标签 mbedTLS 下的文章

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基于mbedTLS算法库实现国密SM2签名和验签算法
update:2021-9-28
曲线参数：
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),  
};  

签名过程：
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），得到e;
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）.
code:

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;  
    
   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  
   {  
        
      MBEDTLS_MPI_CHK(derive_mpi(grp, &e, buf, blen));  
        
       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));  
        
      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));  
  
           
          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);  
  
        
      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);  
}  
  
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);  
  
    
   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);  
}  

验证签名：
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.

code:
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);   
  
     
    if (grp->N.p == NULL)  
       return(MBEDTLS_ERR_ECP_BAD_INPUT_DATA);  
  
     
    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;  
    }  
  
     
   MBEDTLS_MPI_CHK(mbedtls_ecp_check_pubkey(grp, Q));  
  
     
   MBEDTLS_MPI_CHK(derive_mpi(grp, &e, buf, blen));  
  
     
   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;  
    }  
     
   MBEDTLS_MPI_CHK(mbedtls_ecp_muladd(grp, &R, s, &grp->G, &t, Q));  
     
   MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&e, &e, &R.X));  
   MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&result, &e, &grp->N));  
     
    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);  
}  
Referenced from:http://blog.sina.com.cn/s/blog_4b9c791e0102xqeq.html

打印私钥，主要使用这个函数：
mbedtls_mpi_write_file

int mbedtls_mpi_write_file( const char p, const mbedtls_mpi X,　int radix, FILE *fout );

当fout为NULL，就输出到标准输出了。

When reading from files with mbedtls_mpi_read_file() and writing to files with
mbedtls_mpi_write_file() the buffer should have space
for a (short) label, the MPI (in the provided radix), the newline
characters and the '0'.

int main( int argc, char *argv[] )
{
    int ret = 1;
    int exit_code = MBEDTLS_EXIT_FAILURE;
    mbedtls_ecdsa_context ctx_sign, ctx_verify;
    mbedtls_entropy_context entropy;
    mbedtls_ctr_drbg_context ctr_drbg;
    unsigned char message[100];
    unsigned char hash[32];
    unsigned char sig[MBEDTLS_ECDSA_MAX_LEN];
    size_t sig_len;
    const char *pers = "ecdsa";
    ((void) argv);

    mbedtls_ecdsa_init( &ctx_sign );
    mbedtls_ecdsa_init( &ctx_verify );
    mbedtls_ctr_drbg_init( &ctr_drbg );

    memset( sig, 0, sizeof( sig ) );
    memset( message, 0x25, sizeof( message ) );

    if( argc != 1 )
    {
        mbedtls_printf( "usage: ecdsa\n" );

#if defined(_WIN32)
        mbedtls_printf( "\n" );
#endif

        goto exit;
    }

    /*
     * Generate a key pair for signing
     */
    mbedtls_printf( "\n  . Seeding the random number generator..." );
    fflush( stdout );

    mbedtls_entropy_init( &entropy );
    if( ( ret = mbedtls_ctr_drbg_seed( &ctr_drbg, mbedtls_entropy_func, &entropy,
                               (const unsigned char *) pers,
                               strlen( pers ) ) ) != 0 )
    {
        mbedtls_printf( " failed\n  ! mbedtls_ctr_drbg_seed returned %d\n", ret );
        goto exit;
    }

    mbedtls_printf( " ok\n  . Generating key pair..." );
    fflush( stdout );

    if( ( ret = mbedtls_ecdsa_genkey( &ctx_sign, ECPARAMS,
                              mbedtls_ctr_drbg_random, &ctr_drbg ) ) != 0 )
    {
        mbedtls_printf( " failed\n  ! mbedtls_ecdsa_genkey returned %d\n", ret );
        goto exit;
    }

    mbedtls_printf( " ok (key size: %d bits)\n", (int) ctx_sign.MBEDTLS_PRIVATE(grp).pbits );

    dump_pubkey( "  + Public key: ", &ctx_sign );
    mbedtls_mpi_write_file( "D   : ", &ctx_sign.MBEDTLS_PRIVATE(d)  , 16, NULL );
exit:

#if defined(_WIN32)
    mbedtls_printf( "  + Press Enter to exit this program.\n" );
    fflush( stdout ); getchar();
#endif

    mbedtls_ecdsa_free( &ctx_verify );
    mbedtls_ecdsa_free( &ctx_sign );
    mbedtls_ctr_drbg_free( &ctr_drbg );
    mbedtls_entropy_free( &entropy );

    mbedtls_exit( exit_code );
}

mbed TLS是为嵌入式设备而开发的一个TLS协议的轻量级实现。其旨在令低性能的嵌入式设备也能流畅运行TLS协议；其API的实现旨在简单易用。 mbed TLS 虽然是为嵌入式设备而开发，但它也能被用于其他各种平台，因此也常常被用作OpenSSL的一个轻量级替代。 维基百科
源代码库： github.com/ARMmbed/mbedtls

mbed TLS（原PolarSSL）

编译：

git clone https://github.com/ARMmbed/mbedtls.git
正克隆到 'mbedtls'...
remote: Enumerating objects: 154118, done.
remote: Counting objects: 100% (1256/1256), done.
remote: Compressing objects: 100% (476/476), done.
remote: Total 154118 (delta 899), reused 1032 (delta 780), pack-reused 152862
接收对象中: 100% (154118/154118), 70.33 MiB | 899.00 KiB/s, 完成.
处理 delta 中: 100% (119193/119193), 完成.

mkdir build && cd build
cmake ..
make -j4
sudo make install