CRC – Cyclic Redundancy Check is an algorithm which is widely used in different communication protocols, packing and packaging algorithms for assuring robustness of data. The idea behind it is simple – calculate a unique checksum (frame check sequence) for each data frame, based on its content and stick it at the end of each meaningful message. Once data is received, it’s possible to perform the same calculation and compare results – if results are similar, message is ok.

There are two kinds of CRC – 16 and 32 bit. There are also less used checksums for 8 and 64 bits. All this is about appending a string of zeros to the frame equal in number of frames and modulo two device by using generator polynomial containing one or more bits, then checksum to be generated. This is very similar to performing a bit-wise XOR operation in the frame, while the remainder is actually our CRC.

In many industries, the first polynomial is in use to create CRC tables and then apply it for performance purposes. The default polynomial, defined by IEEE 802.3 is 0xA001 for 16 bit and 0×04C11DB7 for 32 bit. We're in C#, thus we should use its inversed version which is 0×8408 for 16 bit and 0xEDB88320 for 32 bit. We're going to use those polynomials also in our sample.

So let’s start. Because CRC is `HashAlgorithm `

after all, we can derive our classes from `System.Security.Cryptography.HashAlgorithm`

class.

public class CRC16 : HashAlgorithm {
public class CRC32 : HashAlgorithm {

Then, upon first creation we'll generate hashtables with CRC values to enhance future performance. It’s all about values table for bytes from 0 to 255 , so we should calculate it only once and then we can use it statically.

[CLSCompliant(false)]
public CRC16(ushort polynomial)
{
HashSizeValue = 16;
_crc16Table = (ushort[])_crc16TablesCache[polynomial];
if (_crc16Table == null) {
_crc16Table = CRC16._buildCRC16Table(polynomial);
_crc16TablesCache.Add(polynomial, _crc16Table);
}
Initialize();
}
[CLSCompliant(false)]
public CRC32(uint polynomial)
{
HashSizeValue = 32;
_crc32Table = (uint[])_crc32TablesCache[polynomial];
if (_crc32Table == null) {
_crc32Table = CRC32._buildCRC32Table(polynomial);
_crc32TablesCache.Add(polynomial, _crc32Table);
}
Initialize();
}

Then let’s calculate it:

private static ushort[] _buildCRC16Table(ushort polynomial)
{
ushort[] table = new ushort[256];
for (ushort i = 0; i < table.Length; i++)
{
ushort value = 0;
ushort temp = i;
for (byte j = 0; j < 8; j++) {
if (((value ^ temp) & 0×0001) != 0) {
value = (ushort)((value >> 1) ^ polynomial);
} else {
value >>= 1;
}
temp >>= 1;
}
table[i] = value;
}
return table;
}
private static uint[] _buildCRC32Table(uint polynomial)
{
uint crc;
uint[] table = new uint[256];
for (int i = 0; i < 256; i++)
{
crc = (uint)i;
for (int j = 8; j > 0; j–)
{
if ((crc & 1) == 1)
crc = (crc >> 1) ^ polynomial;
else
crc >>= 1;
}
table[i] = crc;
}
return table;
}

The result will look like this for 32 bits:

0x00, 0x31, 0x62, 0x53, 0xC4, 0xF5, 0xA6, 0x97,
0xB9, 0x88, 0xDB, 0xEA, 0x7D, 0x4C, 0x1F, 0x2E,
0x43, 0x72, 0x21, 0x10, 0x87, 0xB6, 0xE5, 0xD4,
0xFA, 0xCB, 0x98, 0xA9, 0x3E, 0x0F, 0x5C, 0x6D,
0x86, 0xB7, 0xE4, 0xD5, 0x42, 0x73, 0x20, 0x11,
0x3F, 0x0E, 0x5D, 0x6C, 0xFB, 0xCA, 0x99, 0xA8,
0xC5, 0xF4, 0xA7, 0x96, 0x01, 0x30, 0x63, 0x52,
0x7C, 0x4D, 0x1E, 0x2F, 0xB8, 0x89, 0xDA, 0xEB,
0x3D, 0x0C, 0x5F, 0x6E, 0xF9, 0xC8, 0x9B, 0xAA,
0x84, 0xB5, 0xE6, 0xD7, 0x40, 0x71, 0x22, 0x13,
0x7E, 0x4F, 0x1C, 0x2D, 0xBA, 0x8B, 0xD8, 0xE9,
0xC7, 0xF6, 0xA5, 0x94, 0x03, 0x32, 0x61, 0x50,
0xBB, 0x8A, 0xD9, 0xE8, 0x7F, 0x4E, 0x1D, 0x2C,
0x02, 0x33, 0x60, 0x51, 0xC6, 0xF7, 0xA4, 0x95,
0xF8, 0xC9, 0x9A, 0xAB, 0x3C, 0x0D, 0x5E, 0x6F,
0x41, 0x70, 0x23, 0x12, 0x85, 0xB4, 0xE7, 0xD6,
0x7A, 0x4B, 0x18, 0x29, 0xBE, 0x8F, 0xDC, 0xED,
0xC3, 0xF2, 0xA1, 0x90, 0x07, 0x36, 0x65, 0x54,
0x39, 0x08, 0x5B, 0x6A, 0xFD, 0xCC, 0x9F, 0xAE,
0x80, 0xB1, 0xE2, 0xD3, 0x44, 0x75, 0x26, 0x17,
0xFC, 0xCD, 0x9E, 0xAF, 0x38, 0x09, 0x5A, 0x6B,
0x45, 0x74, 0x27, 0x16, 0x81, 0xB0, 0xE3, 0xD2,
0xBF, 0x8E, 0xDD, 0xEC, 0x7B, 0x4A, 0x19, 0x28,
0x06, 0x37, 0x64, 0x55, 0xC2, 0xF3, 0xA0, 0x91,
0x47, 0x76, 0x25, 0x14, 0x83, 0xB2, 0xE1, 0xD0,
0xFE, 0xCF, 0x9C, 0xAD, 0x3A, 0x0B, 0x58, 0x69,
0x04, 0x35, 0x66, 0x57, 0xC0, 0xF1, 0xA2, 0x93,
0xBD, 0x8C, 0xDF, 0xEE, 0x79, 0x48, 0x1B, 0x2A,
0xC1, 0xF0, 0xA3, 0x92, 0x05, 0x34, 0x67, 0x56,
0x78, 0x49, 0x1A, 0x2B, 0xBC, 0x8D, 0xDE, 0xEF,
0x82, 0xB3, 0xE0, 0xD1, 0x46, 0x77, 0x24, 0x15,
0x3B, 0x0A, 0x59, 0x68, 0xFF, 0xCE, 0x9D, 0xAC

Now, all we have to do upon request is to lookup into this hash table for related value and XOR it:

protected override void HashCore(byte[] buffer, int offset, int count)
{
for (int i = offset; i < count; i++)
{
ulong ptr = (_crc & 0xFF) ^ buffer[i];
_crc >>= 8;
_crc ^= _crc32Table[ptr];
}
}
new public byte[] ComputeHash(Stream inputStream)
{
byte[] buffer = new byte[4096];
int bytesRead;
while ((bytesRead = inputStream.Read(buffer, 0, 4096)) > 0)
{
HashCore(buffer, 0, bytesRead);
}
return HashFinal();
}
protected override byte[] HashFinal()
{
byte[] finalHash = new byte[4];
ulong finalCRC = _crc ^ _allOnes;
finalHash[0] = (byte)((finalCRC >> 0) & 0xFF);
finalHash[1] = (byte)((finalCRC >> 8) & 0xFF);
finalHash[2] = (byte)((finalCRC >> 16) & 0xFF);
finalHash[3] = (byte)((finalCRC >> 24) & 0xFF);
return finalHash;
}

We're done. Have a good time and be good people. Also, I want to thank Boris for helping me with this article. He promised to write here some day…