CRC循环冗余校验
原理：
要计算n位的CRC值，将待CRC的数据左移n位（即在其最右端添加n个0），如果待CRC数据的最高位为0，不进行任何操作，否则将其与事先设定好的除数(divisor)进行异或操作，然后将除数右移一位。重复上述两个操作直到除数到达待CRC数据的右端。举例如下：
11010011101100 000 <--- input left shifted by 3 bits
1011 <--- divisor
01100011101100 000 <--- result
1011 <--- divisor ...
00111011101100 000
1011
00010111101100 000
1011
00000001101100 000
1011
00000000110100 000
1011
00000000011000 000
1011
00000000001110 000
1011
00000000000101 000
101 1
-----------------
00000000000000 100 <---remainder (3 bits)
实现：
理想的循环冗余校验算法应具有以下特征：
- CRC相同的数据多次，每次得到的CRC值应该相同。这也是通信过程中通过CRC校验数据在收发过程中是否出错的基本依据。
- CRC不同的数据得到的CRC值应该不等。(尽管通过估计伪造可能得到相同的CRC值，但要确保这种概率很小)
- 对于32位的CRC来说，它能区分2^32的数据，即长度为2^32的两个数据，只要有任何两位的值不同，它们分别经过CRC后得到的CRC值就不同。
生成CRC的步骤：
- 生成CRC查找表，CRC可通过静态方式从权威机构查询或自己通过动态方式生成。对于CRC32来说，它的CRC查找表包含256个数字。
- 取待CRC的数据的第一个字节，根据该字节数据内容和当前的CRC值生成新的CRC值。
- 取待待CRC的数据的下一个字节，并返回步骤2，直到待CRC的数据的最后一个字节结束。
静态方式的CRC查找表实例如下：
uint32_t s_arrdwCrc32Table[256] =
{
0x00000000, 0x77073096, 0xEE0E612C, 0x990951BA,
0x076DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3,
0x0EDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988,
0x09B64C2B, 0x7EB17CBD, 0xE7B82D07, 0x90BF1D91,
0x1DB71064, 0x6AB020F2, 0xF3B97148, 0x84BE41DE,
0x1ADAD47D, 0x6DDDE4EB, 0xF4D4B551, 0x83D385C7,
0x136C9856, 0x646BA8C0, 0xFD62F97A, 0x8A65C9EC,
0x14015C4F, 0x63066CD9, 0xFA0F3D63, 0x8D080DF5,
0x3B6E20C8, 0x4C69105E, 0xD56041E4, 0xA2677172,
0x3C03E4D1, 0x4B04D447, 0xD20D85FD, 0xA50AB56B,
0x35B5A8FA, 0x42B2986C, 0xDBBBC9D6, 0xACBCF940,
0x32D86CE3, 0x45DF5C75, 0xDCD60DCF, 0xABD13D59,
0x26D930AC, 0x51DE003A, 0xC8D75180, 0xBFD06116,
0x21B4F4B5, 0x56B3C423, 0xCFBA9599, 0xB8BDA50F,
0x2802B89E, 0x5F058808, 0xC60CD9B2, 0xB10BE924,
0x2F6F7C87, 0x58684C11, 0xC1611DAB, 0xB6662D3D,
0x76DC4190, 0x01DB7106, 0x98D220BC, 0xEFD5102A,
0x71B18589, 0x06B6B51F, 0x9FBFE4A5, 0xE8B8D433,
0x7807C9A2, 0x0F00F934, 0x9609A88E, 0xE10E9818,
0x7F6A0DBB, 0x086D3D2D, 0x91646C97, 0xE6635C01,
0x6B6B51F4, 0x1C6C6162, 0x856530D8, 0xF262004E,
0x6C0695ED, 0x1B01A57B, 0x8208F4C1, 0xF50FC457,
0x65B0D9C6, 0x12B7E950, 0x8BBEB8EA, 0xFCB9887C,
0x62DD1DDF, 0x15DA2D49, 0x8CD37CF3, 0xFBD44C65,
0x4DB26158, 0x3AB551CE, 0xA3BC0074, 0xD4BB30E2,
0x4ADFA541, 0x3DD895D7, 0xA4D1C46D, 0xD3D6F4FB,
0x4369E96A, 0x346ED9FC, 0xAD678846, 0xDA60B8D0,
0x44042D73, 0x33031DE5, 0xAA0A4C5F, 0xDD0D7CC9,
0x5005713C, 0x270241AA, 0xBE0B1010, 0xC90C2086,
0x5768B525, 0x206F85B3, 0xB966D409, 0xCE61E49F,
0x5EDEF90E, 0x29D9C998, 0xB0D09822, 0xC7D7A8B4,
0x59B33D17, 0x2EB40D81, 0xB7BD5C3B, 0xC0BA6CAD,
0xEDB88320, 0x9ABFB3B6, 0x03B6E20C, 0x74B1D29A,
0xEAD54739, 0x9DD277AF, 0x04DB2615, 0x73DC1683,
0xE3630B12, 0x94643B84, 0x0D6D6A3E, 0x7A6A5AA8,
0xE40ECF0B, 0x9309FF9D, 0x0A00AE27, 0x7D079EB1,
0xF00F9344, 0x8708A3D2, 0x1E01F268, 0x6906C2FE,
0xF762575D, 0x806567CB, 0x196C3671, 0x6E6B06E7,
0xFED41B76, 0x89D32BE0, 0x10DA7A5A, 0x67DD4ACC,
0xF9B9DF6F, 0x8EBEEFF9, 0x17B7BE43, 0x60B08ED5,
0xD6D6A3E8, 0xA1D1937E, 0x38D8C2C4, 0x4FDFF252,
0xD1BB67F1, 0xA6BC5767, 0x3FB506DD, 0x48B2364B,
0xD80D2BDA, 0xAF0A1B4C, 0x36034AF6, 0x41047A60,
0xDF60EFC3, 0xA867DF55, 0x316E8EEF, 0x4669BE79,
0xCB61B38C, 0xBC66831A, 0x256FD2A0, 0x5268E236,
0xCC0C7795, 0xBB0B4703, 0x220216B9, 0x5505262F,
0xC5BA3BBE, 0xB2BD0B28, 0x2BB45A92, 0x5CB36A04,
0xC2D7FFA7, 0xB5D0CF31, 0x2CD99E8B, 0x5BDEAE1D,
0x9B64C2B0, 0xEC63F226, 0x756AA39C, 0x026D930A,
0x9C0906A9, 0xEB0E363F, 0x72076785, 0x05005713,
0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0x0CB61B38,
0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0x0BDBDF21,
0x86D3D2D4, 0xF1D4E242, 0x68DDB3F8, 0x1FDA836E,
0x81BE16CD, 0xF6B9265B, 0x6FB077E1, 0x18B74777,
0x88085AE6, 0xFF0F6A70, 0x66063BCA, 0x11010B5C,
0x8F659EFF, 0xF862AE69, 0x616BFFD3, 0x166CCF45,
0xA00AE278, 0xD70DD2EE, 0x4E048354, 0x3903B3C2,
0xA7672661, 0xD06016F7, 0x4969474D, 0x3E6E77DB,
0xAED16A4A, 0xD9D65ADC, 0x40DF0B66, 0x37D83BF0,
0xA9BCAE53, 0xDEBB9EC5, 0x47B2CF7F, 0x30B5FFE9,
0xBDBDF21C, 0xCABAC28A, 0x53B39330, 0x24B4A3A6,
0xBAD03605, 0xCDD70693, 0x54DE5729, 0x23D967BF,
0xB3667A2E, 0xC4614AB8, 0x5D681B02, 0x2A6F2B94,
0xB40BBE37, 0xC30C8EA1, 0x5A05DF1B, 0x2D02EF8D,
};
动态方式生成CRC查找表的代码如下：
void GenerateCRCTable(void)
{
// This is the official polynomial used by CRC32 in PKZip.
// Often times the polynomial shown reversed as 0x04C11DB7.
uint32_t dwPolynomial = 0xEDB88320;
int i, j;
uint32_t *m_pdwCrc32Table = new uint32_t[256];
uint32_t dwCrc;
for(i = 0; i < 256; i++)
{
dwCrc = i;
for(j = 8; j > 0; j--)
{
if(dwCrc & 1)
dwCrc = (dwCrc >> 1) ^ dwPolynomial;
else
dwCrc >>= 1;
}
m_pdwCrc32Table[i] = dwCrc;
}
}
对于字符流数据进行校验的代码如下：
void CalcCrc32(const uint8_t byte, uint32_t &dwCrc32)
{
dwCrc32 = ((dwCrc32) >> 8) ^ s_arrdwCrc32Table[(byte) ^ ((dwCrc32) & 0x000000FF)];
}
uint32_t StringCrc32(const char* szString, uint32_t &dwCrc32)
{
_ASSERTE(szString);
uint32_t dwErrorCode = 0; //NO_ERROR
dwCrc32 = 0xFFFFFFFF;
try
{
while(*szString != _T('\0'))
{
CalcCrc32((uint8_t)*szString, dwCrc32);
szString++;
}
}
catch(...)
{
// An unknown exception happened
dwErrorCode = 1; // ERROR_CRC
}
dwCrc32 = ~dwCrc32;
cout << endl << dwCrc32 << endl;
return dwErrorCode;
}
有关循环冗余校验的原理可参考：
http://en.wikipedia.org/wiki/Cyclic_redundancy_check
有关循环冗余校验的代码可参考：