RSA非对称加密算法
1、对称加密算法
对称加密算法是应用较早的加密算法，数据发送方将明文和密钥经加密算法处理，使其变成密文发送出去；接收方收到密文后，使用和加密算法相同的密钥进行逆算法解密，还原出明文。在对称加密算法中，使用的密钥只有一个，收发双方使用相同的密钥对数据进行加密或解密。
双方都必须保管好密钥，任一方的密钥泄露，都会导致加密信息不安全；尤其是双方协商更换密钥过程中，密钥会出现在传输过程中，严重影响数据的安全性。
对称加密算法常用的AES可以参考。AES加密/解密算法
https://blog.csdn.net/qq_39543984/article/details/152130315?spm=1001.2014.3001.5502
2、非对称加密算法
和对称加密算法最大的区别是，非对称加密算法需要两个密钥，公开密钥（public key 简称公钥）和私有密钥（private key 简称私钥），且公钥与私钥是互相关联的一对。使用公钥对数据进行加密，只有用对应的私钥才能解密，私钥加密签名也只有公钥能解密验签。
非对称加密算法实现机密信息交换的基本过程：
1、甲方生成一对密钥并将公钥公开，私钥保密
2、乙方使用甲方的提供的公钥，对机密信息加密后再发送给甲方；甲方使用自己私钥对加密后的信息进行解密
3、甲方也可以使用自己的私钥对机密信息进行签名后再发送给乙方，乙方用甲方的提供公钥对甲方发来的密文进行验签
非对称加密算法的特点：
1、公钥公开，私钥私藏，无需双方传输密钥协商，所以安全性比对称加密算法更高
2、非对称加密的算法复杂，运算速度比对称加密解密的速度慢很多
3、一般情况下使用非对称加密保护对称加密的密钥，密钥协商后使用对称加密进行通信
4、最佳实现是双方各自保存自己的私钥，使用对方的公钥加密数据传输
3、RSA算法与密钥
非对称加密算法中最常用的当属 RSA ，其算法本身基于一个简单的数论知识，给出两个素数，很容易将它们相乘，然而给出它们的乘积，想得到这两个素数就显得尤为困难。具体的私钥与公钥生成原理和加密、解密过程，不是本文关注的重点。
私钥和公钥的生成，可以借助mbedtls源码或openSSL工具生成，举例如下：
1、安装openSSL，下载地址
https://www.openssl.org/
2、安装后进入openSSL命令行界面，使用命令生成RSA2048的私钥，存入private.key文件
OpenSSL>genrsa -out private.key 2048
3、基于公钥生成私钥，存入文件public.key
OpenSSL> rsa -in private.key -pubout -out public.key
4、有些算法库采用传入指数、模数方式进行加解密，而前面生成的公私钥是PEM格式，需要变成Exponent、Modulus形式，就可以使用以下工具在线转换。
https://www.oren.net.cn/rsa/info.htmlhttps://www.oren.net.cn/rsa/info.html
4、源码
以下是RSA2048的C源码和验证范例
//rsa.h
#include "stdlib.h"#define RSA_ENCODE_LEN (2048/8) //RSA2048即256字节，可以视硬件情况改为1024typedef unsigned char uint8_t;
typedef unsigned short int uint16_t;
typedef unsigned int uint32_t;#define BI_MAXLEN 130
#define DEC 10
#define HEX 16#define CARRYOVER 0x10000
#define CARRYLAST 0xFFFFtypedef struct
{uint32_t m_nLength; //大数在0x1 00 00 00 00进制下的长度uint16_t m_ulValue[BI_MAXLEN]; //用数组记录大数在0x100000000进制下每一位的值
} CBigInt;//rsa.c
#include "rsa.h"
#include "time.h"/******************* 适配API *******************/
#define portable_malloc malloc
#define portable_free free//随机数种子源
uint32_t portable_rand_seed(void)
{time_t timestamp;time(×tamp);return timestamp;
}
/******************* 适配API *******************//*****************************************************************
*****************************************************************/
static CBigInt *Mov_Big_Long(CBigInt *X, uint32_t A);
static CBigInt *Mov_Big_Big(CBigInt *X, CBigInt *A);
static CBigInt *Add_Big_Big(CBigInt *X, CBigInt *A);
static CBigInt *Sub_Big_Big(CBigInt *X, CBigInt *A);
static CBigInt *Mul_Big_Big(CBigInt *X, CBigInt *A);
static CBigInt *Div_Big_Big(CBigInt *X, CBigInt *A);
static CBigInt *Mod_Big_Big(CBigInt *X, CBigInt *A);
static CBigInt *Add_Big_Long(CBigInt *X, uint32_t A);
static CBigInt *Sub_Big_Long(CBigInt *X, uint32_t A);
static CBigInt *Mul_Big_Long(CBigInt *X, uint32_t A);
static CBigInt *Div_Big_Long(CBigInt *X, uint32_t A);
static uint32_t Mod_Big_Long(CBigInt *N, uint32_t A);
static int Cmp(CBigInt *N, CBigInt *A);/*****************************************************************
*****************************************************************/
static CBigInt *Get(CBigInt *N, char *str, uint32_t system);
static char *Put(CBigInt *N, uint32_t system);/*****************************************************************
RSA相关运算
Rab，拉宾米勒算法进行素数测试
Euc，欧几里德算法求解同余方程
RsaTrans，反复平方算法进行幂模运算
GetPrime，产生指定长度的随机大素数
*****************************************************************/
static int Rab(CBigInt *N);
static CBigInt *Euc(CBigInt *X, CBigInt *A);
static CBigInt *RsaTrans(CBigInt *X, CBigInt *A, CBigInt *B);
static CBigInt *GetPrime(CBigInt *X, int bits);/*****************************************************************
大数运算库源文件：BigInt.c
说明：适用于C，linux系统 1024位RSA运算
*****************************************************************/
//小素数表
const static int PrimeTable[550] =
{3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73,79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179,181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283,293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419,421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547,557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661,673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811,821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947,953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229,1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381,1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523,1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663,1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993,1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131,2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293,2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437,2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621,2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749,2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909,2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083,3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259,3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433,3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581,3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733,3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911,3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001
};/****************************************************************************************
****************************************************************************************/
static int Cmp(CBigInt *N, CBigInt *A)
{int i;if(N->m_nLength > A->m_nLength){return 1;}if(N->m_nLength < A->m_nLength){return -1;}for(i = N->m_nLength - 1; i >= 0; i--){if(N->m_ulValue[i] > A->m_ulValue[i]){return 1;}if(N->m_ulValue[i] < A->m_ulValue[i]){return -1;}}return 0;
}/****************************************************************************************
****************************************************************************************/
static CBigInt *Mov_Big_Big(CBigInt *X, CBigInt *A)
{memcpy(X, A, sizeof(CBigInt));return X;
}static CBigInt *Mov_Big_Long(CBigInt *N, uint32_t A)
{int i;if(A > CARRYLAST){N->m_nLength = 2;N->m_ulValue[1] = (uint16_t)(A >> 16);N->m_ulValue[0] = (uint16_t)A;}else{N->m_nLength = 1;N->m_ulValue[0] = (uint16_t)A;}memset((unsigned char*)&N->m_ulValue[N->m_nLength], 0, sizeof(uint16_t) * (BI_MAXLEN - N->m_nLength));return N;
}/********************************************************************************************************************************************************************************/
static CBigInt *Add_Big_Big(CBigInt *X, CBigInt *A)
{uint32_t i;uint16_t carry = 0;uint32_t sum = 0;if(X->m_nLength < A->m_nLength){X->m_nLength = A->m_nLength;}for(i = 0; i < X->m_nLength; i++){sum = A->m_ulValue[i];sum = sum + X->m_ulValue[i] + carry;X->m_ulValue[i] = (uint16_t)sum;carry = (uint16_t)(sum >> 16);}X->m_ulValue[X->m_nLength] = carry;X->m_nLength += carry;return X;
}static CBigInt *Add_Big_Long(CBigInt *X, uint32_t A)
{uint32_t sum;sum = X->m_ulValue[0];sum += A;X->m_ulValue[0] = (uint16_t)sum;if(sum > CARRYLAST){uint32_t i = 1;while(X->m_ulValue[i] == CARRYLAST){X->m_ulValue[i] = 0;i++;}X->m_ulValue[i]++;if(X->m_nLength == i){X->m_nLength++;}}return X;
}/****************************************************************************************
****************************************************************************************/
static CBigInt *Sub_Big_Big(CBigInt *X, CBigInt *A)
{if(Cmp(X, A) <= 0){memset(X, 0, sizeof(CBigInt));return X;}else{uint16_t carry = 0;uint32_t num;uint32_t i;for(i = 0; i < X->m_nLength; i++){if((X->m_ulValue[i] > A->m_ulValue[i]) || ((X->m_ulValue[i] == A->m_ulValue[i]) && (carry == 0))){X->m_ulValue[i] = X->m_ulValue[i] - carry - A->m_ulValue[i];carry = 0;}else{num = CARRYOVER + X->m_ulValue[i];X->m_ulValue[i] = (uint32_t)(num - carry - A->m_ulValue[i]);carry = 1;}}while(X->m_ulValue[X->m_nLength - 1] == 0){X->m_nLength--;}return X;}
}static CBigInt *Sub_Big_Long(CBigInt *X, uint32_t A)
{if(X->m_ulValue[0] >= A){X->m_ulValue[0] -= A;return X;}if(X->m_nLength == 1){memset(X, 0, sizeof(CBigInt));return X;}else{uint32_t num = CARRYOVER + X->m_ulValue[0];int i = 1;X->m_ulValue[0] = (uint16_t)(num - A);while(X->m_ulValue[i] == 0){X->m_ulValue[i] = CARRYLAST;i++;}X->m_ulValue[i]--;if(X->m_ulValue[i] == 0){X->m_nLength--;}return X;}
}/****************************************************************************************
****************************************************************************************/
static CBigInt *Mul_Big_Big(CBigInt *X, CBigInt *A)
{if(A->m_nLength == 1){return Mul_Big_Long(X, A->m_ulValue[0]);}else{uint32_t sum, mul = 0, carry = 0;uint32_t i, j;CBigInt N = {0};memcpy(&N, X, sizeof(CBigInt));memset(X, 0, sizeof(CBigInt));X->m_nLength = N.m_nLength + A->m_nLength - 1;for(i = 0; i < X->m_nLength; i++){sum = carry;carry = 0;for(j = 0; j < A->m_nLength; j++){if(((i - j) >= 0) && ((i - j) < N.m_nLength)){mul = N.m_ulValue[i - j];mul *= A->m_ulValue[j];carry += mul >> 16;mul = mul & CARRYLAST;sum += mul;}}carry += sum >> 16;X->m_ulValue[i] = (uint16_t)sum;}if(carry){X->m_nLength++;X->m_ulValue[X->m_nLength - 1] = (uint16_t)carry;}return X;}
}static CBigInt *Mul_Big_Long(CBigInt *X, uint32_t A)
{uint32_t mul;uint32_t carry = 0;uint32_t i;for(i = 0; i < X->m_nLength; i++){mul = X->m_ulValue[i];mul = mul * A + carry;X->m_ulValue[i] = (uint16_t)mul;carry = (uint16_t)(mul >> 16);}if(carry){X->m_nLength++;X->m_ulValue[X->m_nLength - 1] = carry;}return X;
}/****************************************************************************************
****************************************************************************************/
static CBigInt *Div_Big_Big(CBigInt *X, CBigInt *A)
{CBigInt Y = {0}, Z = {0}, T;if(A->m_nLength == 1){return Div_Big_Long(X, A->m_ulValue[0]);}else{uint32_t i, len;uint32_t num, div;memcpy(&Y, X, sizeof(CBigInt));while(Cmp(&Y, A) >= 0){div = Y.m_ulValue[Y.m_nLength - 1];num = A->m_ulValue[A->m_nLength - 1];len = Y.m_nLength - A->m_nLength;if((div == num) && (len == 0)){Add_Big_Long(X, 1);break;}if((div <= num) && len){len--;div = (div << 16) + Y.m_ulValue[Y.m_nLength - 2];}div = div / (num + 1);Mov_Big_Long(&Z, div);if(len){Z.m_nLength += len;for(i = Z.m_nLength - 1; i >= len; i--){Z.m_ulValue[i] = Z.m_ulValue[i - len];}for(i = 0; i < len; i++){Z.m_ulValue[i] = 0;}}Add_Big_Big(X, &Z);memcpy(&T, A, sizeof(CBigInt));Mul_Big_Big(&T, &Z);Sub_Big_Big(&Y, &T);}return X;}
}
static CBigInt *Div_Big_Long(CBigInt *X, uint32_t A)
{if(X->m_nLength == 1){X->m_ulValue[0] = X->m_ulValue[0] / A;return X;}else{uint32_t div, mul;uint32_t carry = 0;int i;for(i = X->m_nLength - 1; i >= 0; i--){div = carry;div = (div << 16) + X->m_ulValue[i];X->m_ulValue[i] = (uint16_t)(div / A);mul = (div / A) * A;carry = (uint16_t)(div - mul);}if(X->m_ulValue[X->m_nLength - 1] == 0){X->m_nLength--;}return X;}
}/****************************************************************************************
****************************************************************************************/
static CBigInt *Mod_Big_Big(CBigInt *X, CBigInt *A)
{CBigInt Y = {0}, Z;uint32_t div, num;uint32_t carry = 0;uint32_t i, len;while(Cmp(X, A) >= 0){div = X->m_ulValue[X->m_nLength - 1];num = A->m_ulValue[A->m_nLength - 1];len = X->m_nLength - A->m_nLength;if((div == num) && (len == 0)){Sub_Big_Big(X, A);break;}if((div <= num) && len){len--;div = (div << 16) + X->m_ulValue[X->m_nLength - 2];}div = div / (num + 1);Mov_Big_Long(&Y, div);memcpy(&Z, A, sizeof(CBigInt));Mul_Big_Big(&Z, &Y);memcpy(&Y, &Z, sizeof(CBigInt));if(len){Y.m_nLength += len;for(i = Y.m_nLength - 1; i >= len; i--){Y.m_ulValue[i] = Y.m_ulValue[i - len];}for(i = 0; i < len; i++){Y.m_ulValue[i] = 0;}}Sub_Big_Big(X, &Y);}return X;
}static uint32_t Mod_Big_Long(CBigInt *N, uint32_t A)
{if(N->m_nLength == 1){return(N->m_ulValue[0] % A);}else{uint32_t div;uint32_t carry = 0;int i;for(i = N->m_nLength - 1; i >= 0; i--){div = N->m_ulValue[i];div += carry * CARRYOVER;carry = (uint16_t)(div % A);}return carry;}
}/****************************************************************************************
****************************************************************************************/
static CBigInt *Get(CBigInt *N, char *s, uint32_t system)
{int i;int len = strlen(s), k;memset(N, 0, sizeof(CBigInt));N->m_nLength = 1;for(i = 0; i < len; i++){Mul_Big_Long(N, system);if((s[i] >= '0') && (s[i] <= '9')){k = s[i] - 48;}else if((s[i] >= 'A') && (s[i] <= 'F')){k = s[i] - 55;}else if((s[i] >= 'a') && (s[i] <= 'f')){k = s[i] - 87;}else{k = 0;}Add_Big_Long(N, k);}return N;
}
static CBigInt *GetHex(CBigInt *N, unsigned char *s, unsigned short len, uint32_t system)
{int i, j;unsigned char *p = (unsigned char*)N->m_ulValue;memset(N, 0, sizeof(CBigInt));N->m_nLength = 1;for(i = len - 1, j = 0; i >= 0; i--, j++){p[j] = s[i];}i = len % 2;if(i > 0){N->m_nLength = len / 2 + 1;}else{N->m_nLength = len / 2;}return N;
}
/****************************************************************************************
****************************************************************************************/
static char *Put(CBigInt *N, uint32_t system)
{char t[17] = "0123456789ABCDEF";int i, a;static char s[2048];if((N->m_nLength == 1) && (N->m_ulValue[0] == 0)){return NULL;}else{CBigInt X = {0};memcpy(&X, N, sizeof(CBigInt));memset(s, 0, 2048);for(i = 2046; X.m_ulValue[X.m_nLength - 1] > 0 && i > 0; i--){a = Mod_Big_Long(&X, system);s[i] = t[a];Div_Big_Long(&X, system);}if(i % 2 == 0){return &s[i + 1];}else{s[i] = '0';return &s[i];}}
}static void PutHex(CBigInt *N, uint8_t *out, uint16_t *len)
{int i, j, size;if((N->m_nLength == 1) && (N->m_ulValue[0] == 0)){return;}size = N->m_nLength * sizeof(N->m_ulValue[0]);for(i = size - 1, j = 0; i >= 0; i--, j++){out[j] = ((uint8_t*)N->m_ulValue)[i];}*len = size;
}/****************************************************************************************
****************************************************************************************/
static CBigInt *Euc(CBigInt *X, CBigInt *A)
{CBigInt M = {0}, E = {0}, N = {0}, Y = {0}, I = {0}, J = {0};int x, y;memcpy(&E, X, sizeof(CBigInt));memcpy(&M, A, sizeof(CBigInt));Mov_Big_Long(X, 0);Mov_Big_Long(&Y, 1);x = y = 1;while((E.m_nLength != 1) || (E.m_ulValue[0] != 0)){memcpy(&I, &M, sizeof(CBigInt));Div_Big_Big(&I, &E);memcpy(&J, &M, sizeof(CBigInt));Mod_Big_Big(&J, &E);memcpy(&M, &E, sizeof(CBigInt));memcpy(&E, &J, sizeof(CBigInt));memcpy(&J, &Y, sizeof(CBigInt));Mul_Big_Big(&Y, &I);if(x == y){if(Cmp(X, &Y) >= 0){Sub_Big_Big(&Y, X);}else{Sub_Big_Big(&Y, X);y = 0;}}else{Add_Big_Big(&Y, X);x = 1 - x;y = 1 - y;}memcpy(X, &J, sizeof(CBigInt));}if(x == 0){Sub_Big_Big(X, A);}return X;
}/****************************************************************************************
****************************************************************************************/
static CBigInt *RsaTrans(CBigInt *X, CBigInt *A, CBigInt *B)
{CBigInt N = {0}, Y = {0}, Z;int i, j, k;uint32_t n;uint32_t num;k = A->m_nLength * 16 - 16;num = A->m_ulValue[A->m_nLength - 1];while(num){num = num >> 1;k++;}memcpy(&N, X, sizeof(CBigInt));for(i = k - 2; i >= 0; i--){memcpy(&Y, X, sizeof(CBigInt));Mul_Big_Long(&Y, X->m_ulValue[X->m_nLength - 1]);Mod_Big_Big(&Y, B);for(n = 1; n < X->m_nLength; n++){for(j = Y.m_nLength; j > 0; j--){Y.m_ulValue[j] = Y.m_ulValue[j - 1];}Y.m_ulValue[0] = 0;Y.m_nLength++;memcpy(&Z, X, sizeof(CBigInt));Mul_Big_Long(&Z, X->m_ulValue[X->m_nLength - n - 1]);Add_Big_Big(&Y, &Z);Mod_Big_Big(&Y, B);}memcpy(X, &Y, sizeof(CBigInt));if((A->m_ulValue[i >> 4] >> (i & 15)) & 1){memcpy(&Y, &N, sizeof(CBigInt));Mul_Big_Long(&Y, X->m_ulValue[X->m_nLength - 1]);Mod_Big_Big(&Y, B);for(n = 1; n < X->m_nLength; n++){for(j = Y.m_nLength; j > 0; j--){Y.m_ulValue[j] = Y.m_ulValue[j - 1];}Y.m_ulValue[0] = 0;Y.m_nLength++;memcpy(&Z, &N, sizeof(CBigInt));Mul_Big_Long(&Z, X->m_ulValue[X->m_nLength - n - 1]);Add_Big_Big(&Y, &Z);Mod_Big_Big(&Y, B);}memcpy(X, &Y, sizeof(CBigInt));}}return X;
}/****************************************************************************************
****************************************************************************************/
static int Rab(CBigInt *N)
{CBigInt S = {0}, A = {0}, I = {0}, K = {0};uint32_t i, j, pass;for(i = 0; i < 550; i++){if(Mod_Big_Long(N, PrimeTable[i]) == 0){return 0;}}memcpy(&K, N, sizeof(CBigInt));K.m_ulValue[0]--;for(i = 0; i < 5; i++){pass = 0;Mov_Big_Long(&A, rand()*rand());memcpy(&S, &K, sizeof(CBigInt));while((S.m_ulValue[0] & 1) == 0){for(j = 0; j < S.m_nLength; j++){S.m_ulValue[j] = S.m_ulValue[j] >> 1;if(S.m_ulValue[j + 1] & 1){S.m_ulValue[j] = S.m_ulValue[j] | 0x8000;}}if(S.m_ulValue[S.m_nLength - 1] == 0){S.m_nLength--;}memcpy(&I, &A, sizeof(CBigInt));RsaTrans(&I, &S, N);if(Cmp(&I, &K) == 0){pass = 1;break;}}if((I.m_nLength == 1) && (I.m_ulValue[0] == 1)){pass = 1;}if(pass == 0){return 0;}}return 1;
}/****************************************************************************************
产生随机素数
调用方法：GetPrime(N,bits)
返回值：N,被赋值为一个bits位（0x100000000进制长度）的素数
****************************************************************************************/
static CBigInt *GetPrime(CBigInt *N, int bits)
{uint32_t i;CBigInt S = {0}, A = {0}, I = {0}, K = {0};memset(N, 0, sizeof(CBigInt));N->m_nLength = bits;
begin:srand(portable_rand_seed());for(i = 0; i < N->m_nLength; i++){N->m_ulValue[i] = rand() * 0x100 + rand();}N->m_ulValue[0] = N->m_ulValue[0] | 1;for(i = N->m_nLength - 1; i > 0; i--){N->m_ulValue[i] = N->m_ulValue[i] << 1;if(N->m_ulValue[i - 1] & 0x8000){N->m_ulValue[i]++;}}N->m_ulValue[0] = N->m_ulValue[0] << 1;N->m_ulValue[0]++;for(i = 0; i < 550; i++){if(Mod_Big_Long(N, PrimeTable[i]) == 0){goto begin;}}memcpy(&K, N, sizeof(CBigInt));K.m_ulValue[0]--;for(i = 0; i < 5; i++){Mov_Big_Long(&A, rand()*rand());memcpy(&S, &K, sizeof(CBigInt));Div_Big_Long(&S, 2);memcpy(&I, &A, sizeof(CBigInt));RsaTrans(&I, &S, N);if(((I.m_nLength != 1) || (I.m_ulValue[0] != 1)) && (Cmp(&I, &K) != 0)){goto begin;}}return N;
}/***********************************************************************/static void entropy_poll(unsigned char *output, unsigned int len)
{if(len > 0){int i;srand(portable_rand_seed);for(i = 0; i < len; i++){output[i] = rand() % 0xff + 1;}}
}static char *del_PKCS1Padding(char *src)
{int len = strlen(src);if(len % 2 == 1){src++;}while(*src != 0 && *(src + 1) != 0){if(*src == '0' && *(src + 1) == '0'){src += 2;break;}src += 2;}return src;
}static int add_PKCS1Padding(unsigned char *src, unsigned int len, unsigned char *out)
{if(len > RSA_ENCODE_LEN - 11){return -1;}else{/*要加密的msg*/memcpy(&out[RSA_ENCODE_LEN - len], src, len);out[0] = 0;out[1] = 2;/*至少8字节的随机数*/entropy_poll(&out[2], RSA_ENCODE_LEN - 3 - len);out[RSA_ENCODE_LEN - len - 1] = 0;return 0;}
}static int PKCS1PKCS1PaddingHexRemove(unsigned char *input, unsigned short *len, unsigned char *output)
{if(input[0] == 0 && (input[1] == 1 || input[1] == 2)){int i;for(i = 2; i < *len; i++){if(input[i] == 0){*len -= (i + 1);memcpy(output, &input[i + 1], *len);return *len;}}}return -1;
}int RSA2048_pri_PKCS1Padding_Encode(unsigned char *data, unsigned short len, unsigned char *out, char *publicKey, char *ModulusHex)
{unsigned char buf[RSA_ENCODE_LEN];CBigInt N, E;CBigInt mw, mi, jm;uint16_t outlen = RSA_ENCODE_LEN;//Get(&N, Modulus, 16);//stringGetHex(&N, ModulusHex, RSA_ENCODE_LEN, 16);//hex arrayGet(&E, publicKey, 16);add_PKCS1Padding(data, len, buf);GetHex(&mw, buf, RSA_ENCODE_LEN, 16);RsaTrans(&mw, &E, &N);PutHex(&mw, out, &outlen);return outlen;
}int RSA2048_pub_PKCS1Padding_Encode(unsigned char *data, unsigned short len, unsigned char *out, char *publicKey, unsigned char *ModulusHex)
{unsigned char buf[RSA_ENCODE_LEN];CBigInt N, E;CBigInt mw, mi, jm;uint16_t outlen = RSA_ENCODE_LEN;GetHex(&N, ModulusHex, RSA_ENCODE_LEN, 16);//hex arrayGet(&E, publicKey, 16);add_PKCS1Padding(data, len, buf);GetHex(&mw, buf, RSA_ENCODE_LEN, 16);RsaTrans(&mw, &E, &N);PutHex(&mw, out, &outlen);return outlen;
}int RSA2048_pri_PKCS1Padding_Decode(unsigned char *data, unsigned short *len, unsigned char *out, char *privateKey, char *ModulusHex)
{unsigned char buf[RSA_ENCODE_LEN];CBigInt N, D;CBigInt mw, jm;//Get(&N, Modulus, 16);//stringGetHex(&N, ModulusHex, RSA_ENCODE_LEN, 16);//hex arrayGet(&D, privateKey, 16);GetHex(&mw, data, *len, 16);RsaTrans(&mw, &D, &N);PutHex(&mw, buf, len);PKCS1PKCS1PaddingHexRemove(buf, len, out);return 0;
}
int RSA2048_pub_PKCS1Padding_Decode(unsigned char *data, unsigned short *len, unsigned char *out, char *privateKey, unsigned char *ModulusHex)
{unsigned char buf[RSA_ENCODE_LEN];CBigInt N, D;CBigInt mw, jm;int t_len = 0;GetHex(&N, ModulusHex, RSA_ENCODE_LEN, 16);Get(&D, privateKey, 16);GetHex(&mw, data, *len, 16);RsaTrans(&mw, &D, &N);PutHex(&mw, buf, len);t_len = PKCS1PKCS1PaddingHexRemove(buf, len, out);return t_len;
}//test
static const unsigned char base64_table[65] = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";//需要释放内存
unsigned char * base64_encode(const unsigned char *src, size_t len, size_t *out_len)
{unsigned char *out, *pos;const unsigned char *end, *in;size_t olen;int line_len;olen = len * 4 / 3 + 4; /* 3-byte blocks to 4-byte */olen += olen / 72; /* line feeds */olen++; /* nul termination */if(olen < len){return NULL; /* integer overflow */}out = portable_malloc(olen);if(out == NULL){return NULL;}end = src + len;in = src;pos = out;line_len = 0;while(end - in >= 3){*pos++ = base64_table[in[0] >> 2];*pos++ = base64_table[((in[0] & 0x03) << 4) | (in[1] >> 4)];*pos++ = base64_table[((in[1] & 0x0f) << 2) | (in[2] >> 6)];*pos++ = base64_table[in[2] & 0x3f];in += 3;line_len += 4;if(line_len >= 72){*pos++ = '\n';line_len = 0;}}if(end - in){*pos++ = base64_table[in[0] >> 2];if(end - in == 1){*pos++ = base64_table[(in[0] & 0x03) << 4];*pos++ = '=';}else{*pos++ = base64_table[((in[0] & 0x03) << 4) |(in[1] >> 4)];*pos++ = base64_table[(in[1] & 0x0f) << 2];}*pos++ = '=';line_len += 4;}if(line_len){*pos++ = '\n';}*pos = '\0';if(out_len){*out_len = pos - out;}return out;
}//需要释放内存
unsigned char * base64_decode(const unsigned char *src, size_t len,size_t *out_len)
{unsigned char dtable[256], *out, *pos, block[4], tmp;size_t i, count, olen;int pad = 0;memset(dtable, 0x80, 256);for(i = 0; i < sizeof(base64_table) - 1; i++){dtable[base64_table[i]] = (unsigned char) i;}dtable['='] = 0;count = 0;for(i = 0; i < len; i++){if(dtable[src[i]] != 0x80){count++;}}if(count == 0 || count % 4){return NULL;}olen = count / 4 * 3;pos = out = portable_malloc(olen);if(out == NULL){return NULL;}count = 0;for(i = 0; i < len; i++){tmp = dtable[src[i]];if(tmp == 0x80){continue;}if(src[i] == '='){pad++;}block[count] = tmp;count++;if(count == 4){*pos++ = (block[0] << 2) | (block[1] >> 4);*pos++ = (block[1] << 4) | (block[2] >> 2);*pos++ = (block[2] << 6) | block[3];count = 0;if(pad){if(pad == 1){pos--;}else if(pad == 2){pos -= 2;}else{/* Invalid padding */portable_free(out);return NULL;}break;}}}*out_len = pos - out;return out;
}int main(int argc, char *argv[])
{//原始公钥-私钥/*-----BEGIN PUBLIC KEY-----MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAwmejRhw/SB2xB3rgJYhgOWBDX/DponDVVPzTWhn3J4INv6jUa9HDkeHhys4OOZTNajr8kRy4TIemotnIYONJnoW7VyIQEAkEyxcMett5mqRPBLuyc8Fygn4ho/rd9JId4+PgKLmr6NVcuZCpVXPegyqNx0nR/UojISbq/Bu+NlcStmicZUuAeVbkGGUOlvtMzFehkBPwE31EdpYUq+/zLuJ8OaxC+zm5PFo2AZJfI5Gz5lgb1g5ud0TG1JUrm9Dl5/JSNSL3SXBEC77mdfd0BA5VFl8lV7IfTfSTUE9IKoMevqZxoaGpyN+ZcBby5NgsoqJJ6vmcJRFjI92UrFHV1wIDAQAB-----END PUBLIC KEY----------BEGIN PRIVATE KEY-----MIIEvQIBADANBgkqhkiG9w0BAQEFAASCBKcwggSjAgEAAoIBAQDCZ6NGHD9IHbEHeuAliGA5YENf8OmicNVU/NNaGfcngg2/qNRr0cOR4eHKzg45lM1qOvyRHLhMh6ai2chg40mehbtXIhAQCQTLFwx623mapE8Eu7JzwXKCfiGj+t30kh3j4+Aouavo1Vy5kKlVc96DKo3HSdH9SiMhJur8G742VxK2aJxlS4B5VuQYZQ6W+0zMV6GQE/ATfUR2lhSr7/Mu4nw5rEL7Obk8WjYBkl8jkbPmWBvWDm53RMbUlSub0OXn8lI1IvdJcEQLvuZ193QEDlUWXyVXsh9N9JNQT0gqgx6+pnGhoanI35lwFvLk2Cyioknq+ZwlEWMj3ZSsUdXXAgMBAAECggEAEnEUaw0475VpesUsSEM0pZy9J3fKIg/EHQjS3+RAru3Gch0I8aV3gPpFmiCL9uhnyCEKXpWz4gaoRyCTwqUtEa2sBOsFTRAd9Uodc/YoBgR6Pn+zwQlj3H8sn8qnjZDi5wBx/ksGxNKgtjXD6ohQXm8F/hbBpd6HkJiJiBr1o1/a4Kzh9L1OpYVS5QF0EN3idNkt911vfjA+bqBXXjAf9IHvirQ2GeCNzmHygxiRhAWAki2fm0pGbKFUAfo+sgtDPT2jrA4rhSHG4mMr8IWBpr082aKNns7ujxT9ndBCl0Pp7efPNCT4+zqfyVAB6x2rYhtXTqR7wsASMIfSLzyoIQKBgQDi2sb9z4OEl0mTV0Ey1Lia4F06QhD7Kl1mhBWYPA1RO1ieAHHINFvwPJQLjHR2yMRMDmTOc3S9Hy3H3QMGXZlrIl5sgeFzsdqGyd2kscGFUGkH9RY2V/XB0mxQFIGI2PBztqd6e6BJQz4oSyMzcBZq/NH5u95QRlyI0I1u5b5lMQKBgQDbYZdhqHcDYmc61aHRNEhnxbK4ph1bdTiMQbIF0wUssXQKwEzvYzswRlI27rXeSHpJA8vc+XAoD/+Ut30I8Td3yUnnsHZctU2Db/8OTqwFqyrwXM+SvyWZejuvX6IVJuRwPMFG88L88lryEs0ntlQKC/x6wxtcs67X6ZGsLSfJhwKBgQDAo09/kIv6OA4+lEXFSGZK/mOsaRXKcztFJry/vZ8BcAfchDwa6nt4EbkV5XuwsuQeQcrQlbJ4NtXFdqRu72SsWU8djV1Jxanv89PHWzseXh4Sp8jo9OC4aluX1RH6h14IpP6rP/fovrU1ujh2IaSnzXDxRNuQB2/krlSr62Q2wQKBgGNLjbgvBwcqH+06So6lKmyFx/nZfgoqSVj6VzhZpcrv2sUO+wOTF3QnMAkbDIg6p9aqeDhhUklfzF+kmVxVybRXEDNk5H3bteTa6Uexhhzet4WpjG4wRDVuZNtg3rzSKK1AYn7Z0BSrIUzWA7OIzArsF+/8pULVNTsWxc93dL27AoGAT3eaPv07rhzyztxFYTsrdHcgNb+vwroN3Ic7IJnxoa2BjyqczaAG3vMrOcxFg2MLJ7fPmI1W4pPOJyxmUhO0mZhk+F7h+dg7XB7h0lqR1usp3Ak3qyu1f4XZj4imzQWWyETpgE4uA9tBniPQIRK6miXhZ2YoXfdsSZOatWojGLI=-----END PRIVATE KEY-----*///https://www.oren.net.cn/rsa/info.html//在线转换为模数和指数//PEM->模数+指数char *publicKey_exponent = "10001";char *privateKey_exponent = "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";//hex array ,faster than string//直接使用16进制数据可略微提高速度，软件也支持传入字符串// 具体看代码中 GetHex 和 Getstatic unsigned char ModulusHex[RSA_ENCODE_LEN] ={0xC2, 0x67, 0xA3, 0x46, 0x1C, 0x3F, 0x48, 0x1D, 0xB1, 0x07, 0x7A, 0xE0, 0x25, 0x88, 0x60, 0x39,0x60, 0x43, 0x5F, 0xF0, 0xE9, 0xA2, 0x70, 0xD5, 0x54, 0xFC, 0xD3, 0x5A, 0x19, 0xF7, 0x27, 0x82,0x0D, 0xBF, 0xA8, 0xD4, 0x6B, 0xD1, 0xC3, 0x91, 0xE1, 0xE1, 0xCA, 0xCE, 0x0E, 0x39, 0x94, 0xCD,0x6A, 0x3A, 0xFC, 0x91, 0x1C, 0xB8, 0x4C, 0x87, 0xA6, 0xA2, 0xD9, 0xC8, 0x60, 0xE3, 0x49, 0x9E,0x85, 0xBB, 0x57, 0x22, 0x10, 0x10, 0x09, 0x04, 0xCB, 0x17, 0x0C, 0x7A, 0xDB, 0x79, 0x9A, 0xA4,0x4F, 0x04, 0xBB, 0xB2, 0x73, 0xC1, 0x72, 0x82, 0x7E, 0x21, 0xA3, 0xFA, 0xDD, 0xF4, 0x92, 0x1D,0xE3, 0xE3, 0xE0, 0x28, 0xB9, 0xAB, 0xE8, 0xD5, 0x5C, 0xB9, 0x90, 0xA9, 0x55, 0x73, 0xDE, 0x83,0x2A, 0x8D, 0xC7, 0x49, 0xD1, 0xFD, 0x4A, 0x23, 0x21, 0x26, 0xEA, 0xFC, 0x1B, 0xBE, 0x36, 0x57,0x12, 0xB6, 0x68, 0x9C, 0x65, 0x4B, 0x80, 0x79, 0x56, 0xE4, 0x18, 0x65, 0x0E, 0x96, 0xFB, 0x4C,0xCC, 0x57, 0xA1, 0x90, 0x13, 0xF0, 0x13, 0x7D, 0x44, 0x76, 0x96, 0x14, 0xAB, 0xEF, 0xF3, 0x2E,0xE2, 0x7C, 0x39, 0xAC, 0x42, 0xFB, 0x39, 0xB9, 0x3C, 0x5A, 0x36, 0x01, 0x92, 0x5F, 0x23, 0x91,0xB3, 0xE6, 0x58, 0x1B, 0xD6, 0x0E, 0x6E, 0x77, 0x44, 0xC6, 0xD4, 0x95, 0x2B, 0x9B, 0xD0, 0xE5,0xE7, 0xF2, 0x52, 0x35, 0x22, 0xF7, 0x49, 0x70, 0x44, 0x0B, 0xBE, 0xE6, 0x75, 0xF7, 0x74, 0x04,0x0E, 0x55, 0x16, 0x5F, 0x25, 0x57, 0xB2, 0x1F, 0x4D, 0xF4, 0x93, 0x50, 0x4F, 0x48, 0x2A, 0x83,0x1E, 0xBE, 0xA6, 0x71, 0xA1, 0xA1, 0xA9, 0xC8, 0xDF, 0x99, 0x70, 0x16, 0xF2, 0xE4, 0xD8, 0x2C,0xA2, 0xA2, 0x49, 0xEA, 0xF9, 0x9C, 0x25, 0x11, 0x63, 0x23, 0xDD, 0x94, 0xAC, 0x51, 0xD5, 0xD7};unsigned char encode_str[RSA_ENCODE_LEN] = {0};unsigned char decode_str[RSA_ENCODE_LEN] = {0};int outlen = 0;unsigned char * base64_str = NULL;unsigned int base64_str_len = NULL;uint8_t* decode_base64 = NULL;char pub_source_string[] = "embedded-system > Public key to RSA encode,hehe";char pri_source_string[] = "embedded-system > Private key to RSA encode,haha";printf("RSA demo");//---------------------------------------------------memset(encode_str, 0, sizeof(encode_str));memset(decode_str, 0, sizeof(decode_str));//公钥加密outlen = RSA2048_pub_PKCS1Padding_Encode(pub_source_string, strlen(pub_source_string), encode_str, publicKey_exponent, ModulusHex);//密文转base64方便显示，和在线工具对比结果// https://the-x.cn/cryptography/Rsa.aspx//base64_str = base64_encode(encode_str, outlen, &base64_str_len);//printf("Public encode %d\r\n%s\r\n", base64_str_len, base64_str);//portable_free(base64_str);//私钥解密RSA2048_pri_PKCS1Padding_Decode(encode_str, &outlen, decode_str, privateKey_exponent, ModulusHex);printf("Private decode %d\r\n%s\r\n", outlen, decode_str);//---------------------------------------------------memset(encode_str, 0, sizeof(encode_str));memset(decode_str, 0, sizeof(decode_str));//私钥签名outlen = RSA2048_pri_PKCS1Padding_Encode(pri_source_string, strlen(pri_source_string), encode_str, privateKey_exponent, ModulusHex);//公钥验签RSA2048_pub_PKCS1Padding_Decode(encode_str, &outlen, decode_str, publicKey_exponent, ModulusHex);printf("Public decode %d\r\n%s\r\n", outlen, decode_str);//---------------------------------------------------printf("RSA demo done");return 0;
}
5、应用
和AES一样，RSA也是块加密算法（ block cipher algorithm），只针对固定长度数据块，如RSA2048其加密的数据长度需要填充后是2048位即256字节，如果明文长度大于244字节则需要拆分。当然最简单的办法是应用层分配多个244字节缓存，有效数据以外以0x00填充。
RSA算法虽然安全，但其计算量非常大，效率较低，尤其在嵌入式系统中，硬件资源有限的情况下加密、解密时间以秒为单位。而对称加密算法AES算法效率高，但其在密钥协商时，在网络传输中有被拦截的风险，或者任一方保存不当导致密钥泄露，其密钥存在很大的安全隐患。
所以，考虑到安全性和高效性，一般采用多种算法组合加密的方式。使用RSA来加密AES的密钥，密钥协商后，使用AES来对后续数据进行加密。