AES加密算法原理(C++实现)

美国国家标准技术研究所在2001年发布了高级加密标准（AES）。AES是一个对称加密算法，旨在取代DES成为广泛使用的标准，该标准以Rijndael算法为核心。

Rijndael算法是一种对称分组密码体制，采用代替或置换网络，每轮由三层组成：线性混合层确保多轮之上的高度扩散；非线性层由S盒并置起到混淆的作用；密钥加密层将子密钥异或到中间状态。

AES标准规定Rijndael算法的分组长度为128位，而密钥长度可以为128、192或256位，相应的迭代轮数为10轮、12轮或14轮。Rijndael 汇聚了安全性能、效率、可实现性和灵活性等优点。Rijndael 对内存的需求低，使它很适合用于资源受限制的环境中，Rijndael 的操作简单，并可抵御强大和实时的攻击

AES加密算法流程如下：

                                                        图1. AES算法流程

（1）字节代替：用一个S盒完成分组的字节到字节的代替；是一个基于S盒的非线性置换，它用于将每一个字节通过一个简单的查表操作映射为另一个字节。映射方法是把输入字节的高4位作为S盒的行值，低4位作为列值，然后取出S盒中对应行和列交叉位的元素作为输出

                                                        图2.字节代换 

（2）行移位： AES 的行移位也是一个简单的左循环移位操作。当密钥长度为128比特时，状态矩阵的第0行左移0字节，第1行左移1字节，第2行左移2字节，第3行左移3字节

 图3. 行移位

（3）列混合：列混合变换是通过矩阵相乘来实现的，经行移位后的状态矩阵与固定的矩阵相乘，得到混淆后的状态矩阵。 

 图4. 列混合

 （4）轮密钥加：当前分组和扩展密钥的一部分进行按位异或，将输入或中间态S的每一列与一个密钥字ki进行按位异或，即将128位轮密钥 Ki 同状态矩阵中的数据进行逐位异或操作。

 代码：

AES.h

#include 
using namespace std;

#ifndef _AES_H_
#define _AES_H_

// S盒
extern unsigned char S[256];

//逆S盒
extern unsigned char inv_S[256];

// AES-128轮常量
static const unsigned int rcon[10] = {
    0x01000000UL, 0x02000000UL, 0x04000000UL, 0x08000000UL, 0x10000000UL,
    0x20000000UL, 0x40000000UL, 0x80000000UL, 0x1B000000UL, 0x36000000UL
};

//列混淆时用到的正矩阵
extern unsigned char positive_matrix[4][4];

//逆列混淆时用到的逆正矩阵
extern unsigned char inv_positive_matrix[4][4];

//密钥扩展
extern unsigned int W[44];

//可输入明文的最大长度
static const int MAX_LENGTH=1e6;

//明文
extern unsigned char P[MAX_LENGTH];
//解密之后的明文
extern unsigned char De_P[MAX_LENGTH];
//分组后的128明文
extern unsigned char P128[16];

//密文
extern unsigned char C[MAX_LENGTH];
//分组后的128密文
extern unsigned char C128[16];

//将128明文转换为状态矩阵
void array_to_mat(unsigned char p[],unsigned char state_mat[][4]);

//将状态矩阵转换为128密文
void mat_to_array(unsigned char state_mat[][4],unsigned char c[]);

//将1个32位的密钥，转换为4个8位密钥
void key32_to_key8(unsigned int key32,unsigned char* key8);

//将4个8位的密钥，转换为1个32位密钥
unsigned int key8_to_key32(unsigned char* key8);

//字节替换
unsigned char SubBytes(unsigned char input);

//行位移
void ShiftRows(unsigned char state_mat[][4]);

//有限域上的乘法
unsigned char multi_finite_field(unsigned char a,unsigned char b);

//列混合
void MixColumns(unsigned char state_mat[][4]);

//轮密钥加，cnt标记这是第几轮循环
void AddRoundKey(unsigned char state_mat[][4],int cnt);

//密钥扩展时的T函数，cnt代表轮数
unsigned int T(unsigned int input,int cnt);

//密钥扩展函数
void KeyExpansion(unsigned char* init_key);

//加密
void encryption();

//解密方法如下

//逆字节替换
unsigned char Inv_SubBytes(unsigned char input);

//逆行位移
void Inv_ShiftRows(unsigned char state_mat[][4]);

//逆列混合
void Inv_MixColumns(unsigned char state_mat[][4]);

//逆轮密钥加，cnt标记这是第几轮循环
void Inv_AddRoundKey(unsigned char state_mat[][4],int cnt);

//解密
void decryption();


#endif

 AES.cpp

#include "AES.h"
#include 
#include 
using namespace std;
// 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
};

//密钥扩展
unsigned int W[44];

//列混淆时用到的正矩阵
extern unsigned char positive_matrix[4][4]=
{
    0x02, 0x03, 0x01, 0x01,
    0x01, 0x02, 0x03, 0x01,
    0x01, 0x01, 0x02, 0x03,
    0x03, 0x01, 0x01, 0x02
};

//逆列混淆时用到的逆正矩阵
extern unsigned char inv_positive_matrix[4][4]=
{
    0x0e, 0x0b, 0x0d, 0x09,
    0x09, 0x0e, 0x0b, 0x0d,
    0x0d, 0x09, 0x0e, 0x0b,
    0x0b, 0x0d, 0x09, 0x0e
};

//明文
unsigned char P[MAX_LENGTH];
//解密之后的明文
unsigned char De_P[MAX_LENGTH];
//分组后的128明文
unsigned char P128[16];

//密文
unsigned char C[MAX_LENGTH];
//分组后的128密文
unsigned char C128[16];

//将128比特转换为状态矩阵
void array_to_mat(unsigned char p[],unsigned char state_mat[][4])
{
    for(int col=0; col<4; col++)
    {
        for(int row=0; row<4; row++)
        {
            state_mat[row][col] = p[col*4 + row];
        }
    }
}

//将状态矩阵转换为128密文
void mat_to_array(unsigned char state_mat[][4],unsigned char c[])
{
    int cnt=0;
    for(int col=0; col<4; col++)
    {
        for(int row=0; row<4; row++)
        {
            c[cnt++] = state_mat[row][col];
        }
    }
}

//将1个32位的密钥，转换为4个8位密钥,key8[0]为原来key32的高位
void key32_to_key8(unsigned int key32,unsigned char* key8)
{
    unsigned int mark = 0xff;
    int left_bit;
    for(int i=0; i<4; i++)
    {
        left_bit = (3 - i) * 8;
        key8[i] = ((mark << left_bit) & key32) >> left_bit;
    }
}

//将4个8位的密钥，转换为1个32位密钥
unsigned int key8_to_key32(unsigned char* key8)
{
    unsigned int temp_key=0;
    for(int i=0; i<4; i++)
    {
        temp_key ^= ((unsigned int)key8[i]<<((3 - i) * 8) );
        if(i==3)
        {
            return temp_key;
        }
    }

}

//字节替换
unsigned char SubBytes(unsigned char input)
{
    unsigned char pre = 0xf0;
    unsigned char suf = 0x0f;
    unsigned int row = (input & pre)>>4, col = input & suf;
    return S[row*16UL + col];
}

//行位移
void ShiftRows(unsigned char state_mat[][4])
{
    unsigned char temp_row[4];
    for(int i=1; i<4; i++)
    {
        for(int j=0; j<4; j++)
        {
            temp_row[j] = state_mat[i][(j+4+i)%4];
        }
        for(int j=0; j<4; j++)
        {
            state_mat[i][j] = temp_row[j];
        }
    }
}

//有限域上的乘法
unsigned char multi_finite_field(unsigned char a,unsigned char b)
{
    unsigned char ans = 0, v;
    for (int counter = 0; counter < 8; counter++)
    {
        if ((b & 0x01) != 0)
        {
            ans ^= a;
        }
        v = a>>7;
        a <<= 1;
        if(v != 0)
        {
            a ^= 0x1b;
        }
        b >>= 1;
    }
    return ans;

}

//列混合
void MixColumns(unsigned char state_mat[][4])
{
    unsigned char ans_mat[4][4];
    memset(ans_mat,0,sizeof(ans_mat));
    for(int i=0; i<4; i++)
    {
        for(int j=0; j<4; j++)
        {
            for(int k=0; k<4; k++)
            {
                ans_mat[i][j] ^= multi_finite_field(positive_matrix[i][k],state_mat[k][j]);
            }
        }
    }
    memcpy(state_mat,ans_mat,sizeof(ans_mat));
}

//轮密钥加，cnt标记这是第几轮循环，正确
void AddRoundKey(unsigned char state_mat[][4],int cnt)
{
    unsigned char key8[4];
    for(int col=0; col<4; col++)
    {
        key32_to_key8(W[4*cnt+col],key8);
        for(int row=0; row<4; row++)
        {
            state_mat[row][col] ^= key8[row];
        }
    }
}


//密钥扩展时的T函数，cnt代表轮数
unsigned int T(unsigned int input,int cnt)
{
    unsigned char key8[4];
    key32_to_key8(input,key8);
    unsigned char temp[4];
    temp[0] = SubBytes(key8[1]);
    temp[1] = SubBytes(key8[2]);
    temp[2] = SubBytes(key8[3]);
    temp[3] = SubBytes(key8[0]);
    unsigned int ans = key8_to_key32(temp);
    ans = ans ^ rcon[cnt-1];
    return ans;
}

//密钥扩展函数
void KeyExpansion(unsigned char* init_key)
{
    unsigned int temp_key=0;
    for(int i=0; i<16; i++) // 对输入的8位初始密钥，转换到32位的W[0],W[1],W[2],W[3]中
    {
        temp_key ^= ((unsigned int)init_key[i]<<((3 - (i%4)) * 8) );
        if(i%4==3)
        {
            W[i/4] = temp_key;
            temp_key = 0;
        }
    }
    int cnt;
    for(int i=1; i<=10; i++) //10轮密钥扩展
    {
        cnt=i*4; //cnt来当做更新W的下标
        while(1)
        {
            if(cnt%4!=0)
            {
                W[cnt] = W[cnt-1] ^ W[cnt-4];
            }
            else
            {
                W[cnt] = W[cnt-4] ^ T(W[cnt-1],i);
            }
            cnt++;
            if(cnt%4==0)
            {
                break;
            }
        }
    }
}

//加密
void encryption()
{
    int len = strlen((char*)P);
    int group_cnt = (len +  15) / 16; //进行明文分组
    for(int group = 0; group < group_cnt; group++)
    {
        unsigned char state_mat[4][4];
        memcpy(P128,P+(group*16),16);
        array_to_mat(P128,state_mat);
        AddRoundKey(state_mat,0);
        for(int i=1; i<=10; i++)
        {
            for(int row=0; row<4; row++) //字节替换
            {
                for(int col=0; col<4; col++)
                {
                    state_mat[row][col] = SubBytes(state_mat[row][col]);
                }
            }
            ShiftRows(state_mat);
            if(i!=10)
            {
                MixColumns(state_mat);
            }
            AddRoundKey(state_mat,i);
        }
        mat_to_array(state_mat,C128);
        memcpy(C+(group*16),C128,16);
    }

}

//解密方法如下

//逆字节替换
unsigned char Inv_SubBytes(unsigned char input)
{
    unsigned char pre = 0xf0;
    unsigned char suf = 0x0f;
    unsigned int row = (input & pre)>>4, col = input & suf;
    return inv_S[row*16UL + col];
}

//逆行位移
void Inv_ShiftRows(unsigned char state_mat[][4])
{
    unsigned char temp_row[4];
    for(int i=1; i<4; i++)
    {
        for(int j=0; j<4; j++)
        {
            temp_row[(j+4+i)%4] = state_mat[i][j];  //右移i位
        }
        for(int j=0; j<4; j++)
        {
            state_mat[i][j] = temp_row[j];
        }
    }
}

//逆列混合
void Inv_MixColumns(unsigned char state_mat[][4])
{
    unsigned char ans_mat[4][4];
    memset(ans_mat,0,sizeof(ans_mat));
    for(int i=0; i<4; i++)
    {
        for(int j=0; j<4; j++)
        {
            for(int k=0; k<4; k++)
            {
                ans_mat[i][j] ^= multi_finite_field(inv_positive_matrix[i][k],state_mat[k][j]);
            }
        }
    }
    memcpy(state_mat,ans_mat,sizeof(ans_mat));
}

//解密
void decryption()
{
    int len = strlen((char*)C);
    int group_cnt = (len +  15) / 16; //进行密文分组
    for(int group = 0; group < group_cnt; group++)
    {
        unsigned char state_mat[4][4];
        memcpy(C128,C+(group*16),16);
        array_to_mat(C128,state_mat);
        AddRoundKey(state_mat,10);
        for(int i=9; i>=0; i--)
        {
            Inv_ShiftRows(state_mat);
            for(int row=0; row<4; row++) //字节替换
            {
                for(int col=0; col<4; col++)
                {
                    state_mat[row][col] = Inv_SubBytes(state_mat[row][col]);
                }
            }
            AddRoundKey(state_mat,i);
            if(i!=0)
            {
                Inv_MixColumns(state_mat);
            }
        }
        mat_to_array(state_mat,P128);
        memcpy(De_P+(group*16),P128,16);
    }
}

main.cpp

#include 
#include 
#include 
#include 
#include "AES.h"
using namespace std;


//初始密钥
unsigned char key[16];


int main()
{

    ios::sync_with_stdio(false);

    cout << "请输入任意长度明文(按字符输入，最大长度不超过10^6，如'abcdgg125')：";
    cin >> P;

    cout << "请输入初始密钥(按字节输入，共16个字节.如'00 01 ... 0d 0e 0f')：";
    unsigned int xx;//作为“中间人”接收用户输入单字节密钥
    for(int i=0;i<16;i++)  // 输入密钥
    {
    	cin >> hex >> xx;
    	key[i]=xx;
    }

    cout << "输入的密钥是："<< endl;
    for(int i=0; i<16; i++) // 输入密钥
    {
        printf("%02x  ",key[i]);
    }
    cout  << "n" << endl;

    KeyExpansion(key); //密钥扩展

    cout << "输入的明文为:" << endl;
    for(int i=0;i 
运行结果：