使用openssl3.0库 实现CRT加速的RSA加密，并和普通的RSA加密比较，代码实现

使用 OpenSSL 3.0 库实现 CRT 加速的 RSA 加密可以通过以下步骤实现：

1. 初始化 OpenSSL 库和随机数生成器：

#include <openssl/rand.h>
#include <openssl/ssl.h>
#include <openssl/evp.h>

// 初始化 OpenSSL 库和随机数生成器
void init_openssl() {
    SSL_library_init();
    SSL_load_error_strings();
    ERR_load_crypto_strings();
    OpenSSL_add_all_algorithms();

    // 随机数生成器需要初始化
    RAND_poll();
}

2. 生成 RSA 密钥对：

#include <openssl/rsa.h>
#include <openssl/bn.h>

// 生成 RSA 密钥对
RSA* generate_rsa_key_pair(int bits) {
    RSA* rsa = RSA_new();
    BIGNUM* bne = BN_new();

    // 生成指数
    if (BN_set_word(bne, RSA_F4) != 1) {
        printf("Failed to set RSA exponent.\n");
        return NULL;
    }

    // 生成密钥对
    if (RSA_generate_key_ex(rsa, bits, bne, NULL) != 1) {
        printf("Failed to generate RSA key pair.\n");
        return NULL;
    }

    return rsa;
}

3. 加载公钥和私钥：

#include <openssl/pem.h>

// 加载公钥
RSA* load_public_key(const char* public_key_file) {
    RSA* rsa = RSA_new();

    FILE* fp = fopen(public_key_file, "rb");
    if (fp == NULL) {
        printf("Failed to open public key file.\n");
        return NULL;
    }

    PEM_read_RSA_PUBKEY(fp, &rsa, NULL, NULL);

    fclose(fp);

    return rsa;
}

// 加载私钥
RSA* load_private_key(const char* private_key_file) {
    RSA* rsa = RSA_new();

    FILE* fp = fopen(private_key_file, "rb");
    if (fp == NULL) {
        printf("Failed to open private key file.\n");
        return NULL;
    }

    PEM_read_RSAPrivateKey(fp, &rsa, NULL, NULL);

    fclose(fp);

    return rsa;
}

4. 加密和解密：

#include <openssl/rsa.h>

// RSA 加密
int rsa_encrypt(RSA* rsa, const unsigned char* in, size_t inlen,
                unsigned char* out, size_t* outlen) {
    int ret = RSA_public_encrypt(inlen, in, out, rsa, RSA_PKCS1_OAEP_PADDING);
    if (ret == -1) {
        printf("Failed to encrypt.\n");
        return 0;
    }

    *outlen = ret;

    return 1;
}

// RSA 解密
int rsa_decrypt(RSA* rsa, const unsigned char* in, size_t inlen,
                unsigned char* out, size_t* outlen) {
    int ret = RSA_private_decrypt(inlen, in, out, rsa, RSA_PKCS1_OAEP_PADDING);
    if (ret == -1) {
        printf("Failed to decrypt.\n");
        return 0;
    }

    *outlen = ret;

    return 1;
}

5. 使用 CRT 加速的 RSA 加密：

// CRT 加速的 RSA 加密
int rsa_crt_encrypt(RSA* rsa, const unsigned char* in, size_t inlen,
                    unsigned char* out, size_t* outlen) {
    int ret = RSA_private_encrypt(inlen, in, out, rsa, RSA_NO_PADDING);
    if (ret == -1) {
        printf("Failed to CRT-encrypt.\n");
        return 0;
    }

    *outlen = ret;

    return 1;
}

6. 比较加密和解密的时间：

#include <time.h>

// 比较加密和解密的时间
void compare_rsa_and_crt_rsa(RSA* rsa, const unsigned char* plaintext, size_t plaintext_len) {
    clock_t start, end;
    double cpu_time_used;

    // 普通 RSA 加密和解密
    int ret;
    unsigned char ciphertext[4096];
    size_t ciphertext_len;
    unsigned char decryptedtext[4096];
    size_t decryptedtext_len;

    start = clock();

    // 加密
    ret = rsa_encrypt(rsa, plaintext, plaintext_len, ciphertext, &ciphertext_len);
    if (ret == 0) {
        printf("Failed to encrypt.\n");
        return;
    }

    // 解密
    ret = rsa_decrypt(rsa, ciphertext, ciphertext_len, decryptedtext, &decryptedtext_len);
    if (ret == 0) {
        printf("Failed to decrypt.\n");
        return;
    }

    end = clock();
    cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;

    printf("RSA encryption and decryption time: %lf seconds.\n", cpu_time_used);

    // CRT 加速的 RSA 加密
    unsigned char crt_ciphertext[4096];
    size_t crt_ciphertext_len;

    start = clock();

    // 加密
    ret = rsa_crt_encrypt(rsa, plaintext, plaintext_len, crt_ciphertext, &crt_ciphertext_len);
    if (ret == 0) {
        printf("Failed to CRT-encrypt.\n");
        return;
    }

    end = clock();
    cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;

    printf("CRT-RSA encryption time: %lf seconds.\n", cpu_time_used);

    // 比较两种加密方式的结果
    if (ciphertext_len != crt_ciphertext_len) {
        printf("Encryption results are different.\n");
        return;
    }

    if (memcmp(ciphertext, crt_ciphertext, ciphertext_len) != 0) {
        printf("Encryption results are different.\n");
        return;
    }
}

完整的代码实现如下：