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

RSA算法是一种非对称加密算法，其加密速度较慢，其中最耗时的操作是大数模幂运算，而CRT（中国剩余定理）可以加速RSA算法的运算，提高加密速度。在openssl库中，可以使用CRT加速RSA加密。

下面是使用openssl库实现CRT加速的RSA加密的代码实现：

#include <openssl/rsa.h>
#include <openssl/pem.h>
#include <openssl/bio.h>
#include <openssl/err.h>
#include <openssl/evp.h>

// RSA加密函数
int rsa_encrypt(const unsigned char *data, int data_len, const char *pub_key_path, unsigned char *encrypted)
{
    RSA *rsa = NULL;
    FILE *pub_fp = NULL;
    int result = -1;

    // 打开公钥文件
    pub_fp = fopen(pub_key_path, "rb");
    if (!pub_fp) {
        printf("Failed to open public key file!\n");
        return -1;
    }

    // 读取公钥
    rsa = PEM_read_RSA_PUBKEY(pub_fp, NULL, NULL, NULL);
    if (!rsa) {
        printf("Failed to read public key!\n");
        goto cleanup;
    }

    // 加密数据
    int ret = RSA_public_encrypt(data_len, data, encrypted, rsa, RSA_NO_PADDING);
    if (ret <= 0) {
        printf("Failed to encrypt data!\n");
        goto cleanup;
    }

    result = ret;

cleanup:
    if (rsa) {
        RSA_free(rsa);
    }
    if (pub_fp) {
        fclose(pub_fp);
    }
    return result;
}

// 使用CRT加速的RSA加密函数
int rsa_crt_encrypt(const unsigned char *data, int data_len, const char *pub_key_path, unsigned char *encrypted)
{
    RSA *rsa = NULL;
    FILE *pub_fp = NULL;
    BN_CTX *ctx = NULL;
    BIGNUM *n = NULL, *e = NULL, *d = NULL, *p = NULL, *q = NULL, *dmp1 = NULL, *dmq1 = NULL, *iqmp = NULL;
    unsigned char *buf = NULL, *pbuf = NULL, *qbuf = NULL, *dbuf = NULL;
    int result = -1;

    // 打开公钥文件
    pub_fp = fopen(pub_key_path, "rb");
    if (!pub_fp) {
        printf("Failed to open public key file!\n");
        return -1;
    }

    // 读取公钥
    rsa = PEM_read_RSA_PUBKEY(pub_fp, NULL, NULL, NULL);
    if (!rsa) {
        printf("Failed to read public key!\n");
        goto cleanup;
    }

    // 获取RSA参数
    ctx = BN_CTX_new();
    if (!ctx) {
        printf("Failed to create BN context!\n");
        goto cleanup;
    }
    n = rsa->n;
    e = rsa->e;
    p = rsa->p;
    q = rsa->q;
    dmp1 = rsa->dmp1;
    dmq1 = rsa->dmq1;
    iqmp = rsa->iqmp;

    // 计算CRT参数
    buf = (unsigned char *)malloc(RSA_size(rsa));
    if (!buf) {
        printf("Failed to allocate memory!\n");
        goto cleanup;
    }
    int ret = RSA_public_encrypt(1, (unsigned char *)"A", buf, rsa, RSA_NO_PADDING);
    if (ret <= 0) {
        printf("Failed to calculate CRT parameters!\n");
        goto cleanup;
    }
    pbuf = buf + RSA_size(rsa) / 2;
    qbuf = buf;
    dbuf = (unsigned char *)malloc(RSA_size(rsa));
    if (!dbuf) {
        printf("Failed to allocate memory!\n");
        goto cleanup;
    }
    BN_bin2bn(pbuf, RSA_size(rsa) / 2, p);
    BN_bin2bn(qbuf, RSA_size(rsa) / 2, q);
    BN_mod(dmp1, d, p - 1, ctx);
    BN_mod(dmq1, d, q - 1, ctx);
    BN_mod_inverse(iqmp, q, p, ctx);

    // 加密数据
    ret = RSA_padding_add_PKCS1_OAEP(encrypted, RSA_size(rsa), data, data_len, NULL, 0);
    if (ret <= 0) {
        printf("Failed to padding data!\n");
        goto cleanup;
    }
    ret = RSA_private_encrypt(RSA_size(rsa) / 2, encrypted, encrypted, rsa, RSA_NO_PADDING);
    if (ret <= 0) {
        printf("Failed to encrypt data!\n");
        goto cleanup;
    }
    ret = RSA_private_encrypt(RSA_size(rsa) / 2, encrypted + RSA_size(rsa) / 2, encrypted + RSA_size(rsa) / 2, rsa, RSA_NO_PADDING);
    if (ret <= 0) {
        printf("Failed to encrypt data!\n");
        goto cleanup;
    }

    result = RSA_size(rsa);

cleanup:
    if (rsa) {
        RSA_free(rsa);
    }
    if (pub_fp) {
        fclose(pub_fp);
    }
    if (ctx) {
        BN_CTX_free(ctx);
    }
    if (buf) {
        free(buf);
    }
    if (dbuf) {
        free(dbuf);
    }
    return result;
}

以上代码中，`rsa_encrypt`函数实现了普通的RSA加密，`rsa_crt_encrypt`函数实现了使用CRT加速的RSA加密。

需要注意的是，在使用CRT加速的RSA加密中，需要计算CRT参数，因此需要进行额外的计算，这也是该算法的缺点之一。另外，还需要将数据分成两个部分进行加密，因此需要进行两次加密操作。

为了测试这两种加密方式的速度，可以使用以下代码进行测试：

int main()
{
    const char *pub_key_path = "rsa_public.pem";
    const char *data = "Hello, world!";
    int data_len = strlen(data);
    unsigned char encrypted[4096];
    int ret;

    // 测试普通的RSA加密
    clock_t start = clock();
    for (int i = 0; i < 10000; i++) {
        ret = rsa_encrypt((unsigned char *)data, data_len, pub_key_path, encrypted);
        if (ret < 0) {
            printf("Failed to encrypt data!\n");
            return -1;
        }
    }
    clock_t end = clock();
    printf("RSA Encryption Time: %.2fms\n", (double)(end - start) * 1000 / CLOCKS_PER_SEC / 10000);

    // 测试使用CRT加速的RSA加密
    start = clock();
    for (int i = 0; i < 10000; i++) {
        ret = rsa_crt_encrypt((unsigned char *)data, data_len, pub_key_path, encrypted);
        if (ret < 0) {
            printf("Failed to encrypt data!\n");
            return -1;
        }
    }
    end = clock();
    printf("CRT RSA Encryption Time: %.2fms\n", (double)(end - start) * 1000 / CLOCKS_PER_SEC / 10000);

    return 0;
}

可以通过测试结果比较两种加密方式的速度。