mbedtls学习（6）RSA算法

2023-05-16

RSA算法

RSA算法是一种非对称加密算法，特点时加密解密算法不同且加密解密密钥不同，即一般公钥加密，私钥解密。
下面时RSA算法关键参数

n 模数，位长度为1024比特或者2048比特
e 公开指数，一般为3，7或者65537
d 私密指数
（n，e）公钥
（n，d）私钥

RSA加速技术

RSA私钥操作可以用中国剩余定理（CRT）进行加速执行，再mbedtls配置文件中通过MBEDTLS_RSA_NO_CRT宏打开CRT加速，（默认时打开的）

RSA填充方法

对于RSA加密，给定一个明文，给定一个公钥，就会得到特定密文，这样带来一定安全隐患，所以RSA通常包含填充方案，通过填充动作把随机性注入明文，这样每次加密出来的密文不会相同。RSA有2种填充方案：RSAES-OAEP和RSAES-PKCS1-v1_5.前者目前已经不再推荐使用，后者再实现过程种引入了单项散列函数。

RSA加解密例子

下面例子用伪随机生成器生成rsa密钥对，（当然也可以直接拿外部已经生成的rsa密钥对来加密解密）然后对消息进行加密解密。
需要打开以下宏

#define MBEDTLS_AES_C
#define MBEDTLS_SHA256_C
#define MBEDTLS_ENTROPY_C
#define MBEDTLS_CTR_DRBG_C
#define MBEDTLS_BIGNUM_C
#define MBEDTLS_GENPRIME
#define MBEDTLS_MD_C
#define MBEDTLS_OID_C      开启OID数据结构模块
#define MBEDTLS_RSA_C      开启RSA算法
#define MBEDTLS_PKCS1_V21  开启PKCS#1 v2.1方案
#define MBEDTLS_AES_ROM_TABLES

#include <stdio.h>
#include <string.h>
#include <stdint.h>

#include <stdio.h>
#include <string.h>

#include "mbedtls/rsa.h"
#include "mbedtls/entropy.h"
#include "mbedtls/ctr_drbg.h"
#include "mbedtls/platform.h"

#define assert_exit(cond, ret) \
    do { if (!(cond)) { \
        printf("  !. assert: failed [line: %d, error: -0x%04X]\n", __LINE__, -ret); \
        goto cleanup; \
    } } while (0)

static void dump_buf(char *info, uint8_t *buf, uint32_t len)
{
    mbedtls_printf("%s", info);
    for (int i = 0; i < len; i++) {
        mbedtls_printf("%s%02X%s", i % 16 == 0 ? "\n     ":" ", 
                        buf[i], i == len - 1 ? "\n":"");
    }
}
/*
static int entropy_source(void *data, uint8_t *output, size_t len, size_t *olen)
{
    uint32_t seed;

    seed = sys_rand32_get();
    if (len > sizeof(seed)) {
        len = sizeof(seed);
    }

    memcpy(output, &seed, len);

    *olen = len;
    return 0;
}*/

static void dump_rsa_key(mbedtls_rsa_context *ctx)
{
    size_t olen;
    uint8_t buf[516];
    mbedtls_printf("\n  +++++++++++++++++ rsa keypair +++++++++++++++++\n\n");
    mbedtls_mpi_write_string(&ctx->N , 16, buf, sizeof(buf), &olen);
    mbedtls_printf("N: %s\n", buf); 

    mbedtls_mpi_write_string(&ctx->E , 16, buf, sizeof(buf), &olen);
    mbedtls_printf("E: %s\n", buf);

    mbedtls_mpi_write_string(&ctx->D , 16, buf, sizeof(buf), &olen);
    mbedtls_printf("D: %s\n", buf);

    mbedtls_mpi_write_string(&ctx->P , 16, buf, sizeof(buf), &olen);
    mbedtls_printf("P: %s\n", buf);

    mbedtls_mpi_write_string(&ctx->Q , 16, buf, sizeof(buf), &olen);
    mbedtls_printf("Q: %s\n", buf);

    mbedtls_mpi_write_string(&ctx->DP, 16, buf, sizeof(buf), &olen);
    mbedtls_printf("DP: %s\n", buf);

    mbedtls_mpi_write_string(&ctx->DQ, 16, buf, sizeof(buf), &olen);
    mbedtls_printf("DQ: %s\n", buf);

    mbedtls_mpi_write_string(&ctx->QP, 16, buf, sizeof(buf), &olen);
    mbedtls_printf("QP: %s\n", buf);
    mbedtls_printf("\n  +++++++++++++++++ rsa keypair +++++++++++++++++\n\n");
}

int main(void)
{
    int ret;
    size_t olen = 0;
    uint8_t out[2048/8];

    //mbedtls_platform_set_printf(printf);
    //mbedtls_platform_set_snprintf(snprintf);

    mbedtls_rsa_context ctx;    //RSA密钥结构体
    mbedtls_entropy_context entropy;
    mbedtls_ctr_drbg_context ctr_drbg;
    const char *pers = "simple_rsa";
    const char *msg = "Hello, World!";

    mbedtls_entropy_init(&entropy);//初始化熵结构体
    mbedtls_ctr_drbg_init(&ctr_drbg);//初始化随机数结构体
    //rsa结构体初始化
    mbedtls_rsa_init(&ctx, MBEDTLS_RSA_PKCS_V21, //填充方案OAEP
    						MBEDTLS_MD_SHA256); //SHA256做散列算法
    
   /* mbedtls_entropy_add_source(&entropy, entropy_source, NULL,
                               MBEDTLS_ENTROPY_MAX_GATHER,
                               MBEDTLS_ENTROPY_SOURCE_STRONG);*/
    ret = mbedtls_ctr_drbg_seed(&ctr_drbg, mbedtls_entropy_func, &entropy, 
                                    (const uint8_t *) pers, strlen(pers));//根据个性化字符串更新种子
    assert_exit(ret == 0, ret);
    mbedtls_printf("\n  . setup rng ... ok\n");

    mbedtls_printf("\n  ! RSA Generating large primes may take minutes! \n");
	//生成RSA密钥
    ret = mbedtls_rsa_gen_key(&ctx, mbedtls_ctr_drbg_random, //随机数生成接口
                                        &ctr_drbg, //随机数结构体
                                        2048, //模数位长度
                                        65537);//公开指数0x01001
    assert_exit(ret == 0, ret);                                    
    mbedtls_printf("\n  1. RSA generate key ... ok\n");
    dump_rsa_key(&ctx);  
    //RSA加密
    ret = mbedtls_rsa_pkcs1_encrypt(&ctx, mbedtls_ctr_drbg_random, //随机数生成接口
                            &ctr_drbg,          //随机数结构体
                            MBEDTLS_RSA_PUBLIC, //公钥操作
                            strlen(msg),        //消息长度
                            msg,                //输入消息指针
                            out);               //输出密文指针
    assert_exit(ret == 0, ret);                              
    dump_buf("\n  2. RSA encryption ... ok", out, sizeof(out));
	//RSA解密
    ret = mbedtls_rsa_pkcs1_decrypt(&ctx, mbedtls_ctr_drbg_random,//随机数生成接口
    						&ctr_drbg,          //随机数结构体
                            MBEDTLS_RSA_PRIVATE, //私钥操作
                            &olen,           //输出长度
                            out,             //输入密文指针
                            out,             //输出明文指针
                            sizeof(out));    //最大输出明文数组长度
    assert_exit(ret == 0, ret);                              
    
    out[olen] = 0;
    mbedtls_printf("\n  3. RSA decryption ... ok\n     %s\n", out);

    ret = memcmp(out, msg, olen);
    assert_exit(ret == 0, ret);      
    mbedtls_printf("\n  4. RSA Compare results and plaintext ... ok\n");

cleanup:
    mbedtls_ctr_drbg_free(&ctr_drbg);//释放随机数结构体
    mbedtls_entropy_free(&entropy); //释放熵结构体
    mbedtls_rsa_free(&ctx);         //释放rsa结构体

    return ret;
}

log如下


  . setup rng ... ok

  ! RSA Generating large primes may take minutes! 

  1. RSA generate key ... ok

  +++++++++++++++++ rsa keypair +++++++++++++++++

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
E: 010001
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
P: ED163A4809279C687C89B21089889628F1AB331FE89B0EF7100A9154DC95F9673DA4B716A026FE61D5F91B7EBF94E29C41E396A93FBD566A38CF09B112BEF7A8D3EF74B97DEC02D90D11D162CE4D0B76342A13A0A038A19FB4FBBD669AF410471F3924EC26691D58BBCDEEB85E9344194B5279B55D34F5CCBD06A53CDADA5C89
Q: CC1E93364EF40867F75D40B8EA9794BF8B3EBD2252332F0F2E9E5DE77034C5B1168E0B0D3BE3993F6BEDAB2ED07381B77EF3851B8FCBB715BE333587C9B0ECAAE31C4CCB2EE46033EDAB90D1EC55CA9DEBF88AD95A17D2EC28E753DE676D9BB690D5D59F1D69ED459CD13DBA84A4B628F5DD3119484E37F46BF7CF336EFF7C2F
DP: 88580512523976685C5E6F89B51E5884995E841B3090A38D8FAB1423026C392E9733B79B0A65025BCF4ADFF607451F010F9F4B906FB87A0EC236C6730FBDC4FD514C5F0B21906D9ED7364CFD0E791E434F0277A123230E47A334369AE037C578B14B12A1C00129405358BD9547C6571E58C3C87C756AB484969C50C06B77B249
DQ: BFCB8AEFE0C8148DFC34B77809965CC28E88691732BDBD5E3AA3BC0097C23E6FE38D9C7CD6E5493DFA9FDBD5A530A39653C7662F3BB2635A1ED9E756AC017EA023BE97B9E359DBBB6F7B621C9E410E9DCCF8411F7234289096EEA633B8639988B616F71F07785CE6A82F441D5A3D9A9C6A4968B524E7BA54048F59362EFA0929
QP: 9FE7C2E91937AD577C22FF4E07A6F79EF89850B13E9E010E6FEA0173BB1B117F6E6FD12D886FA68E7911DD8A3225A0C3F0FA80882A9A0AC1CA84AE6C7DD962621FC558CD551BFAB7CE22A5D07DB302DAE2CE143565F413E16A6B0998F62C9DF222C33E3695C29E8ABA12FD147B431FF45DC71AC616221BFB782A44B760331DB8

  +++++++++++++++++ rsa keypair +++++++++++++++++


  2. RSA encryption ... ok
     59 BA E5 46 99 AE DF B1 03 35 DF 90 80 51 BC 8A
     7B EC BE 0E 6E 82 2A 9B 24 4E 26 6A 52 3D 75 5E
     24 AF 2E 5E 76 EC C0 78 95 5F 15 0B B1 53 46 4F
     93 07 29 4F A6 10 2F 41 F0 B3 96 1A 02 5C C4 B4
     71 E3 87 67 68 EB 74 69 A8 85 70 08 62 AA 3B 83
     21 EC 35 1C E1 0E 43 B4 01 9C 00 8E AD 9C 3F 90
     21 23 26 2E EF 73 55 3F 30 7F 3C C3 E1 55 4B 0C
     60 BD 76 6B AD 38 09 26 F2 BD CC 01 65 C1 B0 E7
     BE D3 A6 93 D9 81 11 D4 6C 1F 89 02 92 27 3D A5
     35 9A 9E 88 CA D9 76 D5 0B AE DE E2 D6 F6 FD 6F
     FC 7E B0 90 9C 1C DD E5 49 A4 3C CE E3 BB 66 EB
     B8 16 62 FA 82 45 A7 96 5E 9D E9 77 67 22 37 AB
     62 74 B8 91 E4 6C BA E5 C9 B8 47 12 D8 77 C4 F9
     07 93 0F 5A 4D 57 7B 1A 6A 0D F7 63 84 2F AE CC
     DE 78 4F 5B C2 22 CC EA B5 FC BE 1D 7C F3 2E B4
     6A 4E 1E 77 46 0D 62 63 69 18 A7 27 5C 42 2E BF

  3. RSA decryption ... ok
     Hello, World!

  4. RSA Compare results and plaintext ... ok

上面的rsa keypair中
N和E是公钥
N、E、D、P、Q、DP、DQ、QP属于私钥，其中DP、DQ、QP用于加速解密过程

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