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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 <iostream>
- 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 <iostream>
- #include <cstring>
- 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 <cstdio>
- #include <cstring>
- #include <iostream>
- #include <iomanip>
- #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<strlen((char*)P);i++)
- {
- printf("%02x ",P[i]);
- }
-
- cout << endl;
- encryption(); //加密
- cout << endl;
-
- cout << "加密后的密文为:" << endl;
- for(int i=0;i<strlen((char*)C);i++)
- {
- printf("%02x ",C[i]);
- }
- cout << "\n" << endl;
-
- decryption(); //解密
-
- cout << "解密后的明文为:" << endl;
- printf("%s\n",De_P);
-
- return 0;
- }

运行结果:

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