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AES加解密算法Qt实现

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【声明】

(1) 本文源码

在一位未署名网友源码基础上,利用Qt编程,实现了AES加解密算法,并添加了文件加解密功能。在此表示感谢!该源码仅供学习交流,请勿用于商业目的。

(2) 图片及描述

除图1外,图片及部分解析来自http://zh.wikipedia.org/wiki/%E9%AB%98%E7%BA%A7%E5%8A%A0%E5%AF%86%E6%A0%87%E5%87%86。图1为个人劳动成果,请勿盗用此图。

【简介】

AES(Advanced Encryption Standard,高级加密标准),于2001年11月26日发布于FIPS PUB 197,并在2002年5月26日成为有效的标准。2006年,高级加密标准已然成为对称密钥加密中最流行的算法之一。

【算法描述】

AES的区块长度固定为128 比特,密钥长度则可以是128,192或256比特。AES加密过程是在一个4×4的字节矩阵上运作,这个矩阵又称为“体(state)”,其初值就是一个明文区块(矩阵中一个元素大小就是明文区块中的一个Byte)。加密时,各轮AES加密循环(除最后一轮外)均包含4个步骤: 1.AddRoundKey — 矩阵中的每一个字节都与该次轮密钥(round key)做XOR运算;每个子密钥由密钥生成方案产生。 2.SubBytes — 通过一个非线性的替换函数,用查找表的方式把每个字节替换成对应的字节。 3.ShiftRows — 将矩阵中的每个横列进行循环式移位。 4.MixColumns — 为了充分混合矩阵中各个直行的操作。这个步骤使用线性转换来混合每内联的四个字节。 最后一个加密循环中省略MixColumns步骤,而以另一个AddRoundKey取代。 AES算法加解密流程如图1所示:

技术分享

图1 AES加密算法流程图

 

【算法解析】

1 常量定义

S-Box

  1. const unsigned char AES::Sbox[16*16]=  
  2. {// populate the Sbox matrix  
  3.  /* 0     1     2     3     4     5     6     7     8     9     a     b     c     d     e     f */  
  4.  /*0*/  0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5, 0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,  
  5.  /*1*/  0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,  
  6.  /*2*/  0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,  
  7.  /*3*/  0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a, 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,  
  8.  /*4*/  0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,  
  9.  /*5*/  0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b, 0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf,  
  10.  /*6*/  0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8,  
  11.  /*7*/  0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2,  
  12.  /*8*/  0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73,  
  13.  /*9*/  0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb,  
  14.  /*a*/  0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,  
  15.  /*b*/  0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08,  
  16.  /*c*/  0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a,  
  17.  /*d*/  0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e,  
  18.  /*e*/  0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf,  
  19.  /*f*/  0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16  
  20. };  
const unsigned char AES::Sbox[16*16]=
{// populate the Sbox matrix
 /* 0     1     2     3     4     5     6     7     8     9     a     b     c     d     e     f */
 /*0*/  0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5, 0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,
 /*1*/  0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,
 /*2*/  0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,
 /*3*/  0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a, 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,
 /*4*/  0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,
 /*5*/  0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b, 0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf,
 /*6*/  0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8,
 /*7*/  0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2,
 /*8*/  0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73,
 /*9*/  0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb,
 /*a*/  0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,
 /*b*/  0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08,
 /*c*/  0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a,
 /*d*/  0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e,
 /*e*/  0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf,
 /*f*/  0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16
};
  1. const unsigned char AES::iSbox[16*16]=  
  2. {  
  3.     // populate the iSbox matrix  
  4.     /* 0     1     2     3     4     5     6     7     8     9     a     b     c     d     e     f */  
  5.     /*0*/  0x52, 0x09, 0x6a, 0xd5, 0x30, 0x36, 0xa5, 0x38, 0xbf, 0x40, 0xa3, 0x9e, 0x81, 0xf3, 0xd7, 0xfb,  
  6.     /*1*/  0x7c, 0xe3, 0x39, 0x82, 0x9b, 0x2f, 0xff, 0x87, 0x34, 0x8e, 0x43, 0x44, 0xc4, 0xde, 0xe9, 0xcb,  
  7.     /*2*/  0x54, 0x7b, 0x94, 0x32, 0xa6, 0xc2, 0x23, 0x3d, 0xee, 0x4c, 0x95, 0x0b, 0x42, 0xfa, 0xc3, 0x4e,  
  8.     /*3*/  0x08, 0x2e, 0xa1, 0x66, 0x28, 0xd9, 0x24, 0xb2, 0x76, 0x5b, 0xa2, 0x49, 0x6d, 0x8b, 0xd1, 0x25,  
  9.     /*4*/  0x72, 0xf8, 0xf6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xd4, 0xa4, 0x5c, 0xcc, 0x5d, 0x65, 0xb6, 0x92,  
  10.     /*5*/  0x6c, 0x70, 0x48, 0x50, 0xfd, 0xed, 0xb9, 0xda, 0x5e, 0x15, 0x46, 0x57, 0xa7, 0x8d, 0x9d, 0x84,  
  11.     /*6*/  0x90, 0xd8, 0xab, 0x00, 0x8c, 0xbc, 0xd3, 0x0a, 0xf7, 0xe4, 0x58, 0x05, 0xb8, 0xb3, 0x45, 0x06,  
  12.     /*7*/  0xd0, 0x2c, 0x1e, 0x8f, 0xca, 0x3f, 0x0f, 0x02, 0xc1, 0xaf, 0xbd, 0x03, 0x01, 0x13, 0x8a, 0x6b,  
  13.     /*8*/  0x3a, 0x91, 0x11, 0x41, 0x4f, 0x67, 0xdc, 0xea, 0x97, 0xf2, 0xcf, 0xce, 0xf0, 0xb4, 0xe6, 0x73,  
  14.     /*9*/  0x96, 0xac, 0x74, 0x22, 0xe7, 0xad, 0x35, 0x85, 0xe2, 0xf9, 0x37, 0xe8, 0x1c, 0x75, 0xdf, 0x6e,  
  15.     /*a*/  0x47, 0xf1, 0x1a, 0x71, 0x1d, 0x29, 0xc5, 0x89, 0x6f, 0xb7, 0x62, 0x0e, 0xaa, 0x18, 0xbe, 0x1b,  
  16.     /*b*/  0xfc, 0x56, 0x3e, 0x4b, 0xc6, 0xd2, 0x79, 0x20, 0x9a, 0xdb, 0xc0, 0xfe, 0x78, 0xcd, 0x5a, 0xf4,  
  17.     /*c*/  0x1f, 0xdd, 0xa8, 0x33, 0x88, 0x07, 0xc7, 0x31, 0xb1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xec, 0x5f,  
  18.     /*d*/  0x60, 0x51, 0x7f, 0xa9, 0x19, 0xb5, 0x4a, 0x0d, 0x2d, 0xe5, 0x7a, 0x9f, 0x93, 0xc9, 0x9c, 0xef,  
  19.     /*e*/  0xa0, 0xe0, 0x3b, 0x4d, 0xae, 0x2a, 0xf5, 0xb0, 0xc8, 0xeb, 0xbb, 0x3c, 0x83, 0x53, 0x99, 0x61,  
  20.     /*f*/  0x17, 0x2b, 0x04, 0x7e, 0xba, 0x77, 0xd6, 0x26, 0xe1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0c, 0x7d  
  21. };  
const unsigned char AES::iSbox[16*16]=
{
    // populate the iSbox matrix
    /* 0     1     2     3     4     5     6     7     8     9     a     b     c     d     e     f */
    /*0*/  0x52, 0x09, 0x6a, 0xd5, 0x30, 0x36, 0xa5, 0x38, 0xbf, 0x40, 0xa3, 0x9e, 0x81, 0xf3, 0xd7, 0xfb,
    /*1*/  0x7c, 0xe3, 0x39, 0x82, 0x9b, 0x2f, 0xff, 0x87, 0x34, 0x8e, 0x43, 0x44, 0xc4, 0xde, 0xe9, 0xcb,
    /*2*/  0x54, 0x7b, 0x94, 0x32, 0xa6, 0xc2, 0x23, 0x3d, 0xee, 0x4c, 0x95, 0x0b, 0x42, 0xfa, 0xc3, 0x4e,
    /*3*/  0x08, 0x2e, 0xa1, 0x66, 0x28, 0xd9, 0x24, 0xb2, 0x76, 0x5b, 0xa2, 0x49, 0x6d, 0x8b, 0xd1, 0x25,
    /*4*/  0x72, 0xf8, 0xf6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xd4, 0xa4, 0x5c, 0xcc, 0x5d, 0x65, 0xb6, 0x92,
    /*5*/  0x6c, 0x70, 0x48, 0x50, 0xfd, 0xed, 0xb9, 0xda, 0x5e, 0x15, 0x46, 0x57, 0xa7, 0x8d, 0x9d, 0x84,
    /*6*/  0x90, 0xd8, 0xab, 0x00, 0x8c, 0xbc, 0xd3, 0x0a, 0xf7, 0xe4, 0x58, 0x05, 0xb8, 0xb3, 0x45, 0x06,
    /*7*/  0xd0, 0x2c, 0x1e, 0x8f, 0xca, 0x3f, 0x0f, 0x02, 0xc1, 0xaf, 0xbd, 0x03, 0x01, 0x13, 0x8a, 0x6b,
    /*8*/  0x3a, 0x91, 0x11, 0x41, 0x4f, 0x67, 0xdc, 0xea, 0x97, 0xf2, 0xcf, 0xce, 0xf0, 0xb4, 0xe6, 0x73,
    /*9*/  0x96, 0xac, 0x74, 0x22, 0xe7, 0xad, 0x35, 0x85, 0xe2, 0xf9, 0x37, 0xe8, 0x1c, 0x75, 0xdf, 0x6e,
    /*a*/  0x47, 0xf1, 0x1a, 0x71, 0x1d, 0x29, 0xc5, 0x89, 0x6f, 0xb7, 0x62, 0x0e, 0xaa, 0x18, 0xbe, 0x1b,
    /*b*/  0xfc, 0x56, 0x3e, 0x4b, 0xc6, 0xd2, 0x79, 0x20, 0x9a, 0xdb, 0xc0, 0xfe, 0x78, 0xcd, 0x5a, 0xf4,
    /*c*/  0x1f, 0xdd, 0xa8, 0x33, 0x88, 0x07, 0xc7, 0x31, 0xb1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xec, 0x5f,
    /*d*/  0x60, 0x51, 0x7f, 0xa9, 0x19, 0xb5, 0x4a, 0x0d, 0x2d, 0xe5, 0x7a, 0x9f, 0x93, 0xc9, 0x9c, 0xef,
    /*e*/  0xa0, 0xe0, 0x3b, 0x4d, 0xae, 0x2a, 0xf5, 0xb0, 0xc8, 0xeb, 0xbb, 0x3c, 0x83, 0x53, 0x99, 0x61,
    /*f*/  0x17, 0x2b, 0x04, 0x7e, 0xba, 0x77, 0xd6, 0x26, 0xe1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0c, 0x7d
};

Rcon

  1. const unsigned char AES::Rcon[11*4]=  
  2. {  
  3.     0x00, 0x00, 0x00, 0x00,  
  4.     0x01, 0x00, 0x00, 0x00,  
  5.     0x02, 0x00, 0x00, 0x00,  
  6.     0x04, 0x00, 0x00, 0x00,  
  7.     0x08, 0x00, 0x00, 0x00,  
  8.     0x10, 0x00, 0x00, 0x00,  
  9.     0x20, 0x00, 0x00, 0x00,  
  10.     0x40, 0x00, 0x00, 0x00,  
  11.     0x80, 0x00, 0x00, 0x00,  
  12.     0x1b, 0x00, 0x00, 0x00,  
  13.     0x36, 0x00, 0x00, 0x00  
  14. };  
const unsigned char AES::Rcon[11*4]=
{
    0x00, 0x00, 0x00, 0x00,
    0x01, 0x00, 0x00, 0x00,
    0x02, 0x00, 0x00, 0x00,
    0x04, 0x00, 0x00, 0x00,
    0x08, 0x00, 0x00, 0x00,
    0x10, 0x00, 0x00, 0x00,
    0x20, 0x00, 0x00, 0x00,
    0x40, 0x00, 0x00, 0x00,
    0x80, 0x00, 0x00, 0x00,
    0x1b, 0x00, 0x00, 0x00,
    0x36, 0x00, 0x00, 0x00
};

2 密钥扩展(Expand Key) AES算法利用外部输入密钥Key(又称为基密钥,密钥串的字数为Nk),通过密钥扩展可得到共4(Nk+1)字的扩展密钥w[4× (Nr+1)],其中Nr为数据分组密钥的轮数。密钥扩展主要包括3个步骤: (1) 位置变换RotWord() 把一个4字节的基密钥序列[a0,a1,a2,a3],左移一个字节变为[a1,a2,a3,a0]。

  1. void AES::RotWord(unsigned char * word,unsigned char *result)  
  2. {  
  3.     result[0] = word[1];  
  4.     result[1] = word[2];  
  5.     result[2] = word[3];  
  6.     result[3] = word[0];  
  7. }  
void AES::RotWord(unsigned char * word,unsigned char *result)
{
    result[0] = word[1];
    result[1] = word[2];
    result[2] = word[3];
    result[3] = word[0];
}

(2) SubWord() 对一个4字节的输入字[a0,a1,a2,a3],每一个字节进行S盒变换。

  1. void AES::SubWord(unsigned char * word,unsigned char* result)  
  2. {  
  3.     result[0] =  Sbox[ 16*(word[0] >> 4)+ (word[0] & 0x0f) ];  
  4.     result[1] =  Sbox[ 16*(word[1] >> 4)+ (word[1] & 0x0f) ];  
  5.     result[2] =  Sbox[ 16*(word[2] >> 4)+ (word[2] & 0x0f) ];  
  6.     result[3] =  Sbox[ 16*(word[3] >> 4)+ (word[3] & 0x0f) ];  
  7. }  
void AES::SubWord(unsigned char * word,unsigned char* result)
{
    result[0] =  Sbox[ 16*(word[0] >> 4)+ (word[0] & 0x0f) ];
    result[1] =  Sbox[ 16*(word[1] >> 4)+ (word[1] & 0x0f) ];
    result[2] =  Sbox[ 16*(word[2] >> 4)+ (word[2] & 0x0f) ];
    result[3] =  Sbox[ 16*(word[3] >> 4)+ (word[3] & 0x0f) ];
}

 

(3) 变换Rcon[] Rcon[i]表示32比特字符串[xi-1,00,00,00]。

  1. temp[0] = (byte)( (int)temp[0] ^ (int) Rcon[4*(row/Nk)+0] );  
  2. temp[1] = (byte)( (int)temp[1] ^ (int) Rcon[4*(row/Nk)+1] );  
  3. temp[2] = (byte)( (int)temp[2] ^ (int) Rcon[4*(row/Nk)+2] );  
  4. temp[3] = (byte)( (int)temp[3] ^ (int) Rcon[4*(row/Nk)+3] );  
temp[0] = (byte)( (int)temp[0] ^ (int) Rcon[4*(row/Nk)+0] );
temp[1] = (byte)( (int)temp[1] ^ (int) Rcon[4*(row/Nk)+1] );
temp[2] = (byte)( (int)temp[2] ^ (int) Rcon[4*(row/Nk)+2] );
temp[3] = (byte)( (int)temp[3] ^ (int) Rcon[4*(row/Nk)+3] );

 

扩展密钥的前Nk个字就是基密钥Key;以后的字w[i]等于它前一个字w[i-1]与前第Nk个字w[i-Nk]的异或,即w[i]=w[i-1] XOR w[i-Nk]。但如果i是Nk的倍数,则w[i]=w[i-Nk] XOR SubWord(RotWord(w[i-1])) XOR Rcon[i/Nk]。

  1. void AES::KeyExpansion()  
  2. {  
  3.     unsigned char result[4],result2[4];  
  4.     memset(w,0,16*15);//没有根据key的位数进行开辟空间,直接开辟了最大空间  
  5.     int row;  
  6.     for (row = 0; row Nk; row++)//Nk=4,6,8得到初始密码  
  7.     {  
  8.         w[4*row+0] =  key[4*row];  
  9.         w[4*row+1] =  key[4*row+1];  
  10.         w[4*row+2] =  key[4*row+2];  
  11.         w[4*row+3] =  key[4*row+3];  
  12.     }  
  13.     unsigned char temp[4];  
  14.     for (row = Nk; row Nb * (Nr+1); row++)//产生密匙顺序表  
  15.     {  
  16.         temp[0] =  w[4*(row-1)+0];  
  17.         temp[1] =  w[4*(row-1)+1];  
  18.         temp[2] =  w[4*(row-1)+2];  
  19.         temp[3] =  w[4*(row-1)+3];  
  20.         if (row % Nk == 0)  
  21.         {  
  22.             RotWord(temp,result);  
  23.             SubWord(result,result2);  
  24.             memcpy(temp,result2,4);//  
  25.             //RotWord 例程非常简单,它接受 4 字节的数组并将它们向左旋转位移 1 位。  
  26.             //因为轮回次序表 w[] 有四列,所以 RotWord 会将一行 w[] 向左旋转位移.  
  27.             //SubWord 例程使用置换表 Sbox,针对密钥次序表 w[] 的给定行执行逐字节置换。  
  28.             temp[0] = (byte)( (int)temp[0] ^ (int) Rcon[4*(row/Nk)+0] );  
  29.             temp[1] = (byte)( (int)temp[1] ^ (int) Rcon[4*(row/Nk)+1] );  
  30.             temp[2] = (byte)( (int)temp[2] ^ (int) Rcon[4*(row/Nk)+2] );  
  31.             temp[3] = (byte)( (int)temp[3] ^ (int) Rcon[4*(row/Nk)+3] );  
  32.         }  
  33.         else if ( Nk > 6 && (row % Nk == 4) )  
  34.         {  
  35.             SubWord(temp,result);  
  36.             memcpy(temp,result,4);  
  37.         }  
  38.         // w[row] = w[row-Nk] xor temp  
  39.         w[4*row+0] = (byte) ( (int) w[4*(row-Nk)+0] ^ (int)temp[0] );  
  40.         w[4*row+1] = (byte) ( (int) w[4*(row-Nk)+1] ^ (int)temp[1] );  
  41.         w[4*row+2] = (byte) ( (int) w[4*(row-Nk)+2] ^ (int)temp[2] );  
  42.         w[4*row+3] = (byte) ( (int) w[4*(row-Nk)+3] ^ (int)temp[3] );  
  43.     }  // for loop  
  44. }  // KeyExpansion()  
void AES::KeyExpansion()
{
    unsigned char result[4],result2[4];
    memset(w,0,16*15);//没有根据key的位数进行开辟空间,直接开辟了最大空间
    int row;
    for (row = 0; row < Nk; row++)//Nk=4,6,8得到初始密码
    {
        w[4*row+0] =  key[4*row];
        w[4*row+1] =  key[4*row+1];
        w[4*row+2] =  key[4*row+2];
        w[4*row+3] =  key[4*row+3];
    }
    unsigned char temp[4];
    for (row = Nk; row < Nb * (Nr+1); row++)//产生密匙顺序表
    {
        temp[0] =  w[4*(row-1)+0];
        temp[1] =  w[4*(row-1)+1];
        temp[2] =  w[4*(row-1)+2];
        temp[3] =  w[4*(row-1)+3];
        if (row % Nk == 0)
        {
            RotWord(temp,result);
            SubWord(result,result2);
            memcpy(temp,result2,4);//
            //RotWord 例程非常简单,它接受 4 字节的数组并将它们向左旋转位移 1 位。
            //因为轮回次序表 w[] 有四列,所以 RotWord 会将一行 w[] 向左旋转位移.
            //SubWord 例程使用置换表 Sbox,针对密钥次序表 w[] 的给定行执行逐字节置换。
            temp[0] = (byte)( (int)temp[0] ^ (int) Rcon[4*(row/Nk)+0] );
            temp[1] = (byte)( (int)temp[1] ^ (int) Rcon[4*(row/Nk)+1] );
            temp[2] = (byte)( (int)temp[2] ^ (int) Rcon[4*(row/Nk)+2] );
            temp[3] = (byte)( (int)temp[3] ^ (int) Rcon[4*(row/Nk)+3] );
        }
        else if ( Nk > 6 && (row % Nk == 4) )
        {
            SubWord(temp,result);
            memcpy(temp,result,4);
        }
        // w[row] = w[row-Nk] xor temp
        w[4*row+0] = (byte) ( (int) w[4*(row-Nk)+0] ^ (int)temp[0] );
        w[4*row+1] = (byte) ( (int) w[4*(row-Nk)+1] ^ (int)temp[1] );
        w[4*row+2] = (byte) ( (int) w[4*(row-Nk)+2] ^ (int)temp[2] );
        w[4*row+3] = (byte) ( (int) w[4*(row-Nk)+3] ^ (int)temp[3] );
    }  // for loop
}  // KeyExpansion()

3 轮密钥加(Add Round Key) 如图2所示,经过扩展的密钥,根据加密的轮数用相应的扩展密钥的4个数据项和中间状态矩阵上的列进行按位异或:

[s(0,c)’, s(1,c)’, s(2,c)’, s(3,c)’]= [s(0,c), s(1,c), s(2,c), s(3,c)] XOR [W(round×Nb+c)]。

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图2 Add Round Key

  1. void AES::AddRoundKey(int round)  
  2. {  
  3.     int r,c;  
  4.     for (r = 0; r 4; r++)  
  5.     {  
  6.         for (c = 0; c 4; c++)  
  7.         {//w:    4*x+y  
  8.             State[r][c]=(unsigned char)((int)State[r][c]^(int)w[4*((round*4)+c)+r]);  
  9.         }  
  10.     }  
  11. }  // AddRoundKey()  
void AES::AddRoundKey(int round)
{
    int r,c;
    for (r = 0; r < 4; r++)
    {
        for (c = 0; c < 4; c++)
        {//w:    4*x+y
            State[r][c]=(unsigned char)((int)State[r][c]^(int)w[4*((round*4)+c)+r]);
        }
    }
}  // AddRoundKey()

4 字节替代(Substitute Bytes) 如图3所示,从S-Box中找出S[A]=S[x,y]的值,其中A为输入矩阵任一元素。将

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转换为

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图3 Substitute Bytes

 

  1. void AES::SubBytes()  
  2. {  
  3.     int r,c;  
  4.     for (r = 0; r 4; r++)  
  5.     {  
  6.         for (c = 0; c 4; c++)  
  7.         {  
  8.             State[r][c] =  Sbox[ 16*(State[r][c] >> 4)+ ( State[r][c] & 0x0f) ];  
  9.         }  
  10.     }  
  11. }  // SubBytes  
  12.   
  13. void AES::InvSubBytes()  
  14. {  
  15.     int r,c;  
  16.     for (r = 0; r 4; r++)  
  17.     {  
  18.         for (c = 0; c 4; c++)  
  19.         {  
  20.             State[r][c] =  iSbox[ 16*( State[r][c] >> 4)+( State[r][c] & 0x0f) ];  
  21.         }  
  22.     }  
  23. }  // InvSubBytes  
void AES::SubBytes()
{
    int r,c;
    for (r = 0; r < 4; r++)
    {
        for (c = 0; c < 4; c++)
        {
            State[r][c] =  Sbox[ 16*(State[r][c] >> 4)+ ( State[r][c] & 0x0f) ];
        }
    }
}  // SubBytes

void AES::InvSubBytes()
{
    int r,c;
    for (r = 0; r < 4; r++)
    {
        for (c = 0; c < 4; c++)
        {
            State[r][c] =  iSbox[ 16*( State[r][c] >> 4)+( State[r][c] & 0x0f) ];
        }
    }
}  // InvSubBytes

5 行移位(Shift Rows) 如图4所示,将矩阵中的每一个横列进行循环式移位。移位的规则是:第一行维持不变,第二、第三、第四行的每个字节向左循环移位的偏移量分别为1格,2格,3格。

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图4 Shift Rows

  1. void AES::ShiftRows()  
  2. {  
  3.     unsigned char temp[4*4];  
  4.     int r,c;  
  5.     for (r = 0; r 4; r++)  // copy State into temp[]  
  6.     {  
  7.         for (c = 0; c 4; c++)  
  8.         {  
  9.             temp[4*r+c] =  State[r][c];  
  10.         }  
  11.     }  
  12.   
  13.     for (r = 1; r 4; r++)  // shift temp into State  
  14.     {  
  15.         for (c = 0; c 4; c++)  
  16.         {  
  17.             State[r][c] = temp[ 4*r+ (c + r) % Nb ];  
  18.         }  
  19.     }  
  20. }  // ShiftRows()  
  21.   
  22. void AES::InvShiftRows()  
  23. {  
  24.     unsigned char temp[4*4];  
  25.     int r,c;  
  26.     for (r = 0; r 4; r++)  // copy State into temp[]  
  27.     {  
  28.         for (c = 0; c 4; c++)  
  29.         {  
  30.             temp[4*r+c] =  State[r][c];  
  31.         }  
  32.     }  
  33.     for (r = 1; r 4; r++)  // shift temp into State  
  34.     {  
  35.         for (c = 0; c 4; c++)  
  36.         {  
  37.             State[r][ (c + r) % Nb ] = temp[4*r+c];  
  38.         }  
  39.     }  
  40. }  // InvShiftRows()  
void AES::ShiftRows()
{
    unsigned char temp[4*4];
    int r,c;
    for (r = 0; r < 4; r++)  // copy State into temp[]
    {
        for (c = 0; c < 4; c++)
        {
            temp[4*r+c] =  State[r][c];
        }
    }

    for (r = 1; r < 4; r++)  // shift temp into State
    {
        for (c = 0; c < 4; c++)
        {
            State[r][c] = temp[ 4*r+ (c + r) % Nb ];
        }
    }
}  // ShiftRows()

void AES::InvShiftRows()
{
    unsigned char temp[4*4];
    int r,c;
    for (r = 0; r < 4; r++)  // copy State into temp[]
    {
        for (c = 0; c < 4; c++)
        {
            temp[4*r+c] =  State[r][c];
        }
    }
    for (r = 1; r < 4; r++)  // shift temp into State
    {
        for (c = 0; c < 4; c++)
        {
            State[r][ (c + r) % Nb ] = temp[4*r+c];
        }
    }
}  // InvShiftRows()

6 列混淆(Mix Columns) 如图5所示,列变换的中间状态矩阵State如下所示:

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经过上述变换,原来的列被混淆为新列。 技术分享

图5 Mix Column

  1. void AES::MixColumns()  
  2. {  
  3.     unsigned char temp[4*4];  
  4.     int r,c;  
  5.     for (r = 0; r 4; r++)  // copy State into temp[]  
  6.     {  
  7.         for (c = 0; c 4; c++)  
  8.         {  
  9.             temp[4*r+c] =  State[r][c];  
  10.         }  
  11.     }  
  12.     for (c = 0; c 4; c++)  
  13.     {  
  14.         State[0][c] = (unsigned char) ( (int)gfmultby02(temp[0+c]) ^ (int)gfmultby03(temp[4*1+c]) ^  
  15.                                         (int)gfmultby01(temp[4*2+c]) ^ (int)gfmultby01(temp[4*3+c]) );  
  16.         State[1][c] = (unsigned char) ( (int)gfmultby01(temp[0+c]) ^ (int)gfmultby02(temp[4*1+c]) ^  
  17.                                         (int)gfmultby03(temp[4*2+c]) ^ (int)gfmultby01(temp[4*3+c]) );  
  18.         State[2][c] = (unsigned char) ( (int)gfmultby01(temp[0+c]) ^ (int)gfmultby01(temp[4*1+c]) ^  
  19.                                         (int)gfmultby02(temp[4*2+c]) ^ (int)gfmultby03(temp[4*3+c]) );  
  20.         State[3][c] = (unsigned char) ( (int)gfmultby03(temp[0+c]) ^ (int)gfmultby01(temp[4*1+c]) ^  
  21.                                         (int)gfmultby01(temp[4*2+c]) ^ (int)gfmultby02(temp[4*3+c]) );  
  22.     }  
  23. }  // MixColumns  
  24.   
  25. void AES::InvMixColumns()  
  26. {  
  27.     unsigned char temp[4*4];  
  28.     int r,c;  
  29.     for (r = 0; r 4; r++)  // copy State into temp[]  
  30.     {  
  31.         for (c = 0; c 4; c++)  
  32.         {  
  33.             temp[4*r+c] =  State[r][c];  
  34.         }  
  35.     }  
  36.     for (c = 0; c 4; c++)  
  37.     {  
  38.         State[0][c] = (unsigned char) ( (int)gfmultby0e(temp[c]) ^ (int)gfmultby0b(temp[4+c]) ^  
  39.                                         (int)gfmultby0d(temp[4*2+c]) ^ (int)gfmultby09(temp[4*3+c]) );  
  40.         State[1][c] = (unsigned char) ( (int)gfmultby09(temp[c]) ^ (int)gfmultby0e(temp[4+c]) ^  
  41.                                         (int)gfmultby0b(temp[4*2+c]) ^ (int)gfmultby0d(temp[4*3+c]) );  
  42.         State[2][c] = (unsigned char) ( (int)gfmultby0d(temp[c]) ^ (int)gfmultby09(temp[4+c]) ^  
  43.                                         (int)gfmultby0e(temp[4*2+c]) ^ (int)gfmultby0b(temp[4*3+c]) );  
  44.         State[3][c] = (unsigned char) ( (int)gfmultby0b(temp[c]) ^ (int)gfmultby0d(temp[4+c]) ^  
  45.                                         (int)gfmultby09(temp[4*2+c]) ^ (int)gfmultby0e(temp[4*3+c]) );  
  46.     }  
  47. }  // InvMixColumns  
  48.   
  49. unsigned char AES::gfmultby01(unsigned char b)  
  50. {  
  51.     return b;  
  52. }  
  53.   
  54. unsigned char AES::gfmultby02(unsigned char b)  
  55. {  
  56.     if (b 0x80)  
  57.         return (unsigned char)(int)(b <<1);  
  58.     else  
  59.         return (unsigned char)( (int)(b <1) ^ (int)(0x1b) );  
  60. }  
  61.   
  62. unsigned char AES::gfmultby03(unsigned char b)  
  63. {  
  64.     return (unsigned char) ( (int)gfmultby02(b) ^ (int)b );  
  65. }  
  66.   
  67. unsigned char AES::gfmultby09(unsigned char b)  
  68. {  
  69.     return (unsigned char)( (int)gfmultby02(gfmultby02(gfmultby02(b))) ^  
  70.                             (int)b );  
  71. }  
  72.   
  73. unsigned char AES::gfmultby0b(unsigned char b)  
  74. {  
  75.     return (unsigned char)( (int)gfmultby02(gfmultby02(gfmultby02(b))) ^  
  76.                             (int)gfmultby02(b) ^  
  77.                             (int)b );  
  78. }  
  79.   
  80. unsigned char AES::gfmultby0d(unsigned char b)  
  81. {  
  82.     return (unsigned char)( (int)gfmultby02(gfmultby02(gfmultby02(b))) ^  
  83.                             (int)gfmultby02(gfmultby02(b)) ^  
  84.                             (int)(b) );  
  85. }  
  86.   
  87. unsigned char AES::gfmultby0e(unsigned char b)  
  88. {  
  89.     return (unsigned char)( (int)gfmultby02(gfmultby02(gfmultby02(b))) ^  
  90.                             (int)gfmultby02(gfmultby02(b)) ^  
  91.                             (int)gfmultby02(b) );  
  92. }  
void AES::MixColumns()
{
    unsigned char temp[4*4];
    int r,c;
    for (r = 0; r < 4; r++)  // copy State into temp[]
    {
        for (c = 0; c < 4; c++)
        {
            temp[4*r+c] =  State[r][c];
        }
    }
    for (c = 0; c < 4; c++)
    {
        State[0][c] = (unsigned char) ( (int)gfmultby02(temp[0+c]) ^ (int)gfmultby03(temp[4*1+c]) ^
                                        (int)gfmultby01(temp[4*2+c]) ^ (int)gfmultby01(temp[4*3+c]) );
        State[1][c] = (unsigned char) ( (int)gfmultby01(temp[0+c]) ^ (int)gfmultby02(temp[4*1+c]) ^
                                        (int)gfmultby03(temp[4*2+c]) ^ (int)gfmultby01(temp[4*3+c]) );
        State[2][c] = (unsigned char) ( (int)gfmultby01(temp[0+c]) ^ (int)gfmultby01(temp[4*1+c]) ^
                                        (int)gfmultby02(temp[4*2+c]) ^ (int)gfmultby03(temp[4*3+c]) );
        State[3][c] = (unsigned char) ( (int)gfmultby03(temp[0+c]) ^ (int)gfmultby01(temp[4*1+c]) ^
                                        (int)gfmultby01(temp[4*2+c]) ^ (int)gfmultby02(temp[4*3+c]) );
    }
}  // MixColumns

void AES::InvMixColumns()
{
    unsigned char temp[4*4];
    int r,c;
    for (r = 0; r < 4; r++)  // copy State into temp[]
    {
        for (c = 0; c < 4; c++)
        {
            temp[4*r+c] =  State[r][c];
        }
    }
    for (c = 0; c < 4; c++)
    {
        State[0][c] = (unsigned char) ( (int)gfmultby0e(temp[c]) ^ (int)gfmultby0b(temp[4+c]) ^
                                        (int)gfmultby0d(temp[4*2+c]) ^ (int)gfmultby09(temp[4*3+c]) );
        State[1][c] = (unsigned char) ( (int)gfmultby09(temp[c]) ^ (int)gfmultby0e(temp[4+c]) ^
                                        (int)gfmultby0b(temp[4*2+c]) ^ (int)gfmultby0d(temp[4*3+c]) );
        State[2][c] = (unsigned char) ( (int)gfmultby0d(temp[c]) ^ (int)gfmultby09(temp[4+c]) ^
                                        (int)gfmultby0e(temp[4*2+c]) ^ (int)gfmultby0b(temp[4*3+c]) );
        State[3][c] = (unsigned char) ( (int)gfmultby0b(temp[c]) ^ (int)gfmultby0d(temp[4+c]) ^
                                        (int)gfmultby09(temp[4*2+c]) ^ (int)gfmultby0e(temp[4*3+c]) );
    }
}  // InvMixColumns

unsigned char AES::gfmultby01(unsigned char b)
{
    return b;
}

unsigned char AES::gfmultby02(unsigned char b)
{
    if (b < 0x80)
        return (unsigned char)(int)(b <<1);
    else
        return (unsigned char)( (int)(b << 1) ^ (int)(0x1b) );
}

unsigned char AES::gfmultby03(unsigned char b)
{
    return (unsigned char) ( (int)gfmultby02(b) ^ (int)b );
}

unsigned char AES::gfmultby09(unsigned char b)
{
    return (unsigned char)( (int)gfmultby02(gfmultby02(gfmultby02(b))) ^
                            (int)b );
}

unsigned char AES::gfmultby0b(unsigned char b)
{
    return (unsigned char)( (int)gfmultby02(gfmultby02(gfmultby02(b))) ^
                            (int)gfmultby02(b) ^
                            (int)b );
}

unsigned char AES::gfmultby0d(unsigned char b)
{
    return (unsigned char)( (int)gfmultby02(gfmultby02(gfmultby02(b))) ^
                            (int)gfmultby02(gfmultby02(b)) ^
                            (int)(b) );
}

unsigned char AES::gfmultby0e(unsigned char b)
{
    return (unsigned char)( (int)gfmultby02(gfmultby02(gfmultby02(b))) ^
                            (int)gfmultby02(gfmultby02(b)) ^
                            (int)gfmultby02(b) );
}

7 AES加密 加密时,首先进行密钥扩展。密钥扩展的结果是将初始密钥按照一定的移位和置换操作扩展为11组128位的密钥,存储在一个W[44][4]的数组里。将输入的明文,按列顺序组合成4×4的矩阵,直接与第0组密钥W[0,3](即基密钥Key)进行异或,作为轮加密的输入。然后,循环10次进行字节替代(Substitute Bytes)、行位移(Shift Rows)、列混淆(Mix Columns)、轮密钥加运算(Add Round Key)。最后一轮运算不进行列混淆变换。最后,输出128位的密文比特流。

  1. void AES::Cipher(unsigned char* input, unsigned char* output)  // encipher 16-bit input  
  2. {  
  3.     // state = input  
  4.     memset(&State[0][0],0,16);  
  5.     int i;  
  6.     for (i = 0; i < (4 * Nb); i++)//  
  7.     {  
  8.         State[i % 4][ i / 4] = input[i];  
  9.     }  
  10.     AddRoundKey(0);  
  11.     for (int round = 1; round <= (Nr - 1); round++)  // main round loop  
  12.     {  
  13.         SubBytes();  
  14.         ShiftRows();  
  15.         MixColumns();  
  16.         AddRoundKey(round);  
  17.     }  // main round loop  
  18.     SubBytes();  
  19.     ShiftRows();  
  20.     AddRoundKey(Nr);  
  21.     // output = state  
  22.     for (i = 0; i < (4 * Nb); i++)  
  23.     {  
  24.         output[i] =  State[i % 4][ i / 4];  
  25.     }  
  26. }  // Cipher()  
void AES::Cipher(unsigned char* input, unsigned char* output)  // encipher 16-bit input
{
    // state = input
    memset(&State[0][0],0,16);
    int i;
    for (i = 0; i < (4 * Nb); i++)//
    {
        State[i % 4][ i / 4] = input[i];
    }
    AddRoundKey(0);
    for (int round = 1; round <= (Nr - 1); round++)  // main round loop
    {
        SubBytes();
        ShiftRows();
        MixColumns();
        AddRoundKey(round);
    }  // main round loop
    SubBytes();
    ShiftRows();
    AddRoundKey(Nr);
    // output = state
    for (i = 0; i < (4 * Nb); i++)
    {
        output[i] =  State[i % 4][ i / 4];
    }
}  // Cipher()

8 AES解密 解密时,进行加密过程逆运算,除轮密钥加和密钥扩展不变外,其余都需要进行相应的逆变换。当基密钥正确,并且采用正确的解密算法,点击解密,对文件进行正确解密。

  1. void AES::InvCipher(unsigned char * input, unsigned char * output)  // decipher 16-bit input  
  2. {  
  3.     // state = input  
  4.     int i;  
  5.     memset(&State[0][0],0,16);  
  6.     for (i = 0; i < (4 * Nb); i++)  
  7.     {  
  8.         State[i % 4][ i / 4] = input[i];  
  9.     }  
  10.     AddRoundKey(Nr);  
  11.     for (int round = Nr-1; round >= 1; round--)  // main round loop  
  12.     {  
  13.         InvShiftRows();  
  14.         InvSubBytes();  
  15.         AddRoundKey(round);  
  16.         InvMixColumns();  
  17.     }  // end main round loop for InvCipher  
  18.     InvShiftRows();  
  19.     InvSubBytes();  
  20.     AddRoundKey(0);  
  21.     // output = state  
  22.     for (i = 0; i < (4 * Nb); i++)  
  23.     {  
  24.         output[i] =  State[i % 4][ i / 4];  
  25.     }  
  26. }  // InvCipher()  
void AES::InvCipher(unsigned char * input, unsigned char * output)  // decipher 16-bit input
{
    // state = input
    int i;
    memset(&State[0][0],0,16);
    for (i = 0; i < (4 * Nb); i++)
    {
        State[i % 4][ i / 4] = input[i];
    }
    AddRoundKey(Nr);
    for (int round = Nr-1; round >= 1; round--)  // main round loop
    {
        InvShiftRows();
        InvSubBytes();
        AddRoundKey(round);
        InvMixColumns();
    }  // end main round loop for InvCipher
    InvShiftRows();
    InvSubBytes();
    AddRoundKey(0);
    // output = state
    for (i = 0; i < (4 * Nb); i++)
    {
        output[i] =  State[i % 4][ i / 4];
    }
}  // InvCipher()

【算法举例】

  1. void print(const char *key, unsigned char* value)  
  2. {  
  3.     int i;  
  4.     printf("%s:\n", key);  
  5.     for(i=0; i<16; i++)  
  6.     {  
  7.         printf("%s%#x ", value[i]>15 ? "" : "0", value[i]);  
  8.     }  
  9.     printf("\n");  
  10. }  
  11.   
  12. unsigned char input[] =  
  13. {  
  14.         0x32, 0x43, 0xf6, 0xa8,  
  15.         0x88, 0x5a, 0x30, 0x8d,  
  16.         0x31, 0x31, 0x98, 0xa2,  
  17.         0xe0, 0x37, 0x07, 0x34  
  18. };  
  19. unsigned char output[16] = { 0 };  
  20. unsigned char key[] =  
  21. {  
  22.         0x2b, 0x7e, 0x15, 0x16,  
  23.         0x28, 0xae, 0xd2, 0xa6,  
  24.         0xab, 0xf7, 0x15, 0x88,  
  25.         0x09, 0xcf, 0x4f, 0x3c  
  26. };  
  27.   
  28. AES aes(Bits128,key);  
  29.   
  30. //-1-  
  31. print("Input", input);  
  32. aes.Cipher(input,output);  
  33. print("After Cipher", output);  
  34. aes.InvCipher(output,input);  
  35. print("After InvCipher", input);  
void print(const char *key, unsigned char* value)
{
    int i;
    printf("%s:\n", key);
    for(i=0; i<16; i++)
    {
        printf("%s%#x ", value[i]>15 ? "" : "0", value[i]);
    }
    printf("\n");
}

unsigned char input[] =
{
        0x32, 0x43, 0xf6, 0xa8,
        0x88, 0x5a, 0x30, 0x8d,
        0x31, 0x31, 0x98, 0xa2,
        0xe0, 0x37, 0x07, 0x34
};
unsigned char output[16] = { 0 };
unsigned char key[] =
{
        0x2b, 0x7e, 0x15, 0x16,
        0x28, 0xae, 0xd2, 0xa6,
        0xab, 0xf7, 0x15, 0x88,
        0x09, 0xcf, 0x4f, 0x3c
};

AES aes(Bits128,key);

//-1-
print("Input", input);
aes.Cipher(input,output);
print("After Cipher", output);
aes.InvCipher(output,input);
print("After InvCipher", input);

 

【文件加密】

本文仅分析AES算法本身,不就AES文件加密进行分析。源码中的文件加密功能仅供测试用。实际使用时,文件加密可使用多线程,要考虑加锁、明文字节填充等问题。

 

【源码下载】

http://download.csdn.net/detail/tandesir/4613524

 

【参考文献】

1 http://zh.wikipedia.org/wiki/%E9%AB%98%E7%BA%A7%E5%8A%A0%E5%AF%86%E6%A0%87%E5%87%86

AES加解密算法Qt实现

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原文地址:http://www.cnblogs.com/JeffreyCheung/p/5764349.html

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