【AES密码编写】
1. Equipment
（1） operating system version ：WIN 10
（2） CPU instruction set: x 64
（3） software ：Visual Studio 2019
2. process
Problem background analysis
AES密码编写
要编写AES算法，首先了解AES算法原理，AES算法是一个对称分组密码算法。数据分组长度必须是 128 bits，使用的密钥长度为 128，192 或 256 bits。对于三种不同密钥长度的 AES 算法，分别称为“AES-128”、“AES-192”、“AES-256”。AES加密算法涉及4种操作：字节替代（SubBytes）、行移位（ShiftRows）、列混（MixColumns）和轮密钥加（AddRoundKey）。
从AES的加密和解密的流程图中可知：解密算法的每一步分别对应加密算法的逆操作。加解密所有操作的顺序正好是相反的，正是这样才保证了算法的正确性。加解密中每轮的密钥分别由种子密钥经过密钥扩展算法得到，算法中16字节的明文、密文和轮子密钥都以一个4x4的矩阵表示。
AES的加密和解密的流程如下：
按照每一步的具体作用来编写对应的函数，以此实现AES算法过程。
Solution
code：
#include <stdio.h>
#pragma warning(disable:4996)
/*
* @Author:timerring
* @Date: 2021-11-08 21:59:11
* @LastEditTime: 2021-11-12 23:44:19
* @FilePath:c:\Users\timerring\AES.cpp
*/
//定义轮常量表
static const unsigned char Rcon[10] = {
0x01,0x02,0x04,0x08,0x10,0x20,0x40,0x80,0x1b,0x36 };
//定义有限域*2乘法
static unsigned char x2time(unsigned char x)
{
if (x & 0x80)
{
return (((x << 1) ^ 0x1B) & 0xFF);
}
return x << 1;
}
//定义有限域*3乘法
static unsigned char x3time(unsigned char x)
{
return (x2time(x) ^ x);
}
//定义有限域*4乘法
static unsigned char x4time(unsigned char x)
{
return (x2time(x2time(x)));
}
//定义有限域*8乘法
static unsigned char x8time(unsigned char x)
{
return (x2time(x2time(x2time(x))));
}
//定义有限域*9乘法
static unsigned char x9time(unsigned char x)
{
return (x8time(x) ^ x);
}
//定义有限域*B乘法
static unsigned char xBtime(unsigned char x)
{
return (x8time(x) ^ x2time(x) ^ x);
}
//定义有限域*D乘法
static unsigned char xDtime(unsigned char x)
{
return (x8time(x) ^ x4time(x) ^ x);
}
//定义有限域*E乘法
static unsigned char xEtime(unsigned char x)
{
return (x8time(x) ^ x4time(x) ^ x2time(x));
}
//s盒矩阵 Substitution Table
static const unsigned char sbox[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,
};
//逆向S盒矩阵
static const unsigned char contrary_sbox[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,
};
//定义列混合操作
static void MixColumns(unsigned char* col)
{
unsigned char tmp[4], xt[4];
int i;
for (i = 0; i < 4; i++, col += 4)
{ //col代表一列的基地址，col+4:下一列的基地址
//xt[n]代表*2 xt[n]^col[n]代表*3 col[n]代表*1
tmp[0] = x2time(col[0]) ^ x3time(col[1]) ^ col[2] ^ col[3]; //2 3 1 1
tmp[1] = col[0] ^ x2time(col[1]) ^ x3time(col[2]) ^ col[3]; //1 2 3 1
tmp[2] = col[0] ^ col[1] ^ x2time(col[2]) ^ x3time(col[3]); //1 1 2 3
tmp[3] = x3time(col[0]) ^ col[1] ^ col[2] ^ x2time(col[3]); //3 1 1 2
//修改后的值 直接在原矩阵上修改
col[0] = tmp[0];
col[1] = tmp[1];
col[2] = tmp[2];
col[3] = tmp[3];
}
}
//定义逆向列混淆
static void Contrary_MixColumns(unsigned char* col)
{
unsigned char tmp[4];
unsigned char xt2[4];//colx2
unsigned char xt4[4];//colx4
unsigned char xt8[4];//colx8
int x;
for (x = 0; x < 4; x++, col += 4)
{
tmp[0] = xEtime(col[0]) ^ xBtime(col[1]) ^ xDtime(col[2]) ^ x9time(col[3]);
tmp[1] = x9time(col[0]) ^ xEtime(col[1]) ^ xBtime(col[2]) ^ xDtime(col[3]);
tmp[2] = xDtime(col[0]) ^ x9time(col[1]) ^ xEtime(col[2]) ^ xBtime(col[3]);
tmp[3] = xBtime(col[0]) ^ xDtime(col[1]) ^ x9time(col[2]) ^ xEtime(col[3]);
col[0] = tmp[0];
col[1] = tmp[1];
col[2] = tmp[2];
col[3] = tmp[3];
}
}
//定义行移位操作：行左循环移位
static void ShiftRows(unsigned char* col)
{//正向行移位
unsigned char t;
//左移1位
t = col[1]; col[1] = col[5]; col[5] = col[9]; col[9] = col[13]; col[13] = t;
//左移2位，交换2次数字来实现
t = col[2]; col[2] = col[10]; col[10] = t;
t = col[6]; col[6] = col[14]; col[14] = t;
//左移3位，相当于右移1次
t = col[15]; col[15] = col[11]; col[11] = col[7]; col[7] = col[3]; col[3] = t;
//第4行不移位
}
//逆向行移位
static void Contrary_ShiftRows(unsigned char* col)
{
unsigned char t;
t = col[13]; col[13] = col[9]; col[9] = col[5]; col[5] = col[1]; col[1] = t;
t = col[2]; col[2] = col[10]; col[10] = t;
t = col[6]; col[6] = col[14]; col[14] = t;
t = col[3]; col[3] = col[7]; col[7] = col[11]; col[11] = col[15]; col[15] = t;
//同理，第4行不移位
}
//定义s盒字节代换替换操作
static void SubBytes(unsigned char* col)
{//字节代换
int x;
for (x = 0; x < 16; x++)
{
col[x] = sbox[col[x]];
}
}
//逆向字节代换
static void Contrary_SubBytes(unsigned char* col)
{
int x;
for (x = 0; x < 16; x++)
{
col[x] = contrary_sbox[col[x]];
}
}
//密钥编排，16字节--->44列32bit密钥生成--> 11组16字节:分别用于11轮 轮密钥加运算
void ScheduleKey(unsigned char* inkey, unsigned char* outkey, int Nk, int Nr)
{
//inkey:初始16字节密钥key
//outkey：11组*16字节扩展密钥expansionkey
//Nk：4列
//Nr：10轮round
unsigned char temp[4], t;
int x, i;
/*copy the key*/
//第0组：[0-3]直接拷贝
for (i = 0; i < (4 * Nk); i++)
{
outkey[i] = inkey[i];
}
//第1-10组：[4-43]
i = Nk;
while (i < (4 * (Nr + 1))) //i=4~43 WORD 32bit的首字节地址，每一个4字节
{//1次循环生成1个字节扩展密钥，4次循环生成一个WORD
//temp：4字节数组：代表一个WORD密钥
//i不是4的倍数的时候
//每个temp = 每个outkey32bit = 4字节
for (x = 0; x < 4; x++)
temp[x] = outkey[(4 * (i - 1)) + x]; //i：32bit的首字节地址
//i是4的倍数的时候
if (i % Nk == 0)
{
/*字循环：循环左移1字节 RotWord()*/
t = temp[0]; temp[0] = temp[1]; temp[1] = temp[2]; temp[2] = temp[3]; temp[3] = t;
/*字节代换：SubWord()*/
for (x = 0; x < 4; x++)
{
temp[x] = sbox[temp[x]];
}
/*轮常量异或：Rcon[j]*/
temp[0] ^= Rcon[(i / Nk) - 1];
}
for (x = 0; x < 4; x++)
{
outkey[(4 * i) + x] = outkey[(4 * (i - Nk)) + x] ^ temp[x];
}
++i;
}
}
//定义轮密钥加操作
static void AddRoundKey(unsigned char* col, unsigned char* expansionkey, int round)//密匙加
{
//扩展密钥：44*32bit =11*4* 4*8 = 16字节*11轮，每轮用16字节密钥
//第0轮，只进行一次轮密钥加
//第1-10轮，轮密钥加
int x;
for (x = 0; x < 16; x++)
{ //每1轮操作：4*32bit密钥 = 16个字节密钥
col[x] ^= expansionkey[(round << 4) + x];
}
}
//AES加密函数
void AesEncrypt(unsigned char* blk, unsigned char* expansionkey, int Nr)
{//加密一个区块
//输入blk原文，直接在上面修改，输出blk密文
//输入skey：
//输入Nr = 10轮
int round;
//第1轮之前：轮密钥加
AddRoundKey(blk, expansionkey, 0);
//第1-9轮：4类操作：字节代换、行移位、列混合、轮密钥加
for (round = 1; round <= (Nr - 1); round++)
{
SubBytes(blk); //输入16字节数组，直接在原数组上修改
ShiftRows(blk); //输入16字节数组，直接在原数组上修改
MixColumns(blk); //输入16字节数组，直接在原数组上修改
AddRoundKey(blk, expansionkey, round);
}
//第10轮：不进行列混合
SubBytes(blk);
ShiftRows(blk);
AddRoundKey(blk, expansionkey, Nr);
}
//AES 解密函数
void Contrary_AesEncrypt(unsigned char* blk, unsigned char* expansionkey, int Nr)
{
int x;
AddRoundKey(blk, expansionkey, Nr);
Contrary_ShiftRows(blk);
Contrary_SubBytes(blk);
for (x = (Nr - 1); x >= 1; x--)
{
AddRoundKey(blk, expansionkey, x);
Contrary_MixColumns(blk);
Contrary_ShiftRows(blk);
Contrary_SubBytes(blk);
}
AddRoundKey(blk, expansionkey, 0);
}
int main(void) {
unsigned char pt[17], key[17];
//定义原文pt
//定义密钥key
unsigned char expansionkey[15 * 16];
int i;
int j;
printf("You are welcome to use the AES machine in SDU\n");
printf("Please enter plaintext (length = 16):\n");
scanf("%s", pt);
printf("please input key：\n");
scanf("%s", key);
//加密过程
ScheduleKey(key, expansionkey, 4, 10);//密钥扩展生成
AesEncrypt(pt, expansionkey, 10);//调用AES 加密
printf("ciphertext: ");
//输出密文
for (i = 0; i < 16; i++)
{
printf("%02x ", pt[i]);
}
printf("\n");
printf("\n");
//解密过程
Contrary_AesEncrypt(pt, expansionkey, 10);//调用AES 解密
printf("The decrypted plaintext is: ");
//输出明文
for (i = 0; i < 16; i++)
{
printf("%c ", pt[i]);
}
printf("\n");
printf("\n");
while (1);
return 0;
}Test sample：
此处假定测试明文为SDUinQINGDAOcity，设置测试密钥为iloveSDUforeverr，进行加密得到密文，再对密文进行解密，经验证可以得到明文，AES程序编写成功。
3. summary and harvest
我对AES密码的认识更加深入了，除了常见的加轮密钥以外，另外三个过程一起提供了混淆、扩散和非线性功能。这三个过程没有涉及密钥，就它们自身而言，并未提供算法的安全性。然而，该算法经历一个分组的XOR加密（轮密钥加），再对该分组混淆扩散（其他三个阶段），再接着又是XOR加密，如此交替进行，这种方式非常有效非常安全。其次，AES算法的每个阶段均可逆。对字节代替、行移位和列混淆，在解密算法中用它们相对应的逆函数。轮密钥加的逆就是用同样的轮密钥和分组相异或，其原理就是A⊕B⊕B = A。和大多数分组密码一样，AES解密算法按逆序利用扩展密钥，然而其解密算法和加密算法并不一样，这是由AES的特定结构决定的。
而此次实验我印象最深的就是对于各轮AES加密循环（除最后一轮外）4个方法的编写：
- AddRoundKey — 矩阵中的每一个字节都与该次轮秘钥（round key）做XOR运算；每个子密钥由密钥生成方案产生。
- SubBytes — 通过非线性的替换函数，用查找表的方式把每个字节替换成对应的字节。
- ShiftRows — 将矩阵中的每个横列进行循环式移位。
- MixColumns — 为了充分混合矩阵中各个直行的操作。这个步骤使用线性转换来混合每列的四个字节。
其中我觉得难处理的一个功能模块是列混淆。因为混淆变换实际上是使用乘法矩阵（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）。其次这个模块涉及到矩阵运算。好在本次实验矩阵的大小是4*4固定的，其中还要注意矩阵行、列计算的转换，所以还是很复杂的，很考验逻辑思维能力。
还有一个难点就是密钥扩展。把每轮的密钥看成四个w[i]，这一轮的第一个w[i]总是最难生成的。我们首先第n-1组第3列的4个字节循环左移1个字节；再对每个字节进行字节替代变换；再与轮常量相加；最后再与前一组该列相加。
回顾起此AES密码编程，感慨颇多，从理论到实践，在这次的实验中，能够学到很多很多的东西，不仅仅巩固了课上所学过的AES知识，也学到了很多在书本上所没有学到过的知识。在实验操作与设计的过程中遇到问题也颇多，但可喜的是通过查找资料，阅读博客，查阅文献的方式，这些问题最终都得到了解决。
初学信息安全，可能存在错误之处，还请各位不吝赐教。
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