加密算法从0到-1--1SM4加密算法
## SM4
- 密钥长度为128bits
- 加密算法和密钥扩展算法都是32位非线性迭代结构
- 加解密算法结构相同，轮密钥的使用顺序相反
#### 定义运算
32位数$x$向左循环移动$i$位$:x<<<i,\oplus$为异或
```cpp
#define ROL32(x,i) ((x)<<(i)|(((unsigned int)x>>(32-(i)))))
```
#### 定义参量
密钥长度位128bits $MK=(MK_0,MK_1,MK_2,MK_3)$
轮密钥为32*32bits $rk=(rk_0,rk_1,...,rk_{31})$
$FK=(FK_0,FK_1,...,FK_3)$为系统参数，$CK=(CK_0,CK_1,...,CK_{31})$为固定参数
$CK_{i,j}=(4i+j)*7\ mod\ 256$，其中$i$为双字编号，$j$为字节编号，$j$采用大端序
```cpp
#define RK_SIZE 32
static uint32_t mk; // 加密使用的密钥
static uint32_t rk; // 轮密钥
static uint32_t fk={0xA3B1BAC6,0x56AA3350,0x677D9197,0xB27022DC};
// ck会在密钥生成算法中体现
```
#### 轮函数F
$F(X_0,X_1,X_2,X_3,rk)=X_0\oplus T(X_1\oplus X_2\oplus X_3\oplus rk)$
合成置换$T(.)=L(\tau(.))$
若输入为$A=(a_0,a_1,a_2,a_3)$，其中$a_i$为8字节无符号整数，则非线性置换$\tau(A)=(sbox,sbox,sbox,sbox)$
$sbox$为替换用s盒
若输入为$B$，其中$B$为32字节无符号整数，则线性变换$L(B)=B\oplus (B<<<2)\oplus(B<<<10)\oplus(B<<<18)\oplus(B<<<24)$
```cpp
#define L(x) (x)^ROL32(x,2)^ROL32(x,10)^ROL32(x,18)^ROL32(x,24)
#define tau(x) (sbox[(x)>>24]<<24|sbox[((x)>>16)&0xFF]<<16|sbox[((x)>>8)&0xFF]<<8|sbox)
#define T(x) (L(tau(x)))
uint8_t sbox; // s盒，在最终代码中体现
// 轮函数F直接在加密过程中体现
```
#### 加密算法
反序变换$R(a_0,a_1,a_2,a_3)=(a_3,a_2,a_1,a_0),a_i$为8位
设输入为$(X_0,X_1,X_2,X_3),X_i$为32位
输出为$(Y_0,Y_1,Y_2,Y_3)$
则$X_{i+4}=F(X_i,X_{i+1},X_{i+2},X_{i+3},rk_i)$
$(Y_0,Y_1,Y_2,Y_3)=R(X_{32},X_{33},X_{34},X_{35})$
解密过程和加密过程变换结构相同，不同的是轮密钥顺序
加密时$(rk_0,rk_1,...,rk_{31})$
解密时$rk_{31},rk_{30},...,rk_0$
```cpp
void crypt(uint32_t p,uint32_t crk){
uint32_t c;
c=p;
c=p;
c=p;
c=p;
for(size_t i=0;i<RK_SIZE;i++){
c=c^T(c^c^c^crk);
}
p=c;
p=c;
p=c;
p=c;
}
void encrypt(uint32_t p){
crypt(p,rk);
}
void decrypt(uint32_t c){
crypt(p,rrk); // rrk是rk的逆序
}
```
#### 密钥扩展算法
密钥$MK=(MK_0,MK_1,MK_2,MK_3)$
$K=(K_0,K_1,...,K_{31})$
$(K_0,K_1,K_2,K_3)=(MK_0\oplus FK_0,MK_1\oplus FK_1,MK_2\oplus FK_2,MK_3\oplus FK_3)$
轮密钥为$rk,rk_i=K_{i+4}=K_i\oplus T'(K_{i+1}\oplus K_{i+2}\oplus K_{i+3}\oplus CK_i)$
$T'$和$T$基本相同，其中的$L'=B\oplus(B<<<13)\oplus(B<<<23)$
```cpp
#define Lp(x) ((x)^ROL32(x,13)^ROL32(x,23))
#define Tp(x) Lp(tau(x))
#define ck(i) (((4*(i)*7)&0xFF)<<24|(((4*(i)+1)*7)&0xFF)<<16|(((4*(i)+2)*7)&0xFF)<<8|(4*(i)+3)&0xFF)
void initKey(uin32_t mk){
uint32_t k;
k=mk^fk;
for(size_t i=0;i<RK_SIZE;i++){
k=k^Tp(k^k^k^ck(i));
rk=k;
rrk=rk
}
}
```
#### 完整代码
```cpp
#include <string.h>
#include <stdio.h>
#include <stdlib.h>
#include <memory.h>
#include <inttypes.h>
#define cha(x) ((((x)&0x3F)+24)%64)
#define ROL32(x,i) ((x)<<(i)|(((unsigned int)(x)>>(32-(i)))))
#define L(x) (x)^ROL32(x,2)^ROL32(x,10)^ROL32(x,18)^ROL32(x,24)
#define tau(x) (sbox[((x)>>24)&0xFF]<<24|sbox[((x)>>16)&0xFF]<<16|sbox[((x)>>8)&0xFF]<<8|sbox)
#define T(x) (L(tau(x)))
#define Lp(x) ((x)^ROL32(x,13)^ROL32(x,23)) // L'
#define Tp(x) (Lp(tau(x))) // T'
#define ck(i) (((4*(i)*7)&0xFF)<<24|(((4*(i)+1)*7)&0xFF)<<16|(((4*(i)+2)*7)&0xFF)<<8|(4*(i)+3)*7&0xFF)
#define R(x) (((x)>>24)&0xFF|((x)>>8)&0xFF00|((x)<<8)&0xFF0000|((x)<<24))
#define RK_SIZE 32 // 密钥轮数
static uint32_t rk; // 轮密钥
static uint32_t rrk; // 逆序轮密钥
static uint32_t fk = { 0xA3B1BAC6,0x56AA3350,0x677D9197,0xB27022DC };
static uint8_t sbox = {
0xd6,0x90,0xe9,0xfe,0xcc,0xe1,0x3d,0xb7,0x16,0xb6,0x14,0xc2,0x28,0xfb,0x2c,0x05,
0x2b,0x67,0x9a,0x76,0x2a,0xbe,0x04,0xc3,0xaa,0x44,0x13,0x26,0x49,0x86,0x06,0x99,
0x9c,0x42,0x50,0xf4,0x91,0xef,0x98,0x7a,0x33,0x54,0x0b,0x43,0xed,0xcf,0xac,0x62,
0xe4,0xb3,0x1c,0xa9,0xc9,0x08,0xe8,0x95,0x80,0xdf,0x94,0xfa,0x75,0x8f,0x3f,0xa6,
0x47,0x07,0xa7,0xfc,0xf3,0x73,0x17,0xba,0x83,0x59,0x3c,0x19,0xe6,0x85,0x4f,0xa8,
0x68,0x6b,0x81,0xb2,0x71,0x64,0xda,0x8b,0xf8,0xeb,0x0f,0x4b,0x70,0x56,0x9d,0x35,
0x1e,0x24,0x0e,0x5e,0x63,0x58,0xd1,0xa2,0x25,0x22,0x7c,0x3b,0x01,0x21,0x78,0x87,
0xd4,0x00,0x46,0x57,0x9f,0xd3,0x27,0x52,0x4c,0x36,0x02,0xe7,0xa0,0xc4,0xc8,0x9e,
0xea,0xbf,0x8a,0xd2,0x40,0xc7,0x38,0xb5,0xa3,0xf7,0xf2,0xce,0xf9,0x61,0x15,0xa1,
0xe0,0xae,0x5d,0xa4,0x9b,0x34,0x1a,0x55,0xad,0x93,0x32,0x30,0xf5,0x8c,0xb1,0xe3,
0x1d,0xf6,0xe2,0x2e,0x82,0x66,0xca,0x60,0xc0,0x29,0x23,0xab,0x0d,0x53,0x4e,0x6f,
0xd5,0xdb,0x37,0x45,0xde,0xfd,0x8e,0x2f,0x03,0xff,0x6a,0x72,0x6d,0x6c,0x5b,0x51,
0x8d,0x1b,0xaf,0x92,0xbb,0xdd,0xbc,0x7f,0x11,0xd9,0x5c,0x41,0x1f,0x10,0x5a,0xd8,
0x0a,0xc1,0x31,0x88,0xa5,0xcd,0x7b,0xbd,0x2d,0x74,0xd0,0x12,0xb8,0xe5,0xb4,0xb0,
0x89,0x69,0x97,0x4a,0x0c,0x96,0x77,0x7e,0x65,0xb9,0xf1,0x09,0xc5,0x6e,0xc6,0x84,
0x18,0xf0,0x7d,0xec,0x3a,0xdc,0x4d,0x20,0x79,0xee,0x5f,0x3e,0xd7,0xcb,0x39,0x48
};
void crypt(uint32_t p, uint32_t crk) {
uint32_t c;
c = p;
c = p;
c = p;
c = p;
uint32_t t;
for (size_t i = 0; i < RK_SIZE; i++) {
t = (c ^ c ^ c ^ crk);
c = c ^ T(t);
printf("%08x\n", c);
}
p = c;
p = c;
p = c;
p = c;
}
void encrypt(uint32_t p) {
crypt(p, rk);
}
void decrypt(uint32_t c) {
crypt(c, rrk); // rrk是rk的逆序
}
void initKey(uint32_t mk) {
uint32_t k;
k = mk ^ fk;
k = mk ^ fk;
k = mk ^ fk;
k = mk ^ fk;
uint32_t t;
for (size_t i = 0; i < RK_SIZE; i++) {
t = k ^ k ^ k^ck(i);
k = k ^ Tp(t);
rk = k;
rrk = rk;
}
}
void printArray(const char* name, uint32_t* d, size_t len) {
printf("==============%s============\n", name);
for (size_t i = 0; i < len; i++) {
printf("0x%08X,", d);
}
printf("\n============================\n");
}
int main() {
uint8_t data[] = { 0x01,0x23,0x45,0x67,0x89,0xab,0xcd,0xef,0xfe,0xdc,0xba,0x98,0x76,0x54,0x32,0x10 };
uint8_t key[] = { 0x01,0x23,0x45,0x67,0x89,0xab,0xcd,0xef,0xfe,0xdc,0xba,0x98,0x76,0x54,0x32,0x10 };
uint32_t mk;
uint32_t p;
memcpy(p, data, 16);
memcpy(mk, key, 16);
for (size_t i = 0; i < 4; i++) {
mk = R(mk);
p = R(p);
}
initKey(mk);
printArray("plain text", p, 4);
encrypt(p);
printArray("cipher", p, 4);
decrypt(p);
printArray("plain text(after decrypt)", p, 4);
for (size_t i = 0; i < 4; i++) {
p = R(p);
}
memcpy(data, p, 16);
return 0;
}
```
#### 参考资料
SM4算法标准 下周更新AES= =
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