AES加密
AES加密
一.加密流程
AES未使用Feistel结构。其前N-1轮由4个不同的变换组成:字节代替、行移位、列混淆和轮密钥加。最后一轮仅包含三个变换。而在第一轮前面有一个起始的单变换(轮密钥加),可以视为0轮。
字节代替(SubBytes):用一个S盒完成分组的字节到字节的代替。
行移位(ShiftRows):一个简单的置换。
列混淆(MixColumns):利用域GF(28)上的算术特性的一个代替。
轮密钥加(AddRoundKey):当前分组和扩展密钥的一部分进行按位异或XOR
1. 字节替换
字节代替变换是一个简单的查表操作。AES定义了一个S盒,它是由16×16个字节组成是矩阵,包含了8位所能表示的256个数的一个置换。State中每个字节按照如下方式映射为一个新的字节:把该字节的高4位作为行值,低4位作为列值,以这些数值为索引从S盒的对应位置取出元素作为输出。如,十六进制数{95}所对应的S盒行值是9,列值是5。S盒中在此位置的值是{2A},相应的,{95}被映射为{2A}。
2. 行移位变换
操作本身很简单,将state数组的第一行保持不变,第二行循环左移一个字节,第三行循环左移两个字节,第四行循环左移三个字节。
3. 列混淆变换
列混淆变换实际上是使用乘法矩阵(注意:其运算中涉及的加法和乘法都是定义在GF(28)上的加法和乘法,目的就是为了确保运算结果不会溢出定义域),可用以下式子描述。
这个矩阵是给定的。
4. 轮密钥加
将得到的矩阵与密钥进行异或,核心应该是密钥的生成算法。
5. 密钥生成算法
AES密钥扩展算法的输入值是4个字(16字节),输出值是一个由44个字组成(176字节)的一维线性数组。以下伪码描述了这个扩展:
KeyExpansion(byte key[16], word w[44]){
word temp
for(i=0; i<4; i++) //将输入的密钥直接复制到扩展密钥数组的前四个字
w[i]=word(key[4*i],key[4*i+1],key[4*i+2],key[4*i+3]);
temp = w[i-1];
if(i mod 4 == 0) //对w数组下标为4的倍数的元素采用更复杂的函数来计算
temp = SubWord(RotWord(temp))⊕Rcon[i/4];
w[i] = w[i-4] + temp; //每一个新增的字w[i]依赖于w[i-1] 和w[i-4]
}
RotWord的功能是字循环,即使一个字的4个字节循环左移1个字节。
SubWord是利用S盒对输入字的每个字节进行字节代替。
Rcon[i]是轮常量,代表一个字,这个字最右边三个字节总是0,因此字与Rcon异或,其结果只是与该字最左边的那个字节相异或。每一轮的轮常量都不相同,其定义为
Rcon[i] = (RC[i],0,0,0),其中RC[1] = 1,RC[i] = 2•RC[i-1] 乘法是定义在域GF(28)上的。
RC[i]的值按照十六进制表示为
这里其实可以直接通过密钥生成算法得到,在已知起始密钥的情况下,可以直接使用算法得到最后的密钥。
二. 代码实现
#include <stdint.h>
#include <stdio.h>
#include <string.h>
typedef struct{
uint32_t eK[44], dK[44]; // encKey, decKey
int Nr; // 10 rounds
}AesKey;
#define BLOCKSIZE 16 //AES-128分组长度为16字节
// uint8_t y[4] -> uint32_t x
#define LOAD32H(x, y) \
do { (x) = ((uint32_t)((y)[0] & 0xff)<<24) | ((uint32_t)((y)[1] & 0xff)<<16) | \
((uint32_t)((y)[2] & 0xff)<<8) | ((uint32_t)((y)[3] & 0xff));} while(0)
// uint32_t x -> uint8_t y[4]
#define STORE32H(x, y) \
do { (y)[0] = (uint8_t)(((x)>>24) & 0xff); (y)[1] = (uint8_t)(((x)>>16) & 0xff); \
(y)[2] = (uint8_t)(((x)>>8) & 0xff); (y)[3] = (uint8_t)((x) & 0xff); } while(0)
// 从uint32_t x中提取从低位开始的第n个字节
#define BYTE(x, n) (((x) >> (8 * (n))) & 0xff)
/* used for keyExpansion */
// 字节替换然后循环左移1位
#define MIX(x) (((S[BYTE(x, 2)] << 24) & 0xff000000) ^ ((S[BYTE(x, 1)] << 16) & 0xff0000) ^ \
((S[BYTE(x, 0)] << 8) & 0xff00) ^ (S[BYTE(x, 3)] & 0xff))
// uint32_t x循环左移n位
#define ROF32(x, n) (((x) << (n)) | ((x) >> (32-(n))))
// uint32_t x循环右移n位
#define ROR32(x, n) (((x) >> (n)) | ((x) << (32-(n))))
/* for 128-bit blocks, Rijndael never uses more than 10 rcon values */
// AES-128轮常量
static const uint32_t rcon[10] = {
0x01000000UL, 0x02000000UL, 0x04000000UL, 0x08000000UL, 0x10000000UL,
0x20000000UL, 0x40000000UL, 0x80000000UL, 0x1B000000UL, 0x36000000UL
};
// S盒
unsigned char S[256] = {
0x63, 0x7C, 0x77, 0x7B, 0xF2, 0x6B, 0x6F, 0xC5, 0x30, 0x01, 0x67, 0x2B, 0xFE, 0xD7, 0xAB, 0x76,
0xCA, 0x82, 0xC9, 0x7D, 0xFA, 0x59, 0x47, 0xF0, 0xAD, 0xD4, 0xA2, 0xAF, 0x9C, 0xA4, 0x72, 0xC0,
0xB7, 0xFD, 0x93, 0x26, 0x36, 0x3F, 0xF7, 0xCC, 0x34, 0xA5, 0xE5, 0xF1, 0x71, 0xD8, 0x31, 0x15,
0x04, 0xC7, 0x23, 0xC3, 0x18, 0x96, 0x05, 0x9A, 0x07, 0x12, 0x80, 0xE2, 0xEB, 0x27, 0xB2, 0x75,
0x09, 0x83, 0x2C, 0x1A, 0x1B, 0x6E, 0x5A, 0xA0, 0x52, 0x3B, 0xD6, 0xB3, 0x29, 0xE3, 0x2F, 0x84,
0x53, 0xD1, 0x00, 0xED, 0x20, 0xFC, 0xB1, 0x5B, 0x6A, 0xCB, 0xBE, 0x39, 0x4A, 0x4C, 0x58, 0xCF,
0xD0, 0xEF, 0xAA, 0xFB, 0x43, 0x4D, 0x33, 0x85, 0x45, 0xF9, 0x02, 0x7F, 0x50, 0x3C, 0x9F, 0xA8,
0x51, 0xA3, 0x40, 0x8F, 0x92, 0x9D, 0x38, 0xF5, 0xBC, 0xB6, 0xDA, 0x21, 0x10, 0xFF, 0xF3, 0xD2,
0xCD, 0x0C, 0x13, 0xEC, 0x5F, 0x97, 0x44, 0x17, 0xC4, 0xA7, 0x7E, 0x3D, 0x64, 0x5D, 0x19, 0x73,
0x60, 0x81, 0x4F, 0xDC, 0x22, 0x2A, 0x90, 0x88, 0x46, 0xEE, 0xB8, 0x14, 0xDE, 0x5E, 0x0B, 0xDB,
0xE0, 0x32, 0x3A, 0x0A, 0x49, 0x06, 0x24, 0x5C, 0xC2, 0xD3, 0xAC, 0x62, 0x91, 0x95, 0xE4, 0x79,
0xE7, 0xC8, 0x37, 0x6D, 0x8D, 0xD5, 0x4E, 0xA9, 0x6C, 0x56, 0xF4, 0xEA, 0x65, 0x7A, 0xAE, 0x08,
0xBA, 0x78, 0x25, 0x2E, 0x1C, 0xA6, 0xB4, 0xC6, 0xE8, 0xDD, 0x74, 0x1F, 0x4B, 0xBD, 0x8B, 0x8A,
0x70, 0x3E, 0xB5, 0x66, 0x48, 0x03, 0xF6, 0x0E, 0x61, 0x35, 0x57, 0xB9, 0x86, 0xC1, 0x1D, 0x9E,
0xE1, 0xF8, 0x98, 0x11, 0x69, 0xD9, 0x8E, 0x94, 0x9B, 0x1E, 0x87, 0xE9, 0xCE, 0x55, 0x28, 0xDF,
0x8C, 0xA1, 0x89, 0x0D, 0xBF, 0xE6, 0x42, 0x68, 0x41, 0x99, 0x2D, 0x0F, 0xB0, 0x54, 0xBB, 0x16
};
//逆S盒
unsigned char inv_S[256] = {
0x52, 0x09, 0x6A, 0xD5, 0x30, 0x36, 0xA5, 0x38, 0xBF, 0x40, 0xA3, 0x9E, 0x81, 0xF3, 0xD7, 0xFB,
0x7C, 0xE3, 0x39, 0x82, 0x9B, 0x2F, 0xFF, 0x87, 0x34, 0x8E, 0x43, 0x44, 0xC4, 0xDE, 0xE9, 0xCB,
0x54, 0x7B, 0x94, 0x32, 0xA6, 0xC2, 0x23, 0x3D, 0xEE, 0x4C, 0x95, 0x0B, 0x42, 0xFA, 0xC3, 0x4E,
0x08, 0x2E, 0xA1, 0x66, 0x28, 0xD9, 0x24, 0xB2, 0x76, 0x5B, 0xA2, 0x49, 0x6D, 0x8B, 0xD1, 0x25,
0x72, 0xF8, 0xF6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xD4, 0xA4, 0x5C, 0xCC, 0x5D, 0x65, 0xB6, 0x92,
0x6C, 0x70, 0x48, 0x50, 0xFD, 0xED, 0xB9, 0xDA, 0x5E, 0x15, 0x46, 0x57, 0xA7, 0x8D, 0x9D, 0x84,
0x90, 0xD8, 0xAB, 0x00, 0x8C, 0xBC, 0xD3, 0x0A, 0xF7, 0xE4, 0x58, 0x05, 0xB8, 0xB3, 0x45, 0x06,
0xD0, 0x2C, 0x1E, 0x8F, 0xCA, 0x3F, 0x0F, 0x02, 0xC1, 0xAF, 0xBD, 0x03, 0x01, 0x13, 0x8A, 0x6B,
0x3A, 0x91, 0x11, 0x41, 0x4F, 0x67, 0xDC, 0xEA, 0x97, 0xF2, 0xCF, 0xCE, 0xF0, 0xB4, 0xE6, 0x73,
0x96, 0xAC, 0x74, 0x22, 0xE7, 0xAD, 0x35, 0x85, 0xE2, 0xF9, 0x37, 0xE8, 0x1C, 0x75, 0xDF, 0x6E,
0x47, 0xF1, 0x1A, 0x71, 0x1D, 0x29, 0xC5, 0x89, 0x6F, 0xB7, 0x62, 0x0E, 0xAA, 0x18, 0xBE, 0x1B,
0xFC, 0x56, 0x3E, 0x4B, 0xC6, 0xD2, 0x79, 0x20, 0x9A, 0xDB, 0xC0, 0xFE, 0x78, 0xCD, 0x5A, 0xF4,
0x1F, 0xDD, 0xA8, 0x33, 0x88, 0x07, 0xC7, 0x31, 0xB1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xEC, 0x5F,
0x60, 0x51, 0x7F, 0xA9, 0x19, 0xB5, 0x4A, 0x0D, 0x2D, 0xE5, 0x7A, 0x9F, 0x93, 0xC9, 0x9C, 0xEF,
0xA0, 0xE0, 0x3B, 0x4D, 0xAE, 0x2A, 0xF5, 0xB0, 0xC8, 0xEB, 0xBB, 0x3C, 0x83, 0x53, 0x99, 0x61,
0x17, 0x2B, 0x04, 0x7E, 0xBA, 0x77, 0xD6, 0x26, 0xE1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0C, 0x7D
};
/* copy in[16] to state[4][4] */
int loadStateArray(uint8_t (*state)[4], const uint8_t *in) {
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
state[j][i] = *in++;
}
}
return 0;
}
/* copy state[4][4] to out[16] */
int storeStateArray(uint8_t (*state)[4], uint8_t *out) {
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
*out++ = state[j][i];
}
}
return 0;
}
//秘钥扩展
int keyExpansion(const uint8_t *key, uint32_t keyLen, AesKey *aesKey) {
if (NULL == key || NULL == aesKey){
printf("keyExpansion param is NULL\n");
return -1;
}
if (keyLen != 16){
printf("keyExpansion keyLen = %d, Not support.\n", keyLen);
return -1;
}
uint32_t *w = aesKey->eK; //加密秘钥
uint32_t *v = aesKey->dK; //解密秘钥
/* keyLen is 16 Bytes, generate uint32_t W[44]. */
/* W[0-3] */
for (int i = 0; i < 4; ++i) {
LOAD32H(w[i], key + 4*i);
}
/* W[4-43] */
for (int i = 0; i < 10; ++i) {
w[4] = w[0] ^ MIX(w[3]) ^ rcon[i];
w[5] = w[1] ^ w[4];
w[6] = w[2] ^ w[5];
w[7] = w[3] ^ w[6];
w += 4;
}
w = aesKey->eK+44 - 4;
//解密秘钥矩阵为加密秘钥矩阵的倒序,方便使用,把ek的11个矩阵倒序排列分配给dk作为解密秘钥
//即dk[0-3]=ek[41-44], dk[4-7]=ek[37-40]... dk[41-44]=ek[0-3]
for (int j = 0; j < 11; ++j) {
for (int i = 0; i < 4; ++i) {
v[i] = w[i];
}
w -= 4;
v += 4;
}
return 0;
}
// 轮秘钥加
int addRoundKey(uint8_t (*state)[4], const uint32_t *key) {
uint8_t k[4][4];
/* i: row, j: col */
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
k[i][j] = (uint8_t) BYTE(key[j], 3 - i); /* 把 uint32 key[4] 先转换为矩阵 uint8 k[4][4] */
state[i][j] ^= k[i][j];
}
}
return 0;
}
//字节替换
int subBytes(uint8_t (*state)[4]) {
/* i: row, j: col */
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
state[i][j] = S[state[i][j]]; //直接使用原始字节作为S盒数据下标
}
}
return 0;
}
//逆字节替换
int invSubBytes(uint8_t (*state)[4]) {
/* i: row, j: col */
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
state[i][j] = inv_S[state[i][j]];
}
}
return 0;
}
//行移位
int shiftRows(uint8_t (*state)[4]) {
uint32_t block[4] = {0};
/* i: row */
for (int i = 0; i < 4; ++i) {
//便于行循环移位,先把一行4字节拼成uint_32结构,移位后再转成独立的4个字节uint8_t
LOAD32H(block[i], state[i]);
block[i] = ROF32(block[i], 8*i);
STORE32H(block[i], state[i]);
}
return 0;
}
//逆行移位
int invShiftRows(uint8_t (*state)[4]) {
uint32_t block[4] = {0};
/* i: row */
for (int i = 0; i < 4; ++i) {
LOAD32H(block[i], state[i]);
block[i] = ROR32(block[i], 8*i);
STORE32H(block[i], state[i]);
}
return 0;
}
/* Galois Field (256) Multiplication of two Bytes */
// 两字节的伽罗华域乘法运算
uint8_t GMul(uint8_t u, uint8_t v) {
uint8_t p = 0;
for (int i = 0; i < 8; ++i) {
if (u & 0x01) { //
p ^= v;
}
int flag = (v & 0x80);
v <<= 1;
if (flag) {
v ^= 0x1B; /* x^8 + x^4 + x^3 + x + 1 */
}
u >>= 1;
}
return p;
}
// 列混合
int mixColumns(uint8_t (*state)[4]) {
uint8_t tmp[4][4];
uint8_t M[4][4] = {{0x02, 0x03, 0x01, 0x01},
{0x01, 0x02, 0x03, 0x01},
{0x01, 0x01, 0x02, 0x03},
{0x03, 0x01, 0x01, 0x02}};
/* copy state[4][4] to tmp[4][4] */
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j){
tmp[i][j] = state[i][j];
}
}
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) { //伽罗华域加法和乘法
state[i][j] = GMul(M[i][0], tmp[0][j]) ^ GMul(M[i][1], tmp[1][j])
^ GMul(M[i][2], tmp[2][j]) ^ GMul(M[i][3], tmp[3][j]);
}
}
return 0;
}
// 逆列混合
int invMixColumns(uint8_t (*state)[4]) {
uint8_t tmp[4][4];
uint8_t M[4][4] = {{0x0E, 0x0B, 0x0D, 0x09},
{0x09, 0x0E, 0x0B, 0x0D},
{0x0D, 0x09, 0x0E, 0x0B},
{0x0B, 0x0D, 0x09, 0x0E}}; //使用列混合矩阵的逆矩阵
/* copy state[4][4] to tmp[4][4] */
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j){
tmp[i][j] = state[i][j];
}
}
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
state[i][j] = GMul(M[i][0], tmp[0][j]) ^ GMul(M[i][1], tmp[1][j])
^ GMul(M[i][2], tmp[2][j]) ^ GMul(M[i][3], tmp[3][j]);
}
}
return 0;
}
// AES-128加密接口,输入key应为16字节长度,输入长度应该是16字节整倍数,
// 这样输出长度与输入长度相同,函数调用外部为输出数据分配内存
int aesEncrypt(const uint8_t *key, uint32_t keyLen, const uint8_t *pt, uint8_t *ct, uint32_t len) {
AesKey aesKey;
uint8_t *pos = ct;
const uint32_t *rk = aesKey.eK; //解密秘钥指针
uint8_t out[BLOCKSIZE] = {0};
uint8_t actualKey[16] = {0};
uint8_t state[4][4] = {0};
if (NULL == key || NULL == pt || NULL == ct){
printf("param err.\n");
return -1;
}
if (keyLen > 16){
printf("keyLen must be 16.\n");
return -1;
}
if (len % BLOCKSIZE){
printf("inLen is invalid.\n");
return -1;
}
memcpy(actualKey, key, keyLen);
keyExpansion(actualKey, 16, &aesKey); // 秘钥扩展
// 使用ECB模式循环加密多个分组长度的数据
for (int i = 0; i < len; i += BLOCKSIZE) {
// 把16字节的明文转换为4x4状态矩阵来进行处理
loadStateArray(state, pt);
// 轮秘钥加
addRoundKey(state, rk);
for (int j = 1; j < 10; ++j) {
rk += 4;
subBytes(state); // 字节替换
shiftRows(state); // 行移位
mixColumns(state); // 列混合
addRoundKey(state, rk); // 轮秘钥加
}
subBytes(state); // 字节替换
shiftRows(state); // 行移位
// 此处不进行列混合
addRoundKey(state, rk+4); // 轮秘钥加
// 把4x4状态矩阵转换为uint8_t一维数组输出保存
storeStateArray(state, pos);
pos += BLOCKSIZE; // 加密数据内存指针移动到下一个分组
pt += BLOCKSIZE; // 明文数据指针移动到下一个分组
rk = aesKey.eK; // 恢复rk指针到秘钥初始位置
}
return 0;
}
// AES128解密, 参数要求同加密
int aesDecrypt(const uint8_t *key, uint32_t keyLen, const uint8_t *ct, uint8_t *pt, uint32_t len) {
AesKey aesKey;
uint8_t *pos = pt;
const uint32_t *rk = aesKey.dK; //解密秘钥指针
uint8_t out[BLOCKSIZE] = {0};
uint8_t actualKey[16] = {0};
uint8_t state[4][4] = {0};
if (NULL == key || NULL == ct || NULL == pt){
printf("param err.\n");
return -1;
}
if (keyLen > 16){
printf("keyLen must be 16.\n");
return -1;
}
if (len % BLOCKSIZE){
printf("inLen is invalid.\n");
return -1;
}
memcpy(actualKey, key, keyLen);
keyExpansion(actualKey, 16, &aesKey); //秘钥扩展,同加密
for (int i = 0; i < len; i += BLOCKSIZE) {
// 把16字节的密文转换为4x4状态矩阵来进行处理
loadStateArray(state, ct);
// 轮秘钥加,同加密
addRoundKey(state, rk);
for (int j = 1; j < 10; ++j) {
rk += 4;
invShiftRows(state); // 逆行移位
invSubBytes(state); // 逆字节替换,这两步顺序可以颠倒
addRoundKey(state, rk); // 轮秘钥加,同加密
invMixColumns(state); // 逆列混合
}
invSubBytes(state); // 逆字节替换
invShiftRows(state); // 逆行移位
// 此处没有逆列混合
addRoundKey(state, rk+4); // 轮秘钥加,同加密
storeStateArray(state, pos); // 保存明文数据
pos += BLOCKSIZE; // 输出数据内存指针移位分组长度
ct += BLOCKSIZE; // 输入数据内存指针移位分组长度
rk = aesKey.dK; // 恢复rk指针到秘钥初始位置
}
return 0;
}
#include <stdio.h>
// 方便输出16进制数据
void printHex(uint8_t *ptr, int len, char *tag) {
printf("%s\ndata[%d]: ", tag, len);
for (int i = 0; i < len; ++i) {
printf("%.2X ", *ptr++);
}
printf("\n");
}
int main() {
// case 1
const uint8_t key[16] = {0x2b, 0x7e, 0x15, 0x16, 0x28, 0xae, 0xd2, 0xa6, 0xab, 0xf7, 0x15, 0x88, 0x09, 0xcf, 0x4f, 0x3c};
const uint8_t pt[16]={0x32, 0x43, 0xf6, 0xa8, 0x88, 0x5a, 0x30, 0x8d, 0x31, 0x31, 0x98, 0xa2, 0xe0, 0x37, 0x07, 0x34};
uint8_t ct[16] = {0}; // 外部申请输出数据内存,用于加密后的数据
uint8_t plain[16] = {0}; // 外部申请输出数据内存,用于解密后的数据
aesEncrypt(key, 16, pt, ct, 16); // 加密
printHex(pt, 16, "plain data:"); // 打印初始明文数据
printf("expect cipher:\n39 25 84 1D 02 DC 09 FB DC 11 85 97 19 6A 0B 32\n"); // 正常解密后的数据内容
printHex(ct, 16, "after encryption:"); // 打印加密后的密文
aesDecrypt(key, 16, ct, plain, 16); // 解密
printHex(plain, 16, "after decryption:"); // 打印解密后的明文数据
// case 2
// 16字节字符串形式秘钥
const uint8_t key2[]="1234567890123456";
// 32字节长度字符串明文
const uint8_t *data = (uint8_t*)"abcdefghijklmnopqrstuvwxyz123456";
uint8_t ct2[32] = {0}; //外部申请输出数据内存,用于存放加密后数据
uint8_t plain2[32] = {0}; //外部申请输出数据内存,用于存放解密后数据
//加密32字节明文
aesEncrypt(key2, 16, data, ct2, 32);
printf("\nplain text:\n%s\n", data);
printf("expect ciphertext:\nfcad715bd73b5cb0488f840f3bad7889\n");
printHex(ct2, 32, "after encryption:");
// 解密32字节密文
aesDecrypt(key2, 16, ct2, plain2, 32);
// 打印16进制形式的解密后的明文
printHex(plain2, 32, "after decryption:");
// 因为加密前的数据为可见字符的字符串,打印解密后的明文字符,与加密前明文进行对比
printf("output plain text\n");
for (int i = 0; i < 32; ++i) {
printf("%c ", plain2[i]);
}
return 0;
}
三. 参考文章