网上有大量的基于OpenSSL实现的国密算法库，比如著名的GmSSL,可以直接拿来用。我自己常用的是mbedTLS的算法库，比较小巧简单，在mbedTLS的大数算法的基础上实现了国密SM2的签名和验签算法。在基于mbedTLS实现SM2签名和验签算法的过程中走过一些弯路，现在把实现的过程记录下来备忘。

国密SM2算法也是基于椭圆曲线公钥算法，椭圆曲线上的运算都是和国际算法一样的，国密SM2规范中给出了推荐曲线，所以首先需要加载国密推荐参数。

mbedTLS中使用ecp_group_load函数加载参数，需要定义一下SM2的椭圆曲线，在定义曲线参数时字节序跟SM2规范的上的顺序不一样，这里需要注意一下，当时在这里折腾了很久。

static const mbedtls_mpi_uint sm2256_p[] = {
    BYTES_TO_T_UINT_8(0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF),
    BYTES_TO_T_UINT_8(0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF),
    BYTES_TO_T_UINT_8(0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF),
    BYTES_TO_T_UINT_8(0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF),
};
static const mbedtls_mpi_uint sm2256_a[] = {
    BYTES_TO_T_UINT_8(0xFC, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF),
    BYTES_TO_T_UINT_8(0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF),
    BYTES_TO_T_UINT_8(0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF),
    BYTES_TO_T_UINT_8(0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF),
};
static const mbedtls_mpi_uint sm2256_b[] = {
    BYTES_TO_T_UINT_8(0x93, 0x0E, 0x94, 0x4D, 0x41, 0xBD, 0xBC, 0xDD),
    BYTES_TO_T_UINT_8(0x92, 0x8F, 0xAB, 0x15, 0xF5, 0x89, 0x97, 0xF3),
    BYTES_TO_T_UINT_8(0xA7, 0x09, 0x65, 0xCF, 0x4B, 0x9E, 0x5A, 0x4D),
    BYTES_TO_T_UINT_8(0x34, 0x5E, 0x9F, 0x9D, 0x9E, 0xFA, 0xE9, 0x28),
};
static const mbedtls_mpi_uint sm2256_gx[] = {
    BYTES_TO_T_UINT_8(0xC7, 0x74, 0x4C, 0x33, 0x89, 0x45, 0x5A, 0x71),
    BYTES_TO_T_UINT_8(0xE1, 0x0B, 0x66, 0xF2, 0xBF, 0x0B, 0xE3, 0x8F),
    BYTES_TO_T_UINT_8(0x94, 0xC9, 0x39, 0x6A, 0x46, 0x04, 0x99, 0x5F),
    BYTES_TO_T_UINT_8(0x19, 0x81, 0x19, 0x1F, 0x2C, 0xAE, 0xC4, 0x32),
};
static const mbedtls_mpi_uint sm2256_gy[] = {
    BYTES_TO_T_UINT_8(0xA0, 0xF0, 0x39, 0x21, 0xE5, 0x32, 0xDF, 0x02),
    BYTES_TO_T_UINT_8(0x40, 0x47, 0x2A, 0xC6, 0x7C, 0x87, 0xA9, 0xD0),
    BYTES_TO_T_UINT_8(0x53, 0x21, 0x69, 0x6B, 0xE3, 0xCE, 0xBD, 0x59),
    BYTES_TO_T_UINT_8(0x9C, 0x77, 0xF6, 0xF4, 0xA2, 0x36, 0x37, 0xBC),
};
static const mbedtls_mpi_uint sm2256_n[] = {
    BYTES_TO_T_UINT_8(0x23, 0x41, 0xD5, 0x39, 0x09, 0xF4, 0xBB, 0x53),
    BYTES_TO_T_UINT_8(0x2B, 0x05, 0xC6, 0x21, 0x6B, 0xDF, 0x03, 0x72),
    BYTES_TO_T_UINT_8(0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF),
    BYTES_TO_T_UINT_8(0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF),
};

使用这个曲线后，就可以尝试产生一下SM2密钥对了，生成之后可以用其他的支持SM2的算法工具或者算法库来验证，如果没问题，就可以进入下一步，实现SM2签名算法。

SM2的签名算法和ECC的签名过程是有区别的，SM2的过程是：

1.对待签名数据进行哈希算法（国密规范里还规定了使用用户ID，曲线参数等生成Z的过程，这里不考虑那些过程，直接处理最后哈希后的数据）

2.先生成一个SM2密钥对，私钥：k，公钥：kG = (x,y);

3.计算r = (e+x) mod n；

4.如果r=0 或者r+k=n返回步骤2；

5.s=（（1+d）^-1）(k-rd) mod n ;

6.如果s=0 返回 2;

7.签名结果（r,s）.

实现签名的代码如下：

/**
* Compute ECDSA-SM2 signature of a hashed message
* Author: Zhao Yang cnrgc@163.com/sxzhaoyang@gmail.com
* Data: April 25 2018
*/
 
int mbedtls_ecdsa_sm2_sign(mbedtls_ecp_group *grp, mbedtls_mpi *r, mbedtls_mpi *s,
                        const mbedtls_mpi *d, const unsigned char *buf, size_t blen,
                        int(*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
    int ret, key_tries, sign_tries, blind_tries;
    mbedtls_ecp_point R;
    mbedtls_mpi  k, e, t, l, m;
    /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
    if (grp->N.p == NULL)
        return(MBEDTLS_ERR_ECP_BAD_INPUT_DATA);
 
    mbedtls_ecp_point_init(&R);
    mbedtls_mpi_init(&k); mbedtls_mpi_init(&e); mbedtls_mpi_init(&t); mbedtls_mpi_init(&l);
    mbedtls_mpi_init(&m);
 
    sign_tries = 0;
    do
    {
        /*
        * Step 0: derive MPI from hashed message
        */
        MBEDTLS_MPI_CHK(derive_mpi(grp, &e, buf, blen));
        /*
        *       Step 1-3:
        *       set r = (e+x) mod n
        */
        key_tries = 0;
        do
        {
            MBEDTLS_MPI_CHK(mbedtls_ecp_gen_keypair(grp, &k, &R, f_rng, p_rng));
            MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&l, &e, &R.X));
            MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(r, &l, &grp->N));
            
            if (key_tries++ > 10)
            {
                ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
                goto cleanup;
            }
            //r+k != n
            MBEDTLS_MPI_CHK((mbedtls_mpi_add_mpi(&m, r, &k)));
        } while ((mbedtls_mpi_cmp_int(r, 0) == 0)|| (mbedtls_mpi_cmp_mpi(&m, &grp->N) == 0));
        /*
        * Generate a random value to blind inv_mod in next step,
        * avoiding a potential timing leak.
        */
        blind_tries = 0;
        do
        {
            size_t n_size = (grp->nbits + 7) / 8;
            MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(&t, n_size, f_rng, p_rng));
            MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&t, 8 * n_size - grp->nbits));
 
            /* See mbedtls_ecp_gen_keypair() */
            if (++blind_tries > 30)
                return(MBEDTLS_ERR_ECP_RANDOM_FAILED);
        } while (mbedtls_mpi_cmp_int(&t, 1) < 0 ||
            mbedtls_mpi_cmp_mpi(&t, &grp->N) >= 0);
 
        /*
        * Step 6: compute  s = ((1+d)^-1)*(k-r*d) mod n
        * 
        */
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(s, r, d)); //s = r*d
        MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(s, &k, s));   //s = k - s
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(s, s, &t));//s = s*t
        MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&l, d, 1));//l = 1+d
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&l, &l, &t));//l=l*t
        MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&l, &l, &grp->N));// l = l^-1
        MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(s, s, &l));//s = s * l 
        MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(s, s, &grp->N));//s mod n
 
        if (sign_tries++ > 10)
        {
            ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
            goto cleanup;
        }
        //
    } while (mbedtls_mpi_cmp_int(&t, 1) < 0 ||
             mbedtls_mpi_cmp_mpi(&t, &grp->N) >= 0);
cleanup:
    mbedtls_ecp_point_free(&R);
    mbedtls_mpi_free(&k); mbedtls_mpi_free(&e); mbedtls_mpi_free(&t);
    mbedtls_mpi_free(&l); mbedtls_mpi_free(&m);
    return (ret);
}

/*
* Deterministic Guomi SM2 signature wrapper
* Author: Zhao Yang cnrgc@163.com/sxzhaoyang@gmail.com
* Data: April 25 2018
*/
int mbedtls_ecdsa_sm2_sign_det(mbedtls_ecp_group *grp, mbedtls_mpi *r, mbedtls_mpi *s,
    const mbedtls_mpi *d, const unsigned char *buf, size_t blen,
    mbedtls_md_type_t md_alg)
{
    int ret;
    mbedtls_hmac_drbg_context rng_ctx;
    unsigned char data[2 * MBEDTLS_ECP_MAX_BYTES];
    size_t grp_len = (grp->nbits + 7) / 8;
    const mbedtls_md_info_t *md_info;
    mbedtls_mpi h;
 
    if ((md_info = mbedtls_md_info_from_type(md_alg)) == NULL)
        return(MBEDTLS_ERR_ECP_BAD_INPUT_DATA);
 
    mbedtls_mpi_init(&h);
    mbedtls_hmac_drbg_init(&rng_ctx);
 
    /* Use private key and message hash (reduced) to initialize HMAC_DRBG */
    MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(d, data, grp_len));
    MBEDTLS_MPI_CHK(derive_mpi(grp, &h, buf, blen));
    MBEDTLS_MPI_CHK(mbedtls_mpi_write_binary(&h, data + grp_len, grp_len));
    mbedtls_hmac_drbg_seed_buf(&rng_ctx, md_info, data, 2 * grp_len);
 
    ret = mbedtls_ecdsa_sm2_sign(grp, r, s, d, buf, blen,
        mbedtls_hmac_drbg_random, &rng_ctx);
 
cleanup:
    mbedtls_hmac_drbg_free(&rng_ctx);
    mbedtls_mpi_free(&h);
 
    return(ret);
}

然后实现SM2的验证签名算法，同样SM2的验证过程跟ECC也有差别，验证过程如下：

1.e = hash(m);

2.计算t = (r + s) mod n，如果t=0验签失败;

3.计算椭圆曲线上的点(x,y) = sG + tP

4.计算R = (e + x) mod n 如果R=r那么签名正确，否则签名验证失败.

实现验证签名代码如下：

/*
* Verify ECDSA Guomi SM2 signature of hashed message 
* Author: Zhao Yang cnrgc@163.com/sxzhaoyang@gmail.com
* Data: April 25 2018
*/
int mbedtls_ecdsa_sm2_verify(mbedtls_ecp_group *grp,
    const unsigned char *buf, size_t blen,
    const mbedtls_ecp_point *Q, const mbedtls_mpi *r, const mbedtls_mpi *s)
{
    int ret;
    mbedtls_mpi e, s_inv, u1, u2, t, result;
    mbedtls_ecp_point R;
 
    mbedtls_ecp_point_init(&R);
    mbedtls_mpi_init(&e); mbedtls_mpi_init(&s_inv); mbedtls_mpi_init(&u1); mbedtls_mpi_init(&u2);
    mbedtls_mpi_init(&t); mbedtls_mpi_init(&result); 
 
    /* Fail cleanly on curves such as Curve25519 that can't be used for ECDSA */
    if (grp->N.p == NULL)
        return(MBEDTLS_ERR_ECP_BAD_INPUT_DATA);
 
    /*
    * Step 1: make sure r and s are in range 1..n-1
    */
    if (mbedtls_mpi_cmp_int(r, 1) < 0 || mbedtls_mpi_cmp_mpi(r, &grp->N) >= 0 ||
        mbedtls_mpi_cmp_int(s, 1) < 0 || mbedtls_mpi_cmp_mpi(s, &grp->N) >= 0)
    {
        ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
        goto cleanup;
    }
 
    /*
    * Additional precaution: make sure Q is valid
    */
    MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, Q));
 
    /*
    * Step 3: derive MPI from hashed message
    */
    MBEDTLS_MPI_CHK(derive_mpi(grp, &e, buf, blen));
 
    /*
    * Step 4: t = (r+s) mod n
    */
    MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&t, r, s));
    MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&t, &t, &grp->N));
    if (mbedtls_mpi_cmp_int(&t, 0) == 0)
    {
        ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
        goto cleanup;
    }
    /*
    * Step 5: (x,y) = sG + tQ
    */
    MBEDTLS_MPI_CHK(mbedtls_ecp_muladd(grp, &R, s, &grp->G, &t, Q));
    /*
    * Step 6: result = (e+x) mod n
    */
    MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&e, &e, &R.X));
    MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&result, &e, &grp->N));
    /*
    * Step 7: check if result.X (that is, result.X) is equal to r
    **/
    if (mbedtls_mpi_cmp_mpi(&result, r) != 0)
    {
        ret = MBEDTLS_ERR_ECP_VERIFY_FAILED;
        goto cleanup;
    }
    //
cleanup:
    mbedtls_ecp_point_free(&R); 
    mbedtls_mpi_free(&e); mbedtls_mpi_free(&s_inv); mbedtls_mpi_free(&u1); mbedtls_mpi_free(&u2);
    mbedtls_mpi_free(&t); mbedtls_mpi_free(&result);
    return(ret);
}