, 0) != 0) {
        mpz_fdiv_q(q, a, m);
        mpz_mod(r, a, m);
        mpz_set(a, m);
        mpz_set(m, r);
        mpz_set(temp, x2);
        mpz_mul(q, q, x2);
        mpz_sub(x2, x1, q);
        mpz_set(x1, temp);
        mpz_set(temp, y2);
        mpz_mul(q, q, y2);
        mpz_sub(y2, y1, q);
        mpz_set(y1, temp);
    }
    mpz_set(result, x1);
    mpz_clears(x1, x2, y1, y2, q, r, temp, NULL);
}

// 生成RSA密钥对
void generate_rsa_key(int bits, mpz_t n, mpz_t e, mpz_t d) {
    mpz_t p, q, phi, gcd_value;
    mpz_inits(p, q, phi, gcd_value, NULL);
    generate_prime(p, bits / 2);
    generate_prime(q, bits / 2);
    mpz_mul(n, p, q);
    mpz_sub_ui(p, p, 1);
    mpz_sub_ui(q, q, 1);
    mpz_mul(phi, p, q);
    do {
        gmp_randstate_t state;
        gmp_randinit_mt(state);
        mpz_urandomm(e, state, phi);
        gmp_randclear(state);
        gcd(gcd_value, e, phi);
    } while (mpz_cmp_ui(gcd_value, 1) != 0);
    mod_inverse(d, e, phi);
    mpz_clears(p, q, phi, gcd_value, NULL);
}

// 加密
void rsa_encrypt(mpz_t c, mpz_t m, mpz_t e, mpz_t n) {
    mpz_powm(c, m, e, n);
}

// 解密
void rsa_decrypt(mpz_t m, mpz_t c, mpz_t d, mpz_t n) {
    mpz_powm(m, c, d, n);
}

int main() {
    mpz_t n, e, d, m, c;
    mpz_inits(n, e, d, m, c, NULL);
    int bits = 1024;
    generate_rsa_key(bits, n, e, d);
    char plain_text[] = "Hello RSA!";
    mpz_set_str(m, plain_text, 0);
    rsa_encrypt(c, m, e, n);
    gmp_printf("Cipher text: %Zd\n", c);
    rsa_decrypt(m, c, d, n);
    char buffer[1024];
    mpz_get_str(buffer, 0, m);
    printf("Plain text: %s\n", buffer);
    mpz_clears(n, e, d, m, c, NULL);
    return 0;
}

以上代码中使用了GMP库来处理大数运算。其中，`generate_prime`函数用于生成指定位数的大质数，`gcd`函数用于计算最大公约数，`mod_inverse`函数用于计算模反元素，`generate_rsa_key`函数用于生成RSA密钥对，`rsa_encrypt`函数用于加密，`rsa_decrypt`函数用于解密。在`main`函数中，首先生成RSA密钥对，然后将明文转换成数字进行加密，再将密文转换成明文进行解密。