C++中四種加密算法之AES源代碼

來源：本站原創(chuàng)|時(shí)間：2020-01-10|欄目：C語言|點(diǎn)擊：次

摘要：作為新一代的加密標(biāo)準(zhǔn)，AES 旨在取代 DES（請(qǐng)看《DES加密算法的C++實(shí)現(xiàn)》），以適應(yīng)當(dāng)今分布式開放網(wǎng)絡(luò)對(duì)數(shù)據(jù)加密安全性的要求。本文在分析了 AES 加密原理的基礎(chǔ)上著重說明了算法實(shí)現(xiàn)的具體步驟，并用 C++ 實(shí)現(xiàn)了對(duì)文件的加密和解密。

一、AES 介紹

AES（高級(jí)加密標(biāo)準(zhǔn)，Advanced Encryption Standard），在密碼學(xué)中又稱 Rijndael 加密法，是美國聯(lián)邦政府采用的一種分組加密標(biāo)準(zhǔn)。這個(gè)標(biāo)準(zhǔn)用來替代原先的 DES，目前已經(jīng)廣為全世界所使用，成為對(duì)稱密鑰算法中最流行的算法之一。

在 AES 出現(xiàn)之前，最常用的對(duì)稱密鑰算法是 DES 加密算法，它在 1977 年被公布成為美國政府的商用加密標(biāo)準(zhǔn)。DES 的主要問題是密鑰長度較短，漸漸不適合于分布式開放網(wǎng)絡(luò)對(duì)數(shù)據(jù)加密安全性的要求。因此，1998年美國政府決定不再繼續(xù)延用 DES 作為聯(lián)邦加密標(biāo)準(zhǔn)，并發(fā)起了征集 AES 候選算法的活動(dòng)。征集活動(dòng)對(duì) AES 的基本要求是：比三重DES快、至少與三重DES一樣安全、數(shù)據(jù)分組長度為128比特、密鑰長度為128/192/256比特。

經(jīng)過三年多的甄選，比利時(shí)的密碼學(xué)家所設(shè)計(jì)的 Rijndael 算法最終脫穎而出，成為新一代的高級(jí)加密標(biāo)準(zhǔn)，并于 2001 年由美國國家標(biāo)準(zhǔn)與技術(shù)研究院（NIST）發(fā)布于 FIPS PUB 197。

二、AES 算法原理

AES算法（即 Rijndael 算法）是一個(gè)對(duì)稱分組密碼算法。數(shù)據(jù)分組長度必須是 128 bits，使用的密鑰長度為 128，192 或 256 bits。對(duì)于三種不同密鑰長度的 AES 算法，分別稱為“AES-128”、“AES-192”、“AES-256”。（Rijndael 的設(shè)計(jì)還可以處理其它的分組長度和密鑰長度，但 AES 標(biāo)準(zhǔn)中沒有采用）

下圖是 AES 加密解密的整體流程圖：

這里我們需要知道3個(gè)符號(hào)：Nb—— 狀態(tài) State 包含的列（32-bit 字）的個(gè)數(shù)，也就是說 Nb=4；Nk—— 密鑰包含的 32-bit 字的個(gè)數(shù)，也就是說 Nk=4，6 或 8；Nr—— 加密的輪數(shù)，對(duì)于不同密鑰長度，輪數(shù)不一樣，具體如下圖所示：

下面分為密鑰擴(kuò)展、分組加密、分組解密三個(gè)部分來講 AES 算法，我會(huì)盡可能地簡明扼要，若還有不懂的，請(qǐng)自行 Google。

1）密鑰擴(kuò)展

AES 算法通過密鑰擴(kuò)展程序（Key Expansion）將用戶輸入的密鑰 K 擴(kuò)展生成 Nb(Nr+1)個(gè)字，存放在一個(gè)線性數(shù)組w[Nb*(Nr+1)]中。具體如下：

位置變換函數(shù)RotWord()，接受一個(gè)字 [a0, a1, a2, a3] 作為輸入，循環(huán)左移一個(gè)字節(jié)后輸出 [a1, a2, a3, a0]。
S盒變換函數(shù)SubWord()，接受一個(gè)字 [a0, a1, a2, a3] 作為輸入。S盒是一個(gè)16x16的表，其中每一個(gè)元素是一個(gè)字節(jié)。對(duì)于輸入的每一個(gè)字節(jié)，前四位組成十六進(jìn)制數(shù) x 作為行號(hào)，后四位組成的十六進(jìn)制數(shù) y 作為列號(hào)，查找表中對(duì)應(yīng)的值。最后函數(shù)輸出 4 個(gè)新字節(jié)組成的 32-bit 字。
輪常數(shù)Rcon[]，如何計(jì)算的就不說了，直接把它當(dāng)做常量數(shù)組。
擴(kuò)展密鑰數(shù)組w[]的前 Nk 個(gè)元素就是外部密鑰 K，以后的元素w[i]等于它前一個(gè)元素w[i-1]與前第 Nk 個(gè)元素w[i-Nk]的異或，即w[i] = w[i-1] XOR w[i-Nk]；但若 i 為 Nk 的倍數(shù)，則w[i] = w[i-Nk] XOR SubWord(RotWord(w[i-1])) XOR Rcon[i/Nk-1]。

注意，上面的第四步說明適合于 AES-128 和 AES-192，詳細(xì)的偽代碼如下：

密鑰擴(kuò)展程序的 C++ 代碼（AES-128）：

#include <iostream> 
#include <bitset> 
using namespace std;  
typedef bitset<8> byte; 
typedef bitset<32> word; 
 
const int Nr = 10; // AES-128需要 10 輪加密 
const int Nk = 4;  // Nk 表示輸入密鑰的 word 個(gè)數(shù) 
 
byte S_Box[16][16] = { 
  {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} 
}; 
 
// 輪常數(shù)，密鑰擴(kuò)展中用到。（AES-128只需要10輪） 
word Rcon[10] = {0x01000000, 0x02000000, 0x04000000, 0x08000000, 0x10000000,  
         0x20000000, 0x40000000, 0x80000000, 0x1b000000, 0x36000000}; 
 
/** 
 * 將4個(gè) byte 轉(zhuǎn)換為一個(gè) word 
 */ 
word Word(byte& k1, byte& k2, byte& k3, byte& k4) 
{ 
  word result(0x00000000); 
  word temp; 
  temp = kto_ulong(); // K1 
  temp <<= 24; 
  result |= temp; 
  temp = kto_ulong(); // K2 
  temp <<= 16; 
  result |= temp; 
  temp = kto_ulong(); // K3 
  temp <<= 8; 
  result |= temp; 
  temp = kto_ulong(); // K4 
  result |= temp; 
  return result; 
} 
 
/** 
 * 按字節(jié) 循環(huán)左移一位 
 * 即把[a0, a1, a2, a3]變成[a1, a2, a3, a0] 
 */ 
word RotWord(word& rw) 
{ 
  word high = rw << 8; 
  word low = rw >> 24; 
  return high | low; 
} 
 
/** 
 * 對(duì)輸入word中的每一個(gè)字節(jié)進(jìn)行S-盒變換 
 */ 
word SubWord(word& sw) 
{ 
  word temp; 
  for(int i=0; i<32; i+=8) 
  { 
    int row = sw[i+7]*8 + sw[i+6]*4 + sw[i+5]*2 + sw[i+4]; 
    int col = sw[i+3]*8 + sw[i+2]*4 + sw[i+1]*2 + sw[i]; 
    byte val = S_Box[row][col]; 
    for(int j=0; j<8; ++j) 
      temp[i+j] = val[j]; 
  } 
  return temp; 
} 
 
/** 
 * 密鑰擴(kuò)展函數(shù) - 對(duì)128位密鑰進(jìn)行擴(kuò)展得到 w[4*(Nr+1)] 
 */  
void KeyExpansion(byte key[4*Nk], word w[4*(Nr+1)]) 
{ 
  word temp; 
  int i = 0; 
  // w[]的前4個(gè)就是輸入的key 
  while(i < Nk)  
  { 
    w[i] = Word(key[4*i], key[4*i+1], key[4*i+2], key[4*i+3]); 
    ++i; 
  } 
 
  i = Nk; 
 
  while(i < 4*(Nr+1)) 
  { 
    temp = w[i-1]; // 記錄前一個(gè)word 
    if(i % Nk == 0) 
      w[i] = w[i-Nk] ^ SubWord(RotWord(temp)) ^ Rcon[i/Nk-1]; 
    else  
      w[i] = w[i-Nk] ^ temp; 
    ++i; 
  } 
} 
 
int main() 
{ 
  byte key[16] = {0x2b, 0x7e, 0x15, 0x16,  
          0x28, 0xae, 0xd2, 0xa6,  
          0xab, 0xf7, 0x15, 0x88,  
          0x09, 0xcf, 0x4f, 0x3c}; 
 
  word w[4*(Nr+1)]; 
 
  cout << "KEY IS: "; 
  for(int i=0; i<16; ++i) 
    cout << hex << key[i]to_ulong() << " "; 
  cout << endl; 
 
  KeyExpansion(key, w); 
  // 測(cè)試 
  for(int i=0; i<4*(Nr+1); ++i) 
    cout << "w[" << dec << i << "] = " << hex << w[i]to_ulong() << endl; 
 
  return 0; 
}

測(cè)試輸出結(jié)果：

2）加密

根據(jù) AES 加密的整體流程圖（本文開頭），偽代碼如下：

從偽代碼描述中可以看出，AES 加密時(shí)涉及到的子程序有SubBytes()、ShiftRows()、MixColumns()和AddRoundKey()。下面我們一個(gè)一個(gè)進(jìn)行介紹：

① S盒變換-SubBytes()

在密鑰擴(kuò)展部分已經(jīng)講過了，S盒是一個(gè) 16 行 16 列的表，表中每個(gè)元素都是一個(gè)字節(jié)。S盒變換很簡單：函數(shù)SubBytes()接受一個(gè) 4x4 的字節(jié)矩陣作為輸入，對(duì)其中的每個(gè)字節(jié)，前四位組成十六進(jìn)制數(shù) x 作為行號(hào)，后四位組成的十六進(jìn)制數(shù) y 作為列號(hào)，查找表中對(duì)應(yīng)的值替換原來位置上的字節(jié)。

② 行變換-ShiftRows()

行變換也很簡單，它僅僅是將矩陣的每一行以字節(jié)為單位循環(huán)移位：第一行不變，第二行左移一位，第三行左移兩位，第四行左移三位。如下圖所示：

③ 列變換-MixColumns()

函數(shù)MixColumns()同樣接受一個(gè) 4x4 的字節(jié)矩陣作為輸入，并對(duì)矩陣進(jìn)行逐列變換，變換方式如下：

注意公式中用到的乘法是伽羅華域（GF，有限域）上的乘法，高級(jí)加密標(biāo)準(zhǔn)文檔 fips-197 上有講，如果還是不懂，請(qǐng)自行Google。

④ 與擴(kuò)展密鑰的異或-AddRoundKey()

擴(kuò)展密鑰只參與了這一步。根據(jù)當(dāng)前加密的輪數(shù)，用w[]中的 4 個(gè)擴(kuò)展密鑰與矩陣的 4 個(gè)列進(jìn)行按位異或。如下圖：

好了，到這里 AES 加密的各個(gè)部分就講完了。算法實(shí)現(xiàn)的 C++ 源碼在文章后面第三部分。

3）解密

根據(jù) AES 解密的整體流程圖（本文開頭），偽代碼如下：

從偽代碼可以看出，我們需要分別實(shí)現(xiàn) S 盒變換、行變換和列變換的逆變換InvShiftRows()、InvSubBytes()和InvMixColumns()。下面就簡單的講一下這三個(gè)逆變換：

① 逆行變換-InvShiftRows()

上面講到ShiftRows()是對(duì)矩陣的每一行進(jìn)行循環(huán)左移，所以InvShiftRows()是對(duì)矩陣每一行進(jìn)行循環(huán)右移。

② 逆 S 盒變換-InvSubBytes()

與 S 盒變換一樣，也是查表，查表的方式也一樣，只不過查的是另外一個(gè)置換表（S-Box的逆表）。

③ 逆列變換-InvMixColumns()

與列變換的方式一樣，只不過計(jì)算公式的系數(shù)矩陣發(fā)生了變化。如下圖：

好了，AES 解密到這里也講完了。只要寫出三個(gè)逆變換的函數(shù)，然后根據(jù)偽代碼就很容易實(shí)現(xiàn) AES 解密算法了。

三、C++實(shí)現(xiàn)

下面我用 C++ 實(shí)現(xiàn) AES 的加密和解密算法，并實(shí)現(xiàn)了對(duì)文件的加密和解密。這里我使用 C++ STL 的bitset定義了兩個(gè)類型：byte和word。需要提到的是，對(duì)于有限域上的乘法，我們既可以通過查表（6個(gè)結(jié)果表），也可以寫一個(gè)函數(shù)來實(shí)現(xiàn)。當(dāng)然，查表的效率會(huì)更高，但考慮到貼代碼，這里我就用一個(gè)函數(shù)來實(shí)現(xiàn)的。

下面是 AES-128 對(duì)一個(gè) 128 位數(shù)據(jù)加密和解密的源代碼：

/*************************************************************************  
  > File Name: AEScpp 
  > Author: SongLee  
  > E-mail: lisongshine@qqcom  
  > Created Time: 2014年12月12日 星期五 20時(shí)15分50秒  
  > Personal Blog: http://songleegithubcom  
 ************************************************************************/  
#include <iostream> 
#include <bitset> 
#include <string> 
using namespace std;  
typedef bitset<8> byte; 
typedef bitset<32> word; 
 
const int Nr = 10; // AES-128需要 10 輪加密 
const int Nk = 4;  // Nk 表示輸入密鑰的 word 個(gè)數(shù) 
 
byte S_Box[16][16] = { 
  {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} 
}; 
 
byte Inv_S_Box[16][16] = { 
  {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} 
}; 
 
// 輪常數(shù)，密鑰擴(kuò)展中用到。（AES-128只需要10輪） 
word Rcon[10] = {0x01000000, 0x02000000, 0x04000000, 0x08000000, 0x10000000,  
         0x20000000, 0x40000000, 0x80000000, 0x1b000000, 0x36000000}; 
 
/**********************************************************************/  
/*                                  */  
/*               AES算法實(shí)現(xiàn)              */  
/*                                  */  
/**********************************************************************/  
 
/******************************下面是加密的變換函數(shù)**********************/ 
/** 
 * S盒變換 - 前4位為行號(hào)，后4位為列號(hào) 
 */ 
void SubBytes(byte mtx[4*4]) 
{ 
  for(int i=0; i<16; ++i) 
  { 
    int row = mtx[i][7]*8 + mtx[i][6]*4 + mtx[i][5]*2 + mtx[i][4]; 
    int col = mtx[i][3]*8 + mtx[i][2]*4 + mtx[i][1]*2 + mtx[i][0]; 
    mtx[i] = S_Box[row][col]; 
  } 
} 
 
/** 
 * 行變換 - 按字節(jié)循環(huán)移位 
 */ 
void ShiftRows(byte mtx[4*4]) 
{ 
  // 第二行循環(huán)左移一位 
  byte temp = mtx[4]; 
  for(int i=0; i<3; ++i) 
    mtx[i+4] = mtx[i+5]; 
  mtx[7] = temp; 
  // 第三行循環(huán)左移兩位 
  for(int i=0; i<2; ++i) 
  { 
    temp = mtx[i+8]; 
    mtx[i+8] = mtx[i+10]; 
    mtx[i+10] = temp; 
  } 
  // 第四行循環(huán)左移三位 
  temp = mtx[15]; 
  for(int i=3; i>0; --i) 
    mtx[i+12] = mtx[i+11]; 
  mtx[12] = temp; 
} 
 
/** 
 * 有限域上的乘法 GF(2^8) 
 */ 
byte GFMul(byte a, byte b) {  
  byte p = 0; 
  byte hi_bit_set; 
  for (int counter = 0; counter < 8; counter++) { 
    if ((b & byte(1)) != 0) { 
      p ^= a; 
    } 
    hi_bit_set = (byte) (a & byte(0x80)); 
    a <<= 1; 
    if (hi_bit_set != 0) { 
      a ^= 0x1b; /* x^8 + x^4 + x^3 + x + 1 */ 
    } 
    b >>= 1; 
  } 
  return p; 
} 
 
/** 
 * 列變換 
 */ 
void MixColumns(byte mtx[4*4]) 
{ 
  byte arr[4]; 
  for(int i=0; i<4; ++i) 
  { 
    for(int j=0; j<4; ++j) 
      arr[j] = mtx[i+j*4]; 
 
    mtx[i] = GFMul(0x02, arr[0]) ^ GFMul(0x03, arr[1]) ^ arr[2] ^ arr[3]; 
    mtx[i+4] = arr[0] ^ GFMul(0x02, arr[1]) ^ GFMul(0x03, arr[2]) ^ arr[3]; 
    mtx[i+8] = arr[0] ^ arr[1] ^ GFMul(0x02, arr[2]) ^ GFMul(0x03, arr[3]); 
    mtx[i+12] = GFMul(0x03, arr[0]) ^ arr[1] ^ arr[2] ^ GFMul(0x02, arr[3]); 
  } 
} 
 
/** 
 * 輪密鑰加變換 - 將每一列與擴(kuò)展密鑰進(jìn)行異或 
 */ 
void AddRoundKey(byte mtx[4*4], word k[4]) 
{ 
  for(int i=0; i<4; ++i) 
  { 
    word k1 = k[i] >> 24; 
    word k2 = (k[i] << 8) >> 24; 
    word k3 = (k[i] << 16) >> 24; 
    word k4 = (k[i] << 24) >> 24; 
     
    mtx[i] = mtx[i] ^ byte(kto_ulong()); 
    mtx[i+4] = mtx[i+4] ^ byte(kto_ulong()); 
    mtx[i+8] = mtx[i+8] ^ byte(kto_ulong()); 
    mtx[i+12] = mtx[i+12] ^ byte(kto_ulong()); 
  } 
} 
 
/**************************下面是解密的逆變換函數(shù)***********************/ 
/** 
 * 逆S盒變換 
 */ 
void InvSubBytes(byte mtx[4*4]) 
{ 
  for(int i=0; i<16; ++i) 
  { 
    int row = mtx[i][7]*8 + mtx[i][6]*4 + mtx[i][5]*2 + mtx[i][4]; 
    int col = mtx[i][3]*8 + mtx[i][2]*4 + mtx[i][1]*2 + mtx[i][0]; 
    mtx[i] = Inv_S_Box[row][col]; 
  } 
} 
 
/** 
 * 逆行變換 - 以字節(jié)為單位循環(huán)右移 
 */ 
void InvShiftRows(byte mtx[4*4]) 
{ 
  // 第二行循環(huán)右移一位 
  byte temp = mtx[7]; 
  for(int i=3; i>0; --i) 
    mtx[i+4] = mtx[i+3]; 
  mtx[4] = temp; 
  // 第三行循環(huán)右移兩位 
  for(int i=0; i<2; ++i) 
  { 
    temp = mtx[i+8]; 
    mtx[i+8] = mtx[i+10]; 
    mtx[i+10] = temp; 
  } 
  // 第四行循環(huán)右移三位 
  temp = mtx[12]; 
  for(int i=0; i<3; ++i) 
    mtx[i+12] = mtx[i+13]; 
  mtx[15] = temp; 
} 
 
void InvMixColumns(byte mtx[4*4]) 
{ 
  byte arr[4]; 
  for(int i=0; i<4; ++i) 
  { 
    for(int j=0; j<4; ++j) 
      arr[j] = mtx[i+j*4]; 
 
    mtx[i] = GFMul(0x0e, arr[0]) ^ GFMul(0x0b, arr[1]) ^ GFMul(0x0d, arr[2]) ^ GFMul(0x09, arr[3]); 
    mtx[i+4] = GFMul(0x09, arr[0]) ^ GFMul(0x0e, arr[1]) ^ GFMul(0x0b, arr[2]) ^ GFMul(0x0d, arr[3]); 
    mtx[i+8] = GFMul(0x0d, arr[0]) ^ GFMul(0x09, arr[1]) ^ GFMul(0x0e, arr[2]) ^ GFMul(0x0b, arr[3]); 
    mtx[i+12] = GFMul(0x0b, arr[0]) ^ GFMul(0x0d, arr[1]) ^ GFMul(0x09, arr[2]) ^ GFMul(0x0e, arr[3]); 
  } 
} 
 
/******************************下面是密鑰擴(kuò)展部分***********************/ 
/** 
 * 將4個(gè) byte 轉(zhuǎn)換為一個(gè) word 
 */ 
word Word(byte& k1, byte& k2, byte& k3, byte& k4) 
{ 
  word result(0x00000000); 
  word temp; 
  temp = kto_ulong(); // K1 
  temp <<= 24; 
  result |= temp; 
  temp = kto_ulong(); // K2 
  temp <<= 16; 
  result |= temp; 
  temp = kto_ulong(); // K3 
  temp <<= 8; 
  result |= temp; 
  temp = kto_ulong(); // K4 
  result |= temp; 
  return result; 
} 
 
/** 
 * 按字節(jié) 循環(huán)左移一位 
 * 即把[a0, a1, a2, a3]變成[a1, a2, a3, a0] 
 */ 
word RotWord(word& rw) 
{ 
  word high = rw << 8; 
  word low = rw >> 24; 
  return high | low; 
} 
 
/** 
 * 對(duì)輸入word中的每一個(gè)字節(jié)進(jìn)行S-盒變換 
 */ 
word SubWord(word& sw) 
{ 
  word temp; 
  for(int i=0; i<32; i+=8) 
  { 
    int row = sw[i+7]*8 + sw[i+6]*4 + sw[i+5]*2 + sw[i+4]; 
    int col = sw[i+3]*8 + sw[i+2]*4 + sw[i+1]*2 + sw[i]; 
    byte val = S_Box[row][col]; 
    for(int j=0; j<8; ++j) 
      temp[i+j] = val[j]; 
  } 
  return temp; 
} 
 
/** 
 * 密鑰擴(kuò)展函數(shù) - 對(duì)128位密鑰進(jìn)行擴(kuò)展得到 w[4*(Nr+1)] 
 */  
void KeyExpansion(byte key[4*Nk], word w[4*(Nr+1)]) 
{ 
  word temp; 
  int i = 0; 
  // w[]的前4個(gè)就是輸入的key 
  while(i < Nk)  
  { 
    w[i] = Word(key[4*i], key[4*i+1], key[4*i+2], key[4*i+3]); 
    ++i; 
  } 
 
  i = Nk; 
 
  while(i < 4*(Nr+1)) 
  { 
    temp = w[i-1]; // 記錄前一個(gè)word 
    if(i % Nk == 0) 
      w[i] = w[i-Nk] ^ SubWord(RotWord(temp)) ^ Rcon[i/Nk-1]; 
    else  
      w[i] = w[i-Nk] ^ temp; 
    ++i; 
  } 
} 
 
/******************************下面是加密和解密函數(shù)**************************/ 
/** 
 * 加密 
 */ 
void encrypt(byte in[4*4], word w[4*(Nr+1)]) 
{ 
  word key[4]; 
  for(int i=0; i<4; ++i) 
    key[i] = w[i]; 
  AddRoundKey(in, key); 
 
  for(int round=1; round<Nr; ++round) 
  { 
    SubBytes(in); 
    ShiftRows(in); 
    MixColumns(in); 
    for(int i=0; i<4; ++i) 
      key[i] = w[4*round+i]; 
    AddRoundKey(in, key); 
  } 
 
  SubBytes(in); 
  ShiftRows(in); 
  for(int i=0; i<4; ++i) 
    key[i] = w[4*Nr+i]; 
  AddRoundKey(in, key); 
} 
 
/** 
 * 解密 
 */ 
void decrypt(byte in[4*4], word w[4*(Nr+1)]) 
{ 
  word key[4]; 
  for(int i=0; i<4; ++i) 
    key[i] = w[4*Nr+i]; 
  AddRoundKey(in, key); 
 
  for(int round=Nr-1; round>0; --round) 
  { 
    InvShiftRows(in); 
    InvSubBytes(in); 
    for(int i=0; i<4; ++i) 
      key[i] = w[4*round+i]; 
    AddRoundKey(in, key); 
    InvMixColumns(in); 
  } 
 
  InvShiftRows(in); 
  InvSubBytes(in); 
  for(int i=0; i<4; ++i) 
    key[i] = w[i]; 
  AddRoundKey(in, key); 
} 
 
/**********************************************************************/  
/*                                  */  
/*               測(cè)試                 */  
/*                                  */  
/**********************************************************************/  
int main() 
{ 
  byte key[16] = {0x2b, 0x7e, 0x15, 0x16,  
          0x28, 0xae, 0xd2, 0xa6,  
          0xab, 0xf7, 0x15, 0x88,  
          0x09, 0xcf, 0x4f, 0x3c}; 
 
  byte plain[16] = {0x32, 0x88, 0x31, 0xe0,  
          0x43, 0x5a, 0x31, 0x37, 
          0xf6, 0x30, 0x98, 0x07, 
          0xa8, 0x8d, 0xa2, 0x34};  
  // 輸出密鑰 
  cout << "密鑰是："; 
  for(int i=0; i<16; ++i) 
    cout << hex << key[i]to_ulong() << " "; 
  cout << endl; 
 
  word w[4*(Nr+1)]; 
  KeyExpansion(key, w); 
 
  // 輸出待加密的明文 
  cout << endl << "待加密的明文："<<endl; 
  for(int i=0; i<16; ++i) 
  { 
    cout << hex << plain[i]to_ulong() << " "; 
    if((i+1)%4 == 0) 
      cout << endl; 
  } 
  cout << endl; 
 
  // 加密，輸出密文 
  encrypt(plain, w); 
  cout << "加密后的密文："<<endl; 
  for(int i=0; i<16; ++i) 
  { 
    cout << hex << plain[i]to_ulong() << " "; 
    if((i+1)%4 == 0) 
      cout << endl; 
  } 
  cout << endl; 
 
  // 解密，輸出明文 
  decrypt(plain, w); 
  cout << "解密后的明文："<<endl; 
  for(int i=0; i<16; ++i) 
  { 
    cout << hex << plain[i]to_ulong() << " "; 
    if((i+1)%4 == 0) 
      cout << endl; 
  } 
  cout << endl; 
  return 0; 
}

測(cè)試用例如下圖：

測(cè)試結(jié)果截圖：

可見，測(cè)試結(jié)果和預(yù)期輸出相同，表明對(duì)數(shù)據(jù)的加密和解密成功?。?！

下面我們來寫 AES 對(duì)文件的加密和解密，在對(duì) 128 位的數(shù)據(jù)加解密成功以后，對(duì)文件的加解密就很簡單了！只需要每次讀 128 位，加密以后，將 128 位的密文寫入另外一個(gè)文件…如此循環(huán)，直到文件尾。下面是對(duì)一張圖片進(jìn)行 AES 加密和解密的測(cè)試代碼（效率先不管了，有時(shí)間我再優(yōu)化）：

//#include <fstream> 
typedef bitset<8> byte; 
typedef bitset<32> word; 
/** 
 * 將一個(gè)char字符數(shù)組轉(zhuǎn)化為二進(jìn)制 
 * 存到一個(gè) byte 數(shù)組中 
 */ 
void charToByte(byte out[16], const char s[16]) 
{  
  for(int i=0; i<16; ++i)  
    for(int j=0; j<8; ++j)  
      out[i][j]= ((s[i]>>j) & 1);  
} 
 
/** 
 * 將連續(xù)的128位分成16組，存到一個(gè) byte 數(shù)組中 
 */ 
void divideToByte(byte out[16], bitset<128>& data) 
{ 
  bitset<128> temp; 
  for(int i=0; i<16; ++i) 
  { 
    temp = (data << 8*i) >> 120; 
    out[i] = tempto_ulong(); 
  } 
} 
 
/** 
 * 將16個(gè) byte 合并成連續(xù)的128位 
 */ 
bitset<128> mergeByte(byte in[16]) 
{ 
  bitset<128> res; 
  resreset(); // 置0 
  bitset<128> temp; 
  for(int i=0; i<16; ++i) 
  { 
    temp = in[i]to_ulong(); 
    temp <<= 8*(15-i); 
    res |= temp; 
  } 
  return res; 
} 
 
int main() 
{ 
  string keyStr = "abcdefghijklmnop"; 
  byte key[16];  
  charToByte(key, keyStrc_str()); 
  // 密鑰擴(kuò)展 
  word w[4*(Nr+1)]; 
  KeyExpansion(key, w); 
 
  bitset<128> data; 
  byte plain[16]; 
  // 將文件 flowerjpg 加密到 ciphertxt 中 
  ifstream in; 
  ofstream out; 
  inopen("D://flowerjpg", ios::binary); 
  outopen("D://ciphertxt", ios::binary); 
  while(inread((char*)&data, sizeof(data))) 
  { 
    divideToByte(plain, data); 
    encrypt(plain, w); 
    data = mergeByte(plain); 
    outwrite((char*)&data, sizeof(data)); 
    datareset(); // 置0 
  } 
  inclose(); 
  outclose(); 
 
  // 解密 ciphertxt，并寫入圖片 flowerjpg 
  inopen("D://ciphertxt", ios::binary); 
  outopen("D://flowerjpg", ios::binary); 
  while(inread((char*)&data, sizeof(data))) 
  { 
    divideToByte(plain, data); 
    decrypt(plain, w); 
    data = mergeByte(plain); 
    outwrite((char*)&data, sizeof(data)); 
    datareset(); // 置0 
  } 
  inclose(); 
  outclose(); 
 
  return 0; 
}

有限域 GF(28) 上的乘法改用查表的方式實(shí)現(xiàn)，AES的加密速度馬上提升 80% 以上，所以建議最好使用查表的方式。下面是 AES 算法中用到的 6 個(gè)乘法結(jié)果表：

byte Mul_02[256] = { 
  0x00,0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,0x10,0x12,0x14,0x16,0x18,0x1a,0x1c,0x1e, 
  0x20,0x22,0x24,0x26,0x28,0x2a,0x2c,0x2e,0x30,0x32,0x34,0x36,0x38,0x3a,0x3c,0x3e, 
  0x40,0x42,0x44,0x46,0x48,0x4a,0x4c,0x4e,0x50,0x52,0x54,0x56,0x58,0x5a,0x5c,0x5e, 
  0x60,0x62,0x64,0x66,0x68,0x6a,0x6c,0x6e,0x70,0x72,0x74,0x76,0x78,0x7a,0x7c,0x7e, 
  0x80,0x82,0x84,0x86,0x88,0x8a,0x8c,0x8e,0x90,0x92,0x94,0x96,0x98,0x9a,0x9c,0x9e, 
  0xa0,0xa2,0xa4,0xa6,0xa8,0xaa,0xac,0xae,0xb0,0xb2,0xb4,0xb6,0xb8,0xba,0xbc,0xbe, 
  0xc0,0xc2,0xc4,0xc6,0xc8,0xca,0xcc,0xce,0xd0,0xd2,0xd4,0xd6,0xd8,0xda,0xdc,0xde, 
  0xe0,0xe2,0xe4,0xe6,0xe8,0xea,0xec,0xee,0xf0,0xf2,0xf4,0xf6,0xf8,0xfa,0xfc,0xfe, 
  0x1b,0x19,0x1f,0x1d,0x13,0x11,0x17,0x15,0x0b,0x09,0x0f,0x0d,0x03,0x01,0x07,0x05, 
  0x3b,0x39,0x3f,0x3d,0x33,0x31,0x37,0x35,0x2b,0x29,0x2f,0x2d,0x23,0x21,0x27,0x25, 
  0x5b,0x59,0x5f,0x5d,0x53,0x51,0x57,0x55,0x4b,0x49,0x4f,0x4d,0x43,0x41,0x47,0x45, 
  0x7b,0x79,0x7f,0x7d,0x73,0x71,0x77,0x75,0x6b,0x69,0x6f,0x6d,0x63,0x61,0x67,0x65, 
  0x9b,0x99,0x9f,0x9d,0x93,0x91,0x97,0x95,0x8b,0x89,0x8f,0x8d,0x83,0x81,0x87,0x85, 
  0xbb,0xb9,0xbf,0xbd,0xb3,0xb1,0xb7,0xb5,0xab,0xa9,0xaf,0xad,0xa3,0xa1,0xa7,0xa5, 
  0xdb,0xd9,0xdf,0xdd,0xd3,0xd1,0xd7,0xd5,0xcb,0xc9,0xcf,0xcd,0xc3,0xc1,0xc7,0xc5, 
  0xfb,0xf9,0xff,0xfd,0xf3,0xf1,0xf7,0xf5,0xeb,0xe9,0xef,0xed,0xe3,0xe1,0xe7,0xe5 
}; 
 
byte Mul_03[256] = { 
  0x00,0x03,0x06,0x05,0x0c,0x0f,0x0a,0x09,0x18,0x1b,0x1e,0x1d,0x14,0x17,0x12,0x11, 
  0x30,0x33,0x36,0x35,0x3c,0x3f,0x3a,0x39,0x28,0x2b,0x2e,0x2d,0x24,0x27,0x22,0x21, 
  0x60,0x63,0x66,0x65,0x6c,0x6f,0x6a,0x69,0x78,0x7b,0x7e,0x7d,0x74,0x77,0x72,0x71, 
  0x50,0x53,0x56,0x55,0x5c,0x5f,0x5a,0x59,0x48,0x4b,0x4e,0x4d,0x44,0x47,0x42,0x41, 
  0xc0,0xc3,0xc6,0xc5,0xcc,0xcf,0xca,0xc9,0xd8,0xdb,0xde,0xdd,0xd4,0xd7,0xd2,0xd1, 
  0xf0,0xf3,0xf6,0xf5,0xfc,0xff,0xfa,0xf9,0xe8,0xeb,0xee,0xed,0xe4,0xe7,0xe2,0xe1, 
  0xa0,0xa3,0xa6,0xa5,0xac,0xaf,0xaa,0xa9,0xb8,0xbb,0xbe,0xbd,0xb4,0xb7,0xb2,0xb1, 
  0x90,0x93,0x96,0x95,0x9c,0x9f,0x9a,0x99,0x88,0x8b,0x8e,0x8d,0x84,0x87,0x82,0x81, 
  0x9b,0x98,0x9d,0x9e,0x97,0x94,0x91,0x92,0x83,0x80,0x85,0x86,0x8f,0x8c,0x89,0x8a, 
  0xab,0xa8,0xad,0xae,0xa7,0xa4,0xa1,0xa2,0xb3,0xb0,0xb5,0xb6,0xbf,0xbc,0xb9,0xba, 
  0xfb,0xf8,0xfd,0xfe,0xf7,0xf4,0xf1,0xf2,0xe3,0xe0,0xe5,0xe6,0xef,0xec,0xe9,0xea, 
  0xcb,0xc8,0xcd,0xce,0xc7,0xc4,0xc1,0xc2,0xd3,0xd0,0xd5,0xd6,0xdf,0xdc,0xd9,0xda, 
  0x5b,0x58,0x5d,0x5e,0x57,0x54,0x51,0x52,0x43,0x40,0x45,0x46,0x4f,0x4c,0x49,0x4a, 
  0x6b,0x68,0x6d,0x6e,0x67,0x64,0x61,0x62,0x73,0x70,0x75,0x76,0x7f,0x7c,0x79,0x7a, 
  0x3b,0x38,0x3d,0x3e,0x37,0x34,0x31,0x32,0x23,0x20,0x25,0x26,0x2f,0x2c,0x29,0x2a, 
  0x0b,0x08,0x0d,0x0e,0x07,0x04,0x01,0x02,0x13,0x10,0x15,0x16,0x1f,0x1c,0x19,0x1a 
}; 
 
byte Mul_09[256] = { 
  0x00,0x09,0x12,0x1b,0x24,0x2d,0x36,0x3f,0x48,0x41,0x5a,0x53,0x6c,0x65,0x7e,0x77, 
  0x90,0x99,0x82,0x8b,0xb4,0xbd,0xa6,0xaf,0xd8,0xd1,0xca,0xc3,0xfc,0xf5,0xee,0xe7, 
  0x3b,0x32,0x29,0x20,0x1f,0x16,0x0d,0x04,0x73,0x7a,0x61,0x68,0x57,0x5e,0x45,0x4c, 
  0xab,0xa2,0xb9,0xb0,0x8f,0x86,0x9d,0x94,0xe3,0xea,0xf1,0xf8,0xc7,0xce,0xd5,0xdc, 
  0x76,0x7f,0x64,0x6d,0x52,0x5b,0x40,0x49,0x3e,0x37,0x2c,0x25,0x1a,0x13,0x08,0x01, 
  0xe6,0xef,0xf4,0xfd,0xc2,0xcb,0xd0,0xd9,0xae,0xa7,0xbc,0xb5,0x8a,0x83,0x98,0x91, 
  0x4d,0x44,0x5f,0x56,0x69,0x60,0x7b,0x72,0x05,0x0c,0x17,0x1e,0x21,0x28,0x33,0x3a, 
  0xdd,0xd4,0xcf,0xc6,0xf9,0xf0,0xeb,0xe2,0x95,0x9c,0x87,0x8e,0xb1,0xb8,0xa3,0xaa, 
  0xec,0xe5,0xfe,0xf7,0xc8,0xc1,0xda,0xd3,0xa4,0xad,0xb6,0xbf,0x80,0x89,0x92,0x9b, 
  0x7c,0x75,0x6e,0x67,0x58,0x51,0x4a,0x43,0x34,0x3d,0x26,0x2f,0x10,0x19,0x02,0x0b, 
  0xd7,0xde,0xc5,0xcc,0xf3,0xfa,0xe1,0xe8,0x9f,0x96,0x8d,0x84,0xbb,0xb2,0xa9,0xa0, 
  0x47,0x4e,0x55,0x5c,0x63,0x6a,0x71,0x78,0x0f,0x06,0x1d,0x14,0x2b,0x22,0x39,0x30, 
  0x9a,0x93,0x88,0x81,0xbe,0xb7,0xac,0xa5,0xd2,0xdb,0xc0,0xc9,0xf6,0xff,0xe4,0xed, 
  0x0a,0x03,0x18,0x11,0x2e,0x27,0x3c,0x35,0x42,0x4b,0x50,0x59,0x66,0x6f,0x74,0x7d, 
  0xa1,0xa8,0xb3,0xba,0x85,0x8c,0x97,0x9e,0xe9,0xe0,0xfb,0xf2,0xcd,0xc4,0xdf,0xd6, 
  0x31,0x38,0x23,0x2a,0x15,0x1c,0x07,0x0e,0x79,0x70,0x6b,0x62,0x5d,0x54,0x4f,0x46 
}; 
 
byte Mul_0b[256] = { 
  0x00,0x0b,0x16,0x1d,0x2c,0x27,0x3a,0x31,0x58,0x53,0x4e,0x45,0x74,0x7f,0x62,0x69, 
  0xb0,0xbb,0xa6,0xad,0x9c,0x97,0x8a,0x81,0xe8,0xe3,0xfe,0xf5,0xc4,0xcf,0xd2,0xd9, 
  0x7b,0x70,0x6d,0x66,0x57,0x5c,0x41,0x4a,0x23,0x28,0x35,0x3e,0x0f,0x04,0x19,0x12, 
  0xcb,0xc0,0xdd,0xd6,0xe7,0xec,0xf1,0xfa,0x93,0x98,0x85,0x8e,0xbf,0xb4,0xa9,0xa2, 
  0xf6,0xfd,0xe0,0xeb,0xda,0xd1,0xcc,0xc7,0xae,0xa5,0xb8,0xb3,0x82,0x89,0x94,0x9f, 
  0x46,0x4d,0x50,0x5b,0x6a,0x61,0x7c,0x77,0x1e,0x15,0x08,0x03,0x32,0x39,0x24,0x2f, 
  0x8d,0x86,0x9b,0x90,0xa1,0xaa,0xb7,0xbc,0xd5,0xde,0xc3,0xc8,0xf9,0xf2,0xef,0xe4, 
  0x3d,0x36,0x2b,0x20,0x11,0x1a,0x07,0x0c,0x65,0x6e,0x73,0x78,0x49,0x42,0x5f,0x54, 
  0xf7,0xfc,0xe1,0xea,0xdb,0xd0,0xcd,0xc6,0xaf,0xa4,0xb9,0xb2,0x83,0x88,0x95,0x9e, 
  0x47,0x4c,0x51,0x5a,0x6b,0x60,0x7d,0x76,0x1f,0x14,0x09,0x02,0x33,0x38,0x25,0x2e, 
  0x8c,0x87,0x9a,0x91,0xa0,0xab,0xb6,0xbd,0xd4,0xdf,0xc2,0xc9,0xf8,0xf3,0xee,0xe5, 
  0x3c,0x37,0x2a,0x21,0x10,0x1b,0x06,0x0d,0x64,0x6f,0x72,0x79,0x48,0x43,0x5e,0x55, 
  0x01,0x0a,0x17,0x1c,0x2d,0x26,0x3b,0x30,0x59,0x52,0x4f,0x44,0x75,0x7e,0x63,0x68, 
  0xb1,0xba,0xa7,0xac,0x9d,0x96,0x8b,0x80,0xe9,0xe2,0xff,0xf4,0xc5,0xce,0xd3,0xd8, 
  0x7a,0x71,0x6c,0x67,0x56,0x5d,0x40,0x4b,0x22,0x29,0x34,0x3f,0x0e,0x05,0x18,0x13, 
  0xca,0xc1,0xdc,0xd7,0xe6,0xed,0xf0,0xfb,0x92,0x99,0x84,0x8f,0xbe,0xb5,0xa8,0xa3 
}; 
 
byte Mul_0d[256] = { 
  0x00,0x0d,0x1a,0x17,0x34,0x39,0x2e,0x23,0x68,0x65,0x72,0x7f,0x5c,0x51,0x46,0x4b, 
  0xd0,0xdd,0xca,0xc7,0xe4,0xe9,0xfe,0xf3,0xb8,0xb5,0xa2,0xaf,0x8c,0x81,0x96,0x9b, 
  0xbb,0xb6,0xa1,0xac,0x8f,0x82,0x95,0x98,0xd3,0xde,0xc9,0xc4,0xe7,0xea,0xfd,0xf0, 
  0x6b,0x66,0x71,0x7c,0x5f,0x52,0x45,0x48,0x03,0x0e,0x19,0x14,0x37,0x3a,0x2d,0x20, 
  0x6d,0x60,0x77,0x7a,0x59,0x54,0x43,0x4e,0x05,0x08,0x1f,0x12,0x31,0x3c,0x2b,0x26, 
  0xbd,0xb0,0xa7,0xaa,0x89,0x84,0x93,0x9e,0xd5,0xd8,0xcf,0xc2,0xe1,0xec,0xfb,0xf6, 
  0xd6,0xdb,0xcc,0xc1,0xe2,0xef,0xf8,0xf5,0xbe,0xb3,0xa4,0xa9,0x8a,0x87,0x90,0x9d, 
  0x06,0x0b,0x1c,0x11,0x32,0x3f,0x28,0x25,0x6e,0x63,0x74,0x79,0x5a,0x57,0x40,0x4d, 
  0xda,0xd7,0xc0,0xcd,0xee,0xe3,0xf4,0xf9,0xb2,0xbf,0xa8,0xa5,0x86,0x8b,0x9c,0x91, 
  0x0a,0x07,0x10,0x1d,0x3e,0x33,0x24,0x29,0x62,0x6f,0x78,0x75,0x56,0x5b,0x4c,0x41, 
  0x61,0x6c,0x7b,0x76,0x55,0x58,0x4f,0x42,0x09,0x04,0x13,0x1e,0x3d,0x30,0x27,0x2a, 
  0xb1,0xbc,0xab,0xa6,0x85,0x88,0x9f,0x92,0xd9,0xd4,0xc3,0xce,0xed,0xe0,0xf7,0xfa, 
  0xb7,0xba,0xad,0xa0,0x83,0x8e,0x99,0x94,0xdf,0xd2,0xc5,0xc8,0xeb,0xe6,0xf1,0xfc, 
  0x67,0x6a,0x7d,0x70,0x53,0x5e,0x49,0x44,0x0f,0x02,0x15,0x18,0x3b,0x36,0x21,0x2c, 
  0x0c,0x01,0x16,0x1b,0x38,0x35,0x22,0x2f,0x64,0x69,0x7e,0x73,0x50,0x5d,0x4a,0x47, 
  0xdc,0xd1,0xc6,0xcb,0xe8,0xe5,0xf2,0xff,0xb4,0xb9,0xae,0xa3,0x80,0x8d,0x9a,0x97 
}; 
 
byte Mul_0e[256] = { 
  0x00,0x0e,0x1c,0x12,0x38,0x36,0x24,0x2a,0x70,0x7e,0x6c,0x62,0x48,0x46,0x54,0x5a, 
  0xe0,0xee,0xfc,0xf2,0xd8,0xd6,0xc4,0xca,0x90,0x9e,0x8c,0x82,0xa8,0xa6,0xb4,0xba, 
  0xdb,0xd5,0xc7,0xc9,0xe3,0xed,0xff,0xf1,0xab,0xa5,0xb7,0xb9,0x93,0x9d,0x8f,0x81, 
  0x3b,0x35,0x27,0x29,0x03,0x0d,0x1f,0x11,0x4b,0x45,0x57,0x59,0x73,0x7d,0x6f,0x61, 
  0xad,0xa3,0xb1,0xbf,0x95,0x9b,0x89,0x87,0xdd,0xd3,0xc1,0xcf,0xe5,0xeb,0xf9,0xf7, 
  0x4d,0x43,0x51,0x5f,0x75,0x7b,0x69,0x67,0x3d,0x33,0x21,0x2f,0x05,0x0b,0x19,0x17, 
  0x76,0x78,0x6a,0x64,0x4e,0x40,0x52,0x5c,0x06,0x08,0x1a,0x14,0x3e,0x30,0x22,0x2c, 
  0x96,0x98,0x8a,0x84,0xae,0xa0,0xb2,0xbc,0xe6,0xe8,0xfa,0xf4,0xde,0xd0,0xc2,0xcc, 
  0x41,0x4f,0x5d,0x53,0x79,0x77,0x65,0x6b,0x31,0x3f,0x2d,0x23,0x09,0x07,0x15,0x1b, 
  0xa1,0xaf,0xbd,0xb3,0x99,0x97,0x85,0x8b,0xd1,0xdf,0xcd,0xc3,0xe9,0xe7,0xf5,0xfb, 
  0x9a,0x94,0x86,0x88,0xa2,0xac,0xbe,0xb0,0xea,0xe4,0xf6,0xf8,0xd2,0xdc,0xce,0xc0, 
  0x7a,0x74,0x66,0x68,0x42,0x4c,0x5e,0x50,0x0a,0x04,0x16,0x18,0x32,0x3c,0x2e,0x20, 
  0xec,0xe2,0xf0,0xfe,0xd4,0xda,0xc8,0xc6,0x9c,0x92,0x80,0x8e,0xa4,0xaa,0xb8,0xb6, 
  0x0c,0x02,0x10,0x1e,0x34,0x3a,0x28,0x26,0x7c,0x72,0x60,0x6e,0x44,0x4a,0x58,0x56, 
  0x37,0x39,0x2b,0x25,0x0f,0x01,0x13,0x1d,0x47,0x49,0x5b,0x55,0x7f,0x71,0x63,0x6d, 
  0xd7,0xd9,0xcb,0xc5,0xef,0xe1,0xf3,0xfd,0xa7,0xa9,0xbb,0xb5,0x9f,0x91,0x83,0x8d 
};

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