参数模型
CRC即循环冗余校验码（Cyclic Redundancy Check）：是数据通信领域中最常用的一种查错校验码，其特征是信息字段和校验字段的长度可以任意选定。循环冗余检查（CRC）是一种数据传输检错功能，对数据进行多项式计算，并将得到的结果附在帧的后面，接收设备也执行类似的算法，以保证数据传输的正确性和完整性。
CRC算法参数模型解释：
- NAME：参数模型名称。
- WIDTH：宽度，即CRC比特数。
- POLY：生成项的简写，以16进制表示。例如：CRC-32即是0x04C11DB7，忽略了最高位的"1"，即完整的生成项是0x104C11DB7。
- INIT：这是算法开始时寄存器（crc）的初始化预置值，十六进制表示。
- REFIN：待测数据的每个字节是否按位反转，True或False。
- REFOUT：在计算后之后，异或输出之前，整个数据是否按位反转，True或False。
- XOROUT：计算结果与此参数异或后得到最终的CRC值。
常见CRC参数模型如下：
| CRC算法名称 | 多项式公式 | 宽度 | 多项式 | 初始值 | 结果异或值 | 输入反转 | 输出反转 |
|---|---|---|---|---|---|---|---|
| CRC-4/ITU | x4 + x + 1 | 4 | 03 | 00 | 00 | true | true |
| CRC-5/EPC | x5 + x3 + 1 | 5 | 09 | 09 | 00 | false | false |
| CRC-5/ITU | x5 + x4 + x2 + 1 | 5 | 15 | 00 | 00 | true | true |
| CRC-5/USB | x5 + x2 + 1 | 5 | 05 | 1F | 1F | true | true |
| CRC-6/ITU | x6 + x + 1 | 6 | 03 | 00 | 00 | true | true |
| CRC-7/MMC | x7 + x3 + 1 | 7 | 09 | 00 | 00 | false | false |
| CRC-8 | x8 + x2 + x + 1 | 8 | 07 | 00 | 00 | false | false |
| CRC-8/ITU | x8 + x2 + x + 1 | 8 | 07 | 00 | 55 | false | false |
| CRC-8/ROHC | x8 + x2 + x + 1 | 8 | 07 | FF | 00 | true | true |
| CRC-8/MAXIM | x8 + x5 + x4 + 1 | 8 | 31 | 00 | 00 | true | true |
| CRC-16/IBM | x16 + x15 + x2 + 1 | 16 | 8005 | 0000 | 0000 | true | true |
| CRC-16/MAXIM | x16 + x15 + x2 + 1 | 16 | 8005 | 0000 | FFFF | true | true |
| CRC-16/USB | x16 + x15 + x2 + 1 | 16 | 8005 | FFFF | FFFF | true | true |
| CRC-16/MODBUS | x16 + x15 + x2 + 1 | 16 | 8005 | FFFF | 0000 | true | true |
| CRC-16/CCITT | x16 + x12 + x5 + 1 | 16 | 1021 | 0000 | 0000 | true | true |
| CRC-16/CCITT-FALSE | x16 + x12 + x5 + 1 | 16 | 1021 | FFFF | 0000 | false | false |
| CRC-16/X25 | x16 + x12 + x5 + 1 | 16 | 1021 | FFFF | FFFF | true | true |
| CRC-16/XMODEM | x16 + x12 + x5 + 1 | 16 | 1021 | 0000 | 0000 | false | false |
| CRC-16/DNP | x16 + x13 + x12 + x11 + x10 + x8 + x6 + x5 + x2 + 1 | 16 | 3D65 | 0000 | FFFF | true | true |
| CRC-32 | x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1 | 32 | 04C11DB7 | FFFFFFFF | FFFFFFFF | true | true |
| CRC-32/MPEG-2 | x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1 | 32 | 04C11DB7 | FFFFFFFF | 00000000 | false | false |
注：CRC算法选取的多项式会影响算法本身检查错误的能力，运用时不可随意定义多项式，选择一个通用的CRC多项式即可。
算法实现
此处只给出CRC-32、CRC-32/MPEG-2两种算法的查表法代码实现，两种的多项式一样但参数模型有很大区别。
通过比较两种算法的实现代码可以很容易的写出其它参数模型CRC算法的查表法实现，再利用表生成算法生成对应的表即可。
CRC-32
代码如下：
public static class Crc32{ // CRC计算表（取决于多项式和输入是否反转） static readonly uint[] crcTable = new uint[256] { 0x00000000u, 0x77073096u, 0xee0e612cu, 0x990951bau, 0x076dc419u, 0x706af48fu, 0xe963a535u, 0x9e6495a3u, 0x0edb8832u, 0x79dcb8a4u, 0xe0d5e91eu, 0x97d2d988u, 0x09b64c2bu, 0x7eb17cbdu, 0xe7b82d07u, 0x90bf1d91u, 0x1db71064u, 0x6ab020f2u, 0xf3b97148u, 0x84be41deu, 0x1adad47du, 0x6ddde4ebu, 0xf4d4b551u, 0x83d385c7u, 0x136c9856u, 0x646ba8c0u, 0xfd62f97au, 0x8a65c9ecu, 0x14015c4fu, 0x63066cd9u, 0xfa0f3d63u, 0x8d080df5u, 0x3b6e20c8u, 0x4c69105eu, 0xd56041e4u, 0xa2677172u, 0x3c03e4d1u, 0x4b04d447u, 0xd20d85fdu, 0xa50ab56bu, 0x35b5a8fau, 0x42b2986cu, 0xdbbbc9d6u, 0xacbcf940u, 0x32d86ce3u, 0x45df5c75u, 0xdcd60dcfu, 0xabd13d59u, 0x26d930acu, 0x51de003au, 0xc8d75180u, 0xbfd06116u, 0x21b4f4b5u, 0x56b3c423u, 0xcfba9599u, 0xb8bda50fu, 0x2802b89eu, 0x5f058808u, 0xc60cd9b2u, 0xb10be924u, 0x2f6f7c87u, 0x58684c11u, 0xc1611dabu, 0xb6662d3du, 0x76dc4190u, 0x01db7106u, 0x98d220bcu, 0xefd5102au, 0x71b18589u, 0x06b6b51fu, 0x9fbfe4a5u, 0xe8b8d433u, 0x7807c9a2u, 0x0f00f934u, 0x9609a88eu, 0xe10e9818u, 0x7f6a0dbbu, 0x086d3d2du, 0x91646c97u, 0xe6635c01u, 0x6b6b51f4u, 0x1c6c6162u, 0x856530d8u, 0xf262004eu, 0x6c0695edu, 0x1b01a57bu, 0x8208f4c1u, 0xf50fc457u, 0x65b0d9c6u, 0x12b7e950u, 0x8bbeb8eau, 0xfcb9887cu, 0x62dd1ddfu, 0x15da2d49u, 0x8cd37cf3u, 0xfbd44c65u, 0x4db26158u, 0x3ab551ceu, 0xa3bc0074u, 0xd4bb30e2u, 0x4adfa541u, 0x3dd895d7u, 0xa4d1c46du, 0xd3d6f4fbu, 0x4369e96au, 0x346ed9fcu, 0xad678846u, 0xda60b8d0u, 0x44042d73u, 0x33031de5u, 0xaa0a4c5fu, 0xdd0d7cc9u, 0x5005713cu, 0x270241aau, 0xbe0b1010u, 0xc90c2086u, 0x5768b525u, 0x206f85b3u, 0xb966d409u, 0xce61e49fu, 0x5edef90eu, 0x29d9c998u, 0xb0d09822u, 0xc7d7a8b4u, 0x59b33d17u, 0x2eb40d81u, 0xb7bd5c3bu, 0xc0ba6cadu, 0xedb88320u, 0x9abfb3b6u, 0x03b6e20cu, 0x74b1d29au, 0xead54739u, 0x9dd277afu, 0x04db2615u, 0x73dc1683u, 0xe3630b12u, 0x94643b84u, 0x0d6d6a3eu, 0x7a6a5aa8u, 0xe40ecf0bu, 0x9309ff9du, 0x0a00ae27u, 0x7d079eb1u, 0xf00f9344u, 0x8708a3d2u, 0x1e01f268u, 0x6906c2feu, 0xf762575du, 0x806567cbu, 0x196c3671u, 0x6e6b06e7u, 0xfed41b76u, 0x89d32be0u, 0x10da7a5au, 0x67dd4accu, 0xf9b9df6fu, 0x8ebeeff9u, 0x17b7be43u, 0x60b08ed5u, 0xd6d6a3e8u, 0xa1d1937eu, 0x38d8c2c4u, 0x4fdff252u, 0xd1bb67f1u, 0xa6bc5767u, 0x3fb506ddu, 0x48b2364bu, 0xd80d2bdau, 0xaf0a1b4cu, 0x36034af6u, 0x41047a60u, 0xdf60efc3u, 0xa867df55u, 0x316e8eefu, 0x4669be79u, 0xcb61b38cu, 0xbc66831au, 0x256fd2a0u, 0x5268e236u, 0xcc0c7795u, 0xbb0b4703u, 0x220216b9u, 0x5505262fu, 0xc5ba3bbeu, 0xb2bd0b28u, 0x2bb45a92u, 0x5cb36a04u, 0xc2d7ffa7u, 0xb5d0cf31u, 0x2cd99e8bu, 0x5bdeae1du, 0x9b64c2b0u, 0xec63f226u, 0x756aa39cu, 0x026d930au, 0x9c0906a9u, 0xeb0e363fu, 0x72076785u, 0x05005713u, 0x95bf4a82u, 0xe2b87a14u, 0x7bb12baeu, 0x0cb61b38u, 0x92d28e9bu, 0xe5d5be0du, 0x7cdcefb7u, 0x0bdbdf21u, 0x86d3d2d4u, 0xf1d4e242u, 0x68ddb3f8u, 0x1fda836eu, 0x81be16cdu, 0xf6b9265bu, 0x6fb077e1u, 0x18b74777u, 0x88085ae6u, 0xff0f6a70u, 0x66063bcau, 0x11010b5cu, 0x8f659effu, 0xf862ae69u, 0x616bffd3u, 0x166ccf45u, 0xa00ae278u, 0xd70dd2eeu, 0x4e048354u, 0x3903b3c2u, 0xa7672661u, 0xd06016f7u, 0x4969474du, 0x3e6e77dbu, 0xaed16a4au, 0xd9d65adcu, 0x40df0b66u, 0x37d83bf0u, 0xa9bcae53u, 0xdebb9ec5u, 0x47b2cf7fu, 0x30b5ffe9u, 0xbdbdf21cu, 0xcabac28au, 0x53b39330u, 0x24b4a3a6u, 0xbad03605u, 0xcdd70693u, 0x54de5729u, 0x23d967bfu, 0xb3667a2eu, 0xc4614ab8u, 0x5d681b02u, 0x2a6f2b94u, 0xb40bbe37u, 0xc30c8ea1u, 0x5a05df1bu, 0x2d02ef8du }; public static readonly string Name = "CRC-32"; public static uint Compute(byte[] buffer) { if (buffer == null) { throw new ArgumentException("参数异常，请检查调用方"); } return Compute(buffer, 0, buffer.Length); } public static uint Compute(byte[] buffer, int offset, int length) { if(!((buffer != null) && (offset >= 0) && (length >= 0) && (offset <= buffer.Length - length))) { throw new ArgumentException("参数异常，请检查调用方"); } //寄存器初始值 uint crc32= 0xffffffffU; while (--length >= 0) { //查表运算（取决于宽度和输出是否反转） crc32 = crcTable[(crc32 ^ buffer[offset++]) & 0xFF] ^ (crc32 >> 8); } //结果异或 crc32 ^= 0xffffffffU; return crc32; }}测试如下：
byte[] data = new byte[] { 0x01, 0x02 , 0x03, 0x04 };uint crc32 = Crc32.Compute(data);byte[] crc32Ary = BitConverter.GetBytes(crc32);string crc32Str = "";for (int i = crc32Ary.Length-1; i >=0; i--){ crc32Str += crc32Ary[i].ToString("X2");}Console.WriteLine(crc32Str);Console.ReadLine();测试结果：
B63CFBCDCRC-32/MPEG-2
代码如下：
public static class Crc32{ // CRC计算表（取决于多项式和输入是否反） static readonly uint[] crcTable = new uint[256] { 0x00000000u,0x4c11db70u,0x9823b6e0u,0xd4326d90u,0x130476dcu, 0x17c56b6bu,0x1a864db2u,0x1e475005u,0x2608edb8u,0x22c9f00fu, 0x2f8ad6d6u,0x2b4bcb61u,0x350c9b64u,0x31cd86d3u,0x3c8ea00au, 0x384fbdbdu,0x4c11db70u,0x48d0c6c7u,0x4593e01eu,0x4152fda9u, 0x5f15adacu,0x5bd4b01bu,0x569796c2u,0x52568b75u,0x6a1936c8u, 0x6ed82b7fu,0x639b0da6u,0x675a1011u,0x791d4014u,0x7ddc5da3u, 0x709f7b7au,0x745e66cdu,0x9823b6e0u,0x9ce2ab57u,0x91a18d8eu, 0x95609039u,0x8b27c03cu,0x8fe6dd8bu,0x82a5fb52u,0x8664e6e5u, 0xbe2b5b58u,0xbaea46efu,0xb7a96036u,0xb3687d81u,0xad2f2d84u, 0xa9ee3033u,0xa4ad16eau,0xa06c0b5du,0xd4326d90u,0xd0f37027u, 0xddb056feu,0xd9714b49u,0xc7361b4cu,0xc3f706fbu,0xceb42022u, 0xca753d95u,0xf23a8028u,0xf6fb9d9fu,0xfbb8bb46u,0xff79a6f1u, 0xe13ef6f4u,0xe5ffeb43u,0xe8bccd9au,0xec7dd02du,0x34867077u, 0x30476dc0u,0x3d044b19u,0x39c556aeu,0x278206abu,0x23431b1cu, 0x2e003dc5u,0x2ac12072u,0x128e9dcfu,0x164f8078u,0x1b0ca6a1u, 0x1fcdbb16u,0x18aeb130u,0x54bf6a40u,0x808d07d0u,0xcc9cdca0u, 0x7897ab07u,0x7c56b6b0u,0x71159069u,0x75d48ddeu,0x6b93dddbu, 0x6f52c06cu,0x6211e6b5u,0x66d0fb02u,0x5e9f46bfu,0x5a5e5b08u, 0x571d7dd1u,0x53dc6066u,0x4d9b3063u,0x495a2dd4u,0x44190b0du, 0x40d816bau,0xaca5c697u,0xa864db20u,0xa527fdf9u,0xa1e6e04eu, 0xbfa1b04bu,0xbb60adfcu,0xb6238b25u,0xb2e29692u,0x8aad2b2fu, 0x8e6c3698u,0x832f1041u,0x87ee0df6u,0x99a95df3u,0x9d684044u, 0x902b669du,0x94ea7b2au,0xe0b41de7u,0xe4750050u,0xe9362689u, 0xedf73b3eu,0xf3b06b3bu,0xf771768cu,0xfa325055u,0xfef34de2u, 0xc6bcf05fu,0xc27dede8u,0xcf3ecb31u,0xcbffd686u,0xd5b88683u, 0xd1799b34u,0xdc3abdedu,0xd8fba05au,0x690ce0eeu,0x6dcdfd59u, 0x608edb80u,0x644fc637u,0x7a089632u,0x7ec98b85u,0x738aad5cu, 0x774bb0ebu,0x4f040d56u,0x4bc510e1u,0x46863638u,0x42472b8fu, 0x5c007b8au,0x58c1663du,0x558240e4u,0x51435d53u,0x251d3b9eu, 0x21dc2629u,0x2c9f00f0u,0x285e1d47u,0x36194d42u,0x32d850f5u, 0x3f9b762cu,0x3b5a6b9bu,0x315d6260u,0x7d4cb910u,0xa97ed480u, 0xe56f0ff0u,0x1011a0fau,0x14d0bd4du,0x19939b94u,0x1d528623u, 0xf12f560eu,0xf5ee4bb9u,0xf8ad6d60u,0xfc6c70d7u,0xe22b20d2u, 0xe6ea3d65u,0xeba91bbcu,0xef68060bu,0xd727bbb6u,0xd3e6a601u, 0xdea580d8u,0xda649d6fu,0xc423cd6au,0xc0e2d0ddu,0xcda1f604u, 0xc960ebb3u,0xbd3e8d7eu,0xb9ff90c9u,0xb4bcb610u,0xb07daba7u, 0xae3afba2u,0xaafbe615u,0xa7b8c0ccu,0xa379dd7bu,0x9b3660c6u, 0x9ff77d71u,0x92b45ba8u,0x9675461fu,0x8832161au,0x8cf30badu, 0x81b02d74u,0x857130c3u,0x5d8a9099u,0x594b8d2eu,0x5408abf7u, 0x50c9b640u,0x4e8ee645u,0x4a4ffbf2u,0x470cdd2bu,0x43cdc09cu, 0x7b827d21u,0x7f436096u,0x7200464fu,0x76c15bf8u,0x68860bfdu, 0x6c47164au,0x61043093u,0x65c52d24u,0x119b4be9u,0x155a565eu, 0x18197087u,0x1cd86d30u,0x29f3d350u,0x65e20820u,0xb1d065b0u, 0xfdc1bec0u,0x3793a651u,0x3352bbe6u,0x3e119d3fu,0x3ad08088u, 0x2497d08du,0x2056cd3au,0x2d15ebe3u,0x29d4f654u,0xc5a92679u, 0xc1683bceu,0xcc2b1d17u,0xc8ea00a0u,0xd6ad50a5u,0xd26c4d12u, 0xdf2f6bcbu,0xdbee767cu,0xe3a1cbc1u,0xe760d676u,0xea23f0afu, 0xeee2ed18u,0xf0a5bd1du,0xf464a0aau,0xf9278673u,0xfde69bc4u, 0x89b8fd09u,0x8d79e0beu,0x803ac667u,0x84fbdbd0u,0x9abc8bd5u, 0x9e7d9662u,0x933eb0bbu,0x97ffad0cu,0xafb010b1u,0xab710d06u, 0xa6322bdfu,0xa2f33668u,0xbcb4666du,0xb8757bdau,0xb5365d03u, 0xb1f740b4u }; public static readonly string Name = "CRC-32/MPEG-2"; public static uint Compute(byte[] buffer) { if (buffer == null) { throw new ArgumentException("参数异常，请检查调用方"); } return Compute(buffer, 0, buffer.Length); } public static uint Compute(byte[] buffer, int offset, int length) { if (!((buffer != null) && (offset >= 0) && (length >= 0) && (offset <= buffer.Length - length))) { throw new ArgumentException("参数异常，请检查调用方"); } //寄存器初始值 uint crc32= 0xffffffffU; //输出反转处理：32是crc校验的宽度 int ToRight = 32 - 8; ToRight = ToRight < 0 ? 0 : ToRight; while (--length >= 0) { //查表运算（取决于输出是否反转） crc32 = crcTable[((crc32 >> ToRight) ^ buffer[offset++]) & 0xFF] ^ (crc32 << 8); } //结果异或处理 crc32 ^= 0x00000000U; return crc32; }}测试如下：
byte[] data = new byte[] { 0x01, 0x02 , 0x03, 0x04 };uint crc32 = Crc32.Compute(data);byte[] crc32Ary = BitConverter.GetBytes(crc32);string crc32Str = "";for (int i = crc32Ary.Length-1; i >=0; i--){ crc32Str += crc32Ary[i].ToString("X2");}Console.WriteLine(crc32Str);Console.ReadLine();测试结果：
793737CD参考资料
CRC（循环冗余校验）在线计算——ip33.com
Crc32Helper——.NET源码
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