AES加密算法（C++ 實現，附源碼）

先搞定AES算法，基本變換包括SubBytes（字節替代）、ShiftRows（行移位）、MixColumns（列混淆）、AddRoundKey(輪密鑰加）

其算法通常描述爲

明文及密鑰的組織排列方式

 

ByteSubstitution（字節替代）

非線性的字節替代，單獨處理每一個字節：

求該字節在有限域GF(2⁸)上的乘法逆，"0"被映射爲自身，即對於α∈GF(2⁸)，求β∈GF(2⁸)，

使得α·β=β·α=1mod(x⁸+x⁴+x²+x+1)。

對上一步求得的乘法逆做仿射變換

y_i=x_i + x_(i+4)mod8 + x_(i+6)mod8 + x_(i+7)mod8 + c_i

(其中c_i是63₁₀即01100011₂的第i位），用矩陣表示爲

原本打算把求乘法逆和仿射變換算法敲上去，最後仍是放棄了...直接打置換表

 

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unsigned char  sBox[] = { /*  0    1    2    3    4    5    6    7    8    9    a    b    c    d    e    f */      0x63,0x7c,0x77,0x7b,0xf2,0x6b,0x6f,0xc5,0x30,0x01,0x67,0x2b,0xfe,0xd7,0xab,0x76, /*0*/       0xca,0x82,0xc9,0x7d,0xfa,0x59,0x47,0xf0,0xad,0xd4,0xa2,0xaf,0x9c,0xa4,0x72,0xc0, /*1*/      0xb7,0xfd,0x93,0x26,0x36,0x3f,0xf7,0xcc,0x34,0xa5,0xe5,0xf1,0x71,0xd8,0x31,0x15, /*2*/      0x04,0xc7,0x23,0xc3,0x18,0x96,0x05,0x9a,0x07,0x12,0x80,0xe2,0xeb,0x27,0xb2,0x75, /*3*/      0x09,0x83,0x2c,0x1a,0x1b,0x6e,0x5a,0xa0,0x52,0x3b,0xd6,0xb3,0x29,0xe3,0x2f,0x84, /*4*/      0x53,0xd1,0x00,0xed,0x20,0xfc,0xb1,0x5b,0x6a,0xcb,0xbe,0x39,0x4a,0x4c,0x58,0xcf, /*5*/      0xd0,0xef,0xaa,0xfb,0x43,0x4d,0x33,0x85,0x45,0xf9,0x02,0x7f,0x50,0x3c,0x9f,0xa8, /*6*/       0x51,0xa3,0x40,0x8f,0x92,0x9d,0x38,0xf5,0xbc,0xb6,0xda,0x21,0x10,0xff,0xf3,0xd2, /*7*/      0xcd,0x0c,0x13,0xec,0x5f,0x97,0x44,0x17,0xc4,0xa7,0x7e,0x3d,0x64,0x5d,0x19,0x73, /*8*/      0x60,0x81,0x4f,0xdc,0x22,0x2a,0x90,0x88,0x46,0xee,0xb8,0x14,0xde,0x5e,0x0b,0xdb, /*9*/      0xe0,0x32,0x3a,0x0a,0x49,0x06,0x24,0x5c,0xc2,0xd3,0xac,0x62,0x91,0x95,0xe4,0x79, /*a*/      0xe7,0xc8,0x37,0x6d,0x8d,0xd5,0x4e,0xa9,0x6c,0x56,0xf4,0xea,0x65,0x7a,0xae,0x08, /*b*/      0xba,0x78,0x25,0x2e,0x1c,0xa6,0xb4,0xc6,0xe8,0xdd,0x74,0x1f,0x4b,0xbd,0x8b,0x8a, /*c*/      0x70,0x3e,0xb5,0x66,0x48,0x03,0xf6,0x0e,0x61,0x35,0x57,0xb9,0x86,0xc1,0x1d,0x9e, /*d*/      0xe1,0xf8,0x98,0x11,0x69,0xd9,0x8e,0x94,0x9b,0x1e,0x87,0xe9,0xce,0x55,0x28,0xdf, /*e*/      0x8c,0xa1,0x89,0x0d,0xbf,0xe6,0x42,0x68,0x41,0x99,0x2d,0x0f,0xb0,0x54,0xbb,0x16  /*f*/ };

 

 下面是逆置換表，解密時使用

 

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unsigned char  invsBox[256] = { /*  0    1    2    3    4    5    6    7    8    9    a    b    c    d    e    f  */       0x52,0x09,0x6a,0xd5,0x30,0x36,0xa5,0x38,0xbf,0x40,0xa3,0x9e,0x81,0xf3,0xd7,0xfb, /*0*/      0x7c,0xe3,0x39,0x82,0x9b,0x2f,0xff,0x87,0x34,0x8e,0x43,0x44,0xc4,0xde,0xe9,0xcb, /*1*/      0x54,0x7b,0x94,0x32,0xa6,0xc2,0x23,0x3d,0xee,0x4c,0x95,0x0b,0x42,0xfa,0xc3,0x4e, /*2*/      0x08,0x2e,0xa1,0x66,0x28,0xd9,0x24,0xb2,0x76,0x5b,0xa2,0x49,0x6d,0x8b,0xd1,0x25, /*3*/      0x72,0xf8,0xf6,0x64,0x86,0x68,0x98,0x16,0xd4,0xa4,0x5c,0xcc,0x5d,0x65,0xb6,0x92, /*4*/      0x6c,0x70,0x48,0x50,0xfd,0xed,0xb9,0xda,0x5e,0x15,0x46,0x57,0xa7,0x8d,0x9d,0x84, /*5*/      0x90,0xd8,0xab,0x00,0x8c,0xbc,0xd3,0x0a,0xf7,0xe4,0x58,0x05,0xb8,0xb3,0x45,0x06, /*6*/      0xd0,0x2c,0x1e,0x8f,0xca,0x3f,0x0f,0x02,0xc1,0xaf,0xbd,0x03,0x01,0x13,0x8a,0x6b, /*7*/      0x3a,0x91,0x11,0x41,0x4f,0x67,0xdc,0xea,0x97,0xf2,0xcf,0xce,0xf0,0xb4,0xe6,0x73, /*8*/      0x96,0xac,0x74,0x22,0xe7,0xad,0x35,0x85,0xe2,0xf9,0x37,0xe8,0x1c,0x75,0xdf,0x6e, /*9*/      0x47,0xf1,0x1a,0x71,0x1d,0x29,0xc5,0x89,0x6f,0xb7,0x62,0x0e,0xaa,0x18,0xbe,0x1b, /*a*/      0xfc,0x56,0x3e,0x4b,0xc6,0xd2,0x79,0x20,0x9a,0xdb,0xc0,0xfe,0x78,0xcd,0x5a,0xf4, /*b*/      0x1f,0xdd,0xa8,0x33,0x88,0x07,0xc7,0x31,0xb1,0x12,0x10,0x59,0x27,0x80,0xec,0x5f, /*c*/      0x60,0x51,0x7f,0xa9,0x19,0xb5,0x4a,0x0d,0x2d,0xe5,0x7a,0x9f,0x93,0xc9,0x9c,0xef, /*d*/      0xa0,0xe0,0x3b,0x4d,0xae,0x2a,0xf5,0xb0,0xc8,0xeb,0xbb,0x3c,0x83,0x53,0x99,0x61, /*e*/      0x17,0x2b,0x04,0x7e,0xba,0x77,0xd6,0x26,0xe1,0x69,0x14,0x63,0x55,0x21,0x0c,0x7d  /*f*/ };

 

這裏遇到問題了，原本用純c初始化數組很正常，封裝成類之後發現不能初始化，無論是聲明、構造函數都沒法初始化，百歌谷度了一通後沒有任何答案，無奈只能在構造函數中聲明一個局部變量數組並初始化，而後用memcpy，（成員變量名爲Sbox/InvSbox，局部變量名sBox/invsBox）

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void  AES::SubBytes(unsigned char  state[][4]) {      int  r,c;      for (r=0; r<4; r++)      {          for (c=0; c<4; c++)          {              state[r][c] = Sbox[state[r][c]];          }      } }

 ShiftRows（行移位變換）

行移位變換完成基於行的循環位移操做，變換方法： 

即行移位變換做用於行上，第0行不變，第1行循環左移1個字節，第2行循環左移2個字節，第3行循環左移3個字節。

 

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void  AES::ShiftRows(unsigned char  state[][4]) {      unsigned char  t[4];      int  r,c;      for (r=1; r<4; r++)      {          for (c=0; c<4; c++)          {              t[c] = state[r][(c+r)%4];          }          for (c=0; c<4; c++)          {              state[r][c] = t[c];          }      } }

MixColumns（列混淆變換） 

 逐列混合，方法：

b(x) = (03·x³ + 01·x² + 01·x + 02) · a(x) mod(x⁴ + 1)

矩陣表示形式：

 

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void  AES::MixColumns(unsigned char  state[][4]) {      unsigned char  t[4];      int  r,c;      for (c=0; c< 4; c++)      {          for (r=0; r<4; r++)          {              t[r] = state[r][c];          }          for (r=0; r<4; r++)          {              state[r][c] = FFmul(0x02, t[r])                          ^ FFmul(0x03, t[(r+1)%4])                          ^ FFmul(0x01, t[(r+2)%4])                          ^ FFmul(0x01, t[(r+3)%4]);          }      } }   unsigned char  AES::FFmul(unsigned char  a, unsigned char  b) {      unsigned char  bw[4];      unsigned char  res=0;      int  i;      bw[0] = b;      for (i=1; i<4; i++)      {          bw[i] = bw[i-1]<<1;          if (bw[i-1]&0x80)          {              bw[i]^=0x1b;          }      }      for (i=0; i<4; i++)      {          if ((a>>i)&0x01)          {              res ^= bw[i];          }      }      return  res; }

 

其中FFmul爲有限域GF(2⁸)上的乘法，標準算法應該是循環8次（b與a的每一位相乘，結果相加），但這裏只用到最低2位，解密時用到的逆列混淆也只用了低4位，因此在這裏高4位的運算是多餘的，只計算低4位。

 

AddRoundKey（輪密鑰加變換） 

 簡單來講就是逐字節相加，有限域GF(2⁸)上的加法是模2加法，即異或

 

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void  AES::AddRoundKey(unsigned char  state[][4], unsigned char  k[][4]) {      int  r,c;      for (c=0; c<4; c++)      {          for (r=0; r<4; r++)          {              state[r][c] ^= k[r][c];          }      } }

 

 KeyExpansion（密鑰擴展）

 將輸入的密鑰擴展爲11組128位密鑰組，其中第0組爲輸入密鑰自己 

 其後第n組第i列 爲 第n-1組第i列 與 第n組第i-1列之和（模2加法，1<= i <=3）

對於每一組 第一列即i=0，有特殊的處理

將前一列即第n-1組第3列的4個字節循環左移1個字節，

並對每一個字節進行字節替代變換SubBytes

將第一行（即第一個字節）與輪常量rc[n]相加 

最後再與前一組該列相加 

 

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void  AES::KeyExpansion(unsigned char * key, unsigned char  w[][4][4]) {      int  i,j,r,c;      unsigned char  rc[] = {0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1b, 0x36};      for (r=0; r<4; r++)      {          for (c=0; c<4; c++)          {              w[0][r][c] = key[r+c*4];          }      }      for (i=1; i<=10; i++)      {          for (j=0; j<4; j++)          {              unsigned char  t[4];              for (r=0; r<4; r++)              {                  t[r] = j ? w[i][r][j-1] : w[i-1][r][3];              }              if (j == 0)              {                  unsigned char  temp = t[0];                  for (r=0; r<3; r++)                  {                      t[r] = Sbox[t[(r+1)%4]];                  }                  t[3] = Sbox[temp];                  t[0] ^= rc[i-1];              }              for (r=0; r<4; r++)              {                  w[i][r][j] = w[i-1][r][j] ^ t[r];              }          }      } }

 

解密的基本運算

AES解密算法與加密不一樣，基本運算中除了AddRoundKey（輪密鑰加）不變外，其他的都須要進行逆變換，即

InvSubBytes（逆字節替代）、InvShiftRows（逆行移位）、InvMixColumns（逆列混淆）

 

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void  AES::InvSubBytes(unsigned char  state[][4]) {      int  r,c;      for (r=0; r<4; r++)      {          for (c=0; c<4; c++)          {              state[r][c] = InvSbox[state[r][c]];          }      } }   void  AES::InvShiftRows(unsigned char  state[][4]) {      unsigned char  t[4];      int  r,c;      for (r=1; r<4; r++)      {          for (c=0; c<4; c++)          {              t[c] = state[r][(c-r+4)%4];          }          for (c=0; c<4; c++)          {              state[r][c] = t[c];          }      } }   void  AES::InvMixColumns(unsigned char  state[][4]) {      unsigned char  t[4];      int  r,c;      for (c=0; c< 4; c++)      {          for (r=0; r<4; r++)          {              t[r] = state[r][c];          }          for (r=0; r<4; r++)          {              state[r][c] = FFmul(0x0e, t[r])                          ^ FFmul(0x0b, t[(r+1)%4])                          ^ FFmul(0x0d, t[(r+2)%4])                          ^ FFmul(0x09, t[(r+3)%4]);          }      } }

 

加密過程

先將輸入的明文按列序組合成4*4的矩陣，直接與第0組密鑰（即輸入的密鑰）相加（異或），做爲輪加密的輸入

而後循環10次進行SubBytes、ShiftRows、MixColumns、AddRoundKey運算，最後恢復原序列

須要注意的是最後一輪並不進行MixColumns（列混淆變換）

 

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unsigned char * AES::Cipher(unsigned char * input) {      unsigned char  state[4][4];      int  i,r,c;        for (r=0; r<4; r++)      {          for (c=0; c<4 ;c++)          {              state[r][c] = input[c*4+r];          }      }        AddRoundKey(state,w[0]);        for (i=1; i<=10; i++)      {          SubBytes(state);          ShiftRows(state);          if (i!=10)MixColumns(state);          AddRoundKey(state,w[i]);      }        for (r=0; r<4; r++)      {          for (c=0; c<4 ;c++)          {              input[c*4+r] = state[r][c];          }      }        return  input; }

 

解密過程

 

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unsigned char * AES::InvCipher(unsigned char * input) {      unsigned char  state[4][4];      int  i,r,c;        for (r=0; r<4; r++)      {          for (c=0; c<4 ;c++)          {              state[r][c] = input[c*4+r];          }      }        AddRoundKey(state, w[10]);      for (i=9; i>=0; i--)      {          InvShiftRows(state);          InvSubBytes(state);          AddRoundKey(state, w[i]);          if (i)InvMixColumns(state);      }            for (r=0; r<4; r++)      {          for (c=0; c<4 ;c++)          {              input[c*4+r] = state[r][c];          }      }        return  input; }

 

對外部數據的加密/解密

至此已經實現了AES加密與解密的原型，在使用的時候通常處理的是字符串等，而不是直接傳入128位的數據，因此要封裝一下對外部數據的加解密處理

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void * AES::Cipher( void * input, int  length) {      unsigned char * in = (unsigned char *) input;      int  i;      if (!length)      {          while (*(in+length++));          in = (unsigned char *) input;      }      for (i=0; i<length; i+=16)      {          Cipher(in+i);      }      return  input; }   void * AES::InvCipher( void * input, int  length) {      unsigned char * in = (unsigned char *) input;      int  i;      for (i=0; i<length; i+=16)      {          InvCipher(in+i);      }      return  input; }

 

加密時默認參數length=0,爲要加密的數據長度，若是使用默認值，則做爲字符串處理，以'\0'爲結尾計算長度

加密時傳進的指針要預留夠16整數倍字節的空間，由於加密操做直接修改原數據，不足128位可能形成內存溢出

 

 最後附上源代碼  Source_AES_Cipher