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AES加密算法原理(C++实现)_c++ aes

c++ aes

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

  1. #include <iostream>
  2. using namespace std;
  3. #ifndef _AES_H_
  4. #define _AES_H_
  5. // S盒
  6. extern unsigned char S[256];
  7. //逆S盒
  8. extern unsigned char inv_S[256];
  9. // AES-128轮常量
  10. static const unsigned int rcon[10] = {
  11. 0x01000000UL, 0x02000000UL, 0x04000000UL, 0x08000000UL, 0x10000000UL,
  12. 0x20000000UL, 0x40000000UL, 0x80000000UL, 0x1B000000UL, 0x36000000UL
  13. };
  14. //列混淆时用到的正矩阵
  15. extern unsigned char positive_matrix[4][4];
  16. //逆列混淆时用到的逆正矩阵
  17. extern unsigned char inv_positive_matrix[4][4];
  18. //密钥扩展
  19. extern unsigned int W[44];
  20. //可输入明文的最大长度
  21. static const int MAX_LENGTH=1e6;
  22. //明文
  23. extern unsigned char P[MAX_LENGTH];
  24. //解密之后的明文
  25. extern unsigned char De_P[MAX_LENGTH];
  26. //分组后的128明文
  27. extern unsigned char P128[16];
  28. //密文
  29. extern unsigned char C[MAX_LENGTH];
  30. //分组后的128密文
  31. extern unsigned char C128[16];
  32. //128明文转换为状态矩阵
  33. void array_to_mat(unsigned char p[],unsigned char state_mat[][4]);
  34. //将状态矩阵转换为128密文
  35. void mat_to_array(unsigned char state_mat[][4],unsigned char c[]);
  36. //132位的密钥,转换为48位密钥
  37. void key32_to_key8(unsigned int key32,unsigned char* key8);
  38. //48位的密钥,转换为132位密钥
  39. unsigned int key8_to_key32(unsigned char* key8);
  40. //字节替换
  41. unsigned char SubBytes(unsigned char input);
  42. //行位移
  43. void ShiftRows(unsigned char state_mat[][4]);
  44. //有限域上的乘法
  45. unsigned char multi_finite_field(unsigned char a,unsigned char b);
  46. //列混合
  47. void MixColumns(unsigned char state_mat[][4]);
  48. //轮密钥加,cnt标记这是第几轮循环
  49. void AddRoundKey(unsigned char state_mat[][4],int cnt);
  50. //密钥扩展时的T函数,cnt代表轮数
  51. unsigned int T(unsigned int input,int cnt);
  52. //密钥扩展函数
  53. void KeyExpansion(unsigned char* init_key);
  54. //加密
  55. void encryption();
  56. //解密方法如下
  57. //逆字节替换
  58. unsigned char Inv_SubBytes(unsigned char input);
  59. //逆行位移
  60. void Inv_ShiftRows(unsigned char state_mat[][4]);
  61. //逆列混合
  62. void Inv_MixColumns(unsigned char state_mat[][4]);
  63. //逆轮密钥加,cnt标记这是第几轮循环
  64. void Inv_AddRoundKey(unsigned char state_mat[][4],int cnt);
  65. //解密
  66. void decryption();
  67. #endif

 AES.cpp

  1. #include "AES.h"
  2. #include <iostream>
  3. #include <cstring>
  4. using namespace std;
  5. // S盒
  6. unsigned char S[256] =
  7. {
  8. 0x63, 0x7C, 0x77, 0x7B, 0xF2, 0x6B, 0x6F, 0xC5, 0x30, 0x01, 0x67, 0x2B, 0xFE, 0xD7, 0xAB, 0x76,
  9. 0xCA, 0x82, 0xC9, 0x7D, 0xFA, 0x59, 0x47, 0xF0, 0xAD, 0xD4, 0xA2, 0xAF, 0x9C, 0xA4, 0x72, 0xC0,
  10. 0xB7, 0xFD, 0x93, 0x26, 0x36, 0x3F, 0xF7, 0xCC, 0x34, 0xA5, 0xE5, 0xF1, 0x71, 0xD8, 0x31, 0x15,
  11. 0x04, 0xC7, 0x23, 0xC3, 0x18, 0x96, 0x05, 0x9A, 0x07, 0x12, 0x80, 0xE2, 0xEB, 0x27, 0xB2, 0x75,
  12. 0x09, 0x83, 0x2C, 0x1A, 0x1B, 0x6E, 0x5A, 0xA0, 0x52, 0x3B, 0xD6, 0xB3, 0x29, 0xE3, 0x2F, 0x84,
  13. 0x53, 0xD1, 0x00, 0xED, 0x20, 0xFC, 0xB1, 0x5B, 0x6A, 0xCB, 0xBE, 0x39, 0x4A, 0x4C, 0x58, 0xCF,
  14. 0xD0, 0xEF, 0xAA, 0xFB, 0x43, 0x4D, 0x33, 0x85, 0x45, 0xF9, 0x02, 0x7F, 0x50, 0x3C, 0x9F, 0xA8,
  15. 0x51, 0xA3, 0x40, 0x8F, 0x92, 0x9D, 0x38, 0xF5, 0xBC, 0xB6, 0xDA, 0x21, 0x10, 0xFF, 0xF3, 0xD2,
  16. 0xCD, 0x0C, 0x13, 0xEC, 0x5F, 0x97, 0x44, 0x17, 0xC4, 0xA7, 0x7E, 0x3D, 0x64, 0x5D, 0x19, 0x73,
  17. 0x60, 0x81, 0x4F, 0xDC, 0x22, 0x2A, 0x90, 0x88, 0x46, 0xEE, 0xB8, 0x14, 0xDE, 0x5E, 0x0B, 0xDB,
  18. 0xE0, 0x32, 0x3A, 0x0A, 0x49, 0x06, 0x24, 0x5C, 0xC2, 0xD3, 0xAC, 0x62, 0x91, 0x95, 0xE4, 0x79,
  19. 0xE7, 0xC8, 0x37, 0x6D, 0x8D, 0xD5, 0x4E, 0xA9, 0x6C, 0x56, 0xF4, 0xEA, 0x65, 0x7A, 0xAE, 0x08,
  20. 0xBA, 0x78, 0x25, 0x2E, 0x1C, 0xA6, 0xB4, 0xC6, 0xE8, 0xDD, 0x74, 0x1F, 0x4B, 0xBD, 0x8B, 0x8A,
  21. 0x70, 0x3E, 0xB5, 0x66, 0x48, 0x03, 0xF6, 0x0E, 0x61, 0x35, 0x57, 0xB9, 0x86, 0xC1, 0x1D, 0x9E,
  22. 0xE1, 0xF8, 0x98, 0x11, 0x69, 0xD9, 0x8E, 0x94, 0x9B, 0x1E, 0x87, 0xE9, 0xCE, 0x55, 0x28, 0xDF,
  23. 0x8C, 0xA1, 0x89, 0x0D, 0xBF, 0xE6, 0x42, 0x68, 0x41, 0x99, 0x2D, 0x0F, 0xB0, 0x54, 0xBB, 0x16
  24. };
  25. //逆S盒
  26. unsigned char inv_S[256] =
  27. {
  28. 0x52, 0x09, 0x6A, 0xD5, 0x30, 0x36, 0xA5, 0x38, 0xBF, 0x40, 0xA3, 0x9E, 0x81, 0xF3, 0xD7, 0xFB,
  29. 0x7C, 0xE3, 0x39, 0x82, 0x9B, 0x2F, 0xFF, 0x87, 0x34, 0x8E, 0x43, 0x44, 0xC4, 0xDE, 0xE9, 0xCB,
  30. 0x54, 0x7B, 0x94, 0x32, 0xA6, 0xC2, 0x23, 0x3D, 0xEE, 0x4C, 0x95, 0x0B, 0x42, 0xFA, 0xC3, 0x4E,
  31. 0x08, 0x2E, 0xA1, 0x66, 0x28, 0xD9, 0x24, 0xB2, 0x76, 0x5B, 0xA2, 0x49, 0x6D, 0x8B, 0xD1, 0x25,
  32. 0x72, 0xF8, 0xF6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xD4, 0xA4, 0x5C, 0xCC, 0x5D, 0x65, 0xB6, 0x92,
  33. 0x6C, 0x70, 0x48, 0x50, 0xFD, 0xED, 0xB9, 0xDA, 0x5E, 0x15, 0x46, 0x57, 0xA7, 0x8D, 0x9D, 0x84,
  34. 0x90, 0xD8, 0xAB, 0x00, 0x8C, 0xBC, 0xD3, 0x0A, 0xF7, 0xE4, 0x58, 0x05, 0xB8, 0xB3, 0x45, 0x06,
  35. 0xD0, 0x2C, 0x1E, 0x8F, 0xCA, 0x3F, 0x0F, 0x02, 0xC1, 0xAF, 0xBD, 0x03, 0x01, 0x13, 0x8A, 0x6B,
  36. 0x3A, 0x91, 0x11, 0x41, 0x4F, 0x67, 0xDC, 0xEA, 0x97, 0xF2, 0xCF, 0xCE, 0xF0, 0xB4, 0xE6, 0x73,
  37. 0x96, 0xAC, 0x74, 0x22, 0xE7, 0xAD, 0x35, 0x85, 0xE2, 0xF9, 0x37, 0xE8, 0x1C, 0x75, 0xDF, 0x6E,
  38. 0x47, 0xF1, 0x1A, 0x71, 0x1D, 0x29, 0xC5, 0x89, 0x6F, 0xB7, 0x62, 0x0E, 0xAA, 0x18, 0xBE, 0x1B,
  39. 0xFC, 0x56, 0x3E, 0x4B, 0xC6, 0xD2, 0x79, 0x20, 0x9A, 0xDB, 0xC0, 0xFE, 0x78, 0xCD, 0x5A, 0xF4,
  40. 0x1F, 0xDD, 0xA8, 0x33, 0x88, 0x07, 0xC7, 0x31, 0xB1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xEC, 0x5F,
  41. 0x60, 0x51, 0x7F, 0xA9, 0x19, 0xB5, 0x4A, 0x0D, 0x2D, 0xE5, 0x7A, 0x9F, 0x93, 0xC9, 0x9C, 0xEF,
  42. 0xA0, 0xE0, 0x3B, 0x4D, 0xAE, 0x2A, 0xF5, 0xB0, 0xC8, 0xEB, 0xBB, 0x3C, 0x83, 0x53, 0x99, 0x61,
  43. 0x17, 0x2B, 0x04, 0x7E, 0xBA, 0x77, 0xD6, 0x26, 0xE1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0C, 0x7D
  44. };
  45. //密钥扩展
  46. unsigned int W[44];
  47. //列混淆时用到的正矩阵
  48. extern unsigned char positive_matrix[4][4]=
  49. {
  50. 0x02, 0x03, 0x01, 0x01,
  51. 0x01, 0x02, 0x03, 0x01,
  52. 0x01, 0x01, 0x02, 0x03,
  53. 0x03, 0x01, 0x01, 0x02
  54. };
  55. //逆列混淆时用到的逆正矩阵
  56. extern unsigned char inv_positive_matrix[4][4]=
  57. {
  58. 0x0e, 0x0b, 0x0d, 0x09,
  59. 0x09, 0x0e, 0x0b, 0x0d,
  60. 0x0d, 0x09, 0x0e, 0x0b,
  61. 0x0b, 0x0d, 0x09, 0x0e
  62. };
  63. //明文
  64. unsigned char P[MAX_LENGTH];
  65. //解密之后的明文
  66. unsigned char De_P[MAX_LENGTH];
  67. //分组后的128明文
  68. unsigned char P128[16];
  69. //密文
  70. unsigned char C[MAX_LENGTH];
  71. //分组后的128密文
  72. unsigned char C128[16];
  73. //128比特转换为状态矩阵
  74. void array_to_mat(unsigned char p[],unsigned char state_mat[][4])
  75. {
  76. for(int col=0; col<4; col++)
  77. {
  78. for(int row=0; row<4; row++)
  79. {
  80. state_mat[row][col] = p[col*4 + row];
  81. }
  82. }
  83. }
  84. //将状态矩阵转换为128密文
  85. void mat_to_array(unsigned char state_mat[][4],unsigned char c[])
  86. {
  87. int cnt=0;
  88. for(int col=0; col<4; col++)
  89. {
  90. for(int row=0; row<4; row++)
  91. {
  92. c[cnt++] = state_mat[row][col];
  93. }
  94. }
  95. }
  96. //132位的密钥,转换为48位密钥,key8[0]为原来key32的高位
  97. void key32_to_key8(unsigned int key32,unsigned char* key8)
  98. {
  99. unsigned int mark = 0xff;
  100. int left_bit;
  101. for(int i=0; i<4; i++)
  102. {
  103. left_bit = (3 - i) * 8;
  104. key8[i] = ((mark << left_bit) & key32) >> left_bit;
  105. }
  106. }
  107. //48位的密钥,转换为132位密钥
  108. unsigned int key8_to_key32(unsigned char* key8)
  109. {
  110. unsigned int temp_key=0;
  111. for(int i=0; i<4; i++)
  112. {
  113. temp_key ^= ((unsigned int)key8[i]<<((3 - i) * 8) );
  114. if(i==3)
  115. {
  116. return temp_key;
  117. }
  118. }
  119. }
  120. //字节替换
  121. unsigned char SubBytes(unsigned char input)
  122. {
  123. unsigned char pre = 0xf0;
  124. unsigned char suf = 0x0f;
  125. unsigned int row = (input & pre)>>4, col = input & suf;
  126. return S[row*16UL + col];
  127. }
  128. //行位移
  129. void ShiftRows(unsigned char state_mat[][4])
  130. {
  131. unsigned char temp_row[4];
  132. for(int i=1; i<4; i++)
  133. {
  134. for(int j=0; j<4; j++)
  135. {
  136. temp_row[j] = state_mat[i][(j+4+i)%4];
  137. }
  138. for(int j=0; j<4; j++)
  139. {
  140. state_mat[i][j] = temp_row[j];
  141. }
  142. }
  143. }
  144. //有限域上的乘法
  145. unsigned char multi_finite_field(unsigned char a,unsigned char b)
  146. {
  147. unsigned char ans = 0, v;
  148. for (int counter = 0; counter < 8; counter++)
  149. {
  150. if ((b & 0x01) != 0)
  151. {
  152. ans ^= a;
  153. }
  154. v = a>>7;
  155. a <<= 1;
  156. if(v != 0)
  157. {
  158. a ^= 0x1b;
  159. }
  160. b >>= 1;
  161. }
  162. return ans;
  163. }
  164. //列混合
  165. void MixColumns(unsigned char state_mat[][4])
  166. {
  167. unsigned char ans_mat[4][4];
  168. memset(ans_mat,0,sizeof(ans_mat));
  169. for(int i=0; i<4; i++)
  170. {
  171. for(int j=0; j<4; j++)
  172. {
  173. for(int k=0; k<4; k++)
  174. {
  175. ans_mat[i][j] ^= multi_finite_field(positive_matrix[i][k],state_mat[k][j]);
  176. }
  177. }
  178. }
  179. memcpy(state_mat,ans_mat,sizeof(ans_mat));
  180. }
  181. //轮密钥加,cnt标记这是第几轮循环,正确
  182. void AddRoundKey(unsigned char state_mat[][4],int cnt)
  183. {
  184. unsigned char key8[4];
  185. for(int col=0; col<4; col++)
  186. {
  187. key32_to_key8(W[4*cnt+col],key8);
  188. for(int row=0; row<4; row++)
  189. {
  190. state_mat[row][col] ^= key8[row];
  191. }
  192. }
  193. }
  194. //密钥扩展时的T函数,cnt代表轮数
  195. unsigned int T(unsigned int input,int cnt)
  196. {
  197. unsigned char key8[4];
  198. key32_to_key8(input,key8);
  199. unsigned char temp[4];
  200. temp[0] = SubBytes(key8[1]);
  201. temp[1] = SubBytes(key8[2]);
  202. temp[2] = SubBytes(key8[3]);
  203. temp[3] = SubBytes(key8[0]);
  204. unsigned int ans = key8_to_key32(temp);
  205. ans = ans ^ rcon[cnt-1];
  206. return ans;
  207. }
  208. //密钥扩展函数
  209. void KeyExpansion(unsigned char* init_key)
  210. {
  211. unsigned int temp_key=0;
  212. 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
  213. {
  214. temp_key ^= ((unsigned int)init_key[i]<<((3 - (i%4)) * 8) );
  215. if(i%4==3)
  216. {
  217. W[i/4] = temp_key;
  218. temp_key = 0;
  219. }
  220. }
  221. int cnt;
  222. for(int i=1; i<=10; i++) //10轮密钥扩展
  223. {
  224. cnt=i*4; //cnt来当做更新W的下标
  225. while(1)
  226. {
  227. if(cnt%4!=0)
  228. {
  229. W[cnt] = W[cnt-1] ^ W[cnt-4];
  230. }
  231. else
  232. {
  233. W[cnt] = W[cnt-4] ^ T(W[cnt-1],i);
  234. }
  235. cnt++;
  236. if(cnt%4==0)
  237. {
  238. break;
  239. }
  240. }
  241. }
  242. }
  243. //加密
  244. void encryption()
  245. {
  246. int len = strlen((char*)P);
  247. int group_cnt = (len + 15) / 16; //进行明文分组
  248. for(int group = 0; group < group_cnt; group++)
  249. {
  250. unsigned char state_mat[4][4];
  251. memcpy(P128,P+(group*16),16);
  252. array_to_mat(P128,state_mat);
  253. AddRoundKey(state_mat,0);
  254. for(int i=1; i<=10; i++)
  255. {
  256. for(int row=0; row<4; row++) //字节替换
  257. {
  258. for(int col=0; col<4; col++)
  259. {
  260. state_mat[row][col] = SubBytes(state_mat[row][col]);
  261. }
  262. }
  263. ShiftRows(state_mat);
  264. if(i!=10)
  265. {
  266. MixColumns(state_mat);
  267. }
  268. AddRoundKey(state_mat,i);
  269. }
  270. mat_to_array(state_mat,C128);
  271. memcpy(C+(group*16),C128,16);
  272. }
  273. }
  274. //解密方法如下
  275. //逆字节替换
  276. unsigned char Inv_SubBytes(unsigned char input)
  277. {
  278. unsigned char pre = 0xf0;
  279. unsigned char suf = 0x0f;
  280. unsigned int row = (input & pre)>>4, col = input & suf;
  281. return inv_S[row*16UL + col];
  282. }
  283. //逆行位移
  284. void Inv_ShiftRows(unsigned char state_mat[][4])
  285. {
  286. unsigned char temp_row[4];
  287. for(int i=1; i<4; i++)
  288. {
  289. for(int j=0; j<4; j++)
  290. {
  291. temp_row[(j+4+i)%4] = state_mat[i][j]; //右移i位
  292. }
  293. for(int j=0; j<4; j++)
  294. {
  295. state_mat[i][j] = temp_row[j];
  296. }
  297. }
  298. }
  299. //逆列混合
  300. void Inv_MixColumns(unsigned char state_mat[][4])
  301. {
  302. unsigned char ans_mat[4][4];
  303. memset(ans_mat,0,sizeof(ans_mat));
  304. for(int i=0; i<4; i++)
  305. {
  306. for(int j=0; j<4; j++)
  307. {
  308. for(int k=0; k<4; k++)
  309. {
  310. ans_mat[i][j] ^= multi_finite_field(inv_positive_matrix[i][k],state_mat[k][j]);
  311. }
  312. }
  313. }
  314. memcpy(state_mat,ans_mat,sizeof(ans_mat));
  315. }
  316. //解密
  317. void decryption()
  318. {
  319. int len = strlen((char*)C);
  320. int group_cnt = (len + 15) / 16; //进行密文分组
  321. for(int group = 0; group < group_cnt; group++)
  322. {
  323. unsigned char state_mat[4][4];
  324. memcpy(C128,C+(group*16),16);
  325. array_to_mat(C128,state_mat);
  326. AddRoundKey(state_mat,10);
  327. for(int i=9; i>=0; i--)
  328. {
  329. Inv_ShiftRows(state_mat);
  330. for(int row=0; row<4; row++) //字节替换
  331. {
  332. for(int col=0; col<4; col++)
  333. {
  334. state_mat[row][col] = Inv_SubBytes(state_mat[row][col]);
  335. }
  336. }
  337. AddRoundKey(state_mat,i);
  338. if(i!=0)
  339. {
  340. Inv_MixColumns(state_mat);
  341. }
  342. }
  343. mat_to_array(state_mat,P128);
  344. memcpy(De_P+(group*16),P128,16);
  345. }
  346. }

main.cpp

  1. #include <cstdio>
  2. #include <cstring>
  3. #include <iostream>
  4. #include <iomanip>
  5. #include "AES.h"
  6. using namespace std;
  7. //初始密钥
  8. unsigned char key[16];
  9. int main()
  10. {
  11. ios::sync_with_stdio(false);
  12. 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'):";
  13. cin >> P;
  14. cout << "请输入初始密钥(按字节输入,共16个字节.如'00 01 ... 0d 0e 0f'):";
  15. unsigned int xx;//作为“中间人”接收用户输入单字节密钥
  16. for(int i=0;i<16;i++) // 输入密钥
  17. {
  18. cin >> hex >> xx;
  19. key[i]=xx;
  20. }
  21. cout << "输入的密钥是:"<< endl;
  22. for(int i=0; i<16; i++) // 输入密钥
  23. {
  24. printf("%02x ",key[i]);
  25. }
  26. cout << "\n" << endl;
  27. KeyExpansion(key); //密钥扩展
  28. cout << "输入的明文为:" << endl;
  29. for(int i=0;i<strlen((char*)P);i++)
  30. {
  31. printf("%02x ",P[i]);
  32. }
  33. cout << endl;
  34. encryption(); //加密
  35. cout << endl;
  36. cout << "加密后的密文为:" << endl;
  37. for(int i=0;i<strlen((char*)C);i++)
  38. {
  39. printf("%02x ",C[i]);
  40. }
  41. cout << "\n" << endl;
  42. decryption(); //解密
  43. cout << "解密后的明文为:" << endl;
  44. printf("%s\n",De_P);
  45. return 0;
  46. }

运行结果:

 

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