User:Xiong/crc

Common polynomials

• As well as the polynomial, the prefix and the value exclusive-ORed with the remainder are important for some more complicated checksums (like most forms of CRC-32 and CRC-64).
• CRCs less than CRC-16 do not tend to use Initial or final XOR values.
• Very often custom versions of checksums are created by changing these values, as it does not alter the overall mechanics (or math) of the checksum algorithm -- and may provide some nominal security features. However a CRC algorithm can be reverse-engineered from a small number of message-CRC pairs by brute force search.

Note: in this table the high-order bit is omitted; see Specifying a CRC above.

Name	Polynomial	Representations: Normal or Reverse (Normal of Reciprocal)
CRC-1	${\displaystyle x+1}$ (most hardware; also known as parity bit)	0x1 or 0x1 (0x1)
CRC-4-ITU	${\displaystyle x^{4}+x+1}$ ( ITU G.704 , p. 12)	0x3 or 0xC (0x9)
CRC-5-ITU	${\displaystyle x^{5}+x^{4}+x^{2}+1}$ ( ITU G.704 , p. 9)	0x15 or 0x15 (0x0B)
CRC-5-USB	${\displaystyle x^{5}+x^{2}+1}$ (USB token packets)	0x05 or 0x14 (0x9)
CRC-6-ITU	${\displaystyle x^{6}+x+1}$ ( ITU G.704 , p. 3)	0x03 or 0x30 (0x21)
CRC-7	${\displaystyle x^{7}+x^{3}+1}$ (telecom systems, MMC)	0x09 or 0x48 (0x11)
CRC-8-ATM	${\displaystyle x^{8}+x^{2}+x+1}$ (ATM HEC)	0x07 or 0xE0 (0xC1)
CRC-8- CCITT	${\displaystyle x^{8}+x^{7}+x^{3}+x^{2}+1}$ (1-Wire bus)	0x8D or 0xB1 (0x63)
CRC-8- Maxim	${\displaystyle x^{8}+x^{5}+x^{4}+1}$ (1-Wire bus)	0x31 or 0x8C (0x19)
CRC-8	${\displaystyle x^{8}+x^{7}+x^{6}+x^{4}+x^{2}+1}$	0xD5 or 0xAB (0x57)
CRC-8-SAE J1850	${\displaystyle x^{8}+x^{4}+x^{3}+x^{2}+1}$	0x1D or 0xB8 (0x71)
CRC-10	${\displaystyle x^{10}+x^{9}+x^{5}+x^{4}+x+1}$	0x233 or 0x331 (0x263)
CRC-11	${\displaystyle x^{11}+x^{9}+x^{8}+x^{7}+x^{2}+1}$ (FlexRay)	0x385 or 0x50E (0x21D)
CRC-12	${\displaystyle x^{12}+x^{11}+x^{3}+x^{2}+x+1}$ (telecom systems, [1][2] )	0x80F or 0xF01 (0xE03)
CRC-15- CAN	${\displaystyle x^{15}+x^{14}+x^{10}+x^{8}+x^{7}+x^{4}+x^{3}+1}$	0x4599 or 0x4CD1 (0x19A3)
CRC-16-Fletcher	Not a CRC; see Fletcher's checksum	Used in Adler-32 A & B CRCs
CRC-16-CCITT	${\displaystyle x^{16}+x^{12}+x^{5}+1}$ ( IrDA, BACnet ; known as CRC-CCITT)	0x1021 or 0x8408 (0x0811)
CRC-16-IBM	${\displaystyle x^{16}+x^{15}+x^{2}+1}$ (SDLC, XMODEM, USB, many others; also known as CRC-16)	0x8005 or 0xA001 (0x4003)
CRC-24- Radix-64	${\displaystyle x^{24}+x^{23}+x^{18}+x^{17}+x^{14}+x^{11}+x^{10}+x^{7}+x^{6}+x^{5}+x^{4}+x^{3}+x+1}$ (FlexRay)	0x864CFB or 0xDF3261 (0xBE64C3)
CRC-30	${\displaystyle x^{30}+x^{29}+x^{21}+x^{20}+x^{15}+x^{13}+x^{12}+x^{11}+x^{8}+x^{7}+x^{6}+x^{2}+x+1}$ ( CDMA )	0x2030B9C7 or 0x38E74301 (0x31CE8603)
CRC-32-Adler	Not a CRC; see Adler-32	See Adler-32
CRC-32-IEEE 802.3	${\displaystyle x^{32}+x^{26}+x^{23}+x^{22}+x^{16}+x^{12}+x^{11}+x^{10}+x^{8}+x^{7}+x^{5}+x^{4}+x^{2}+x+1}$ (V.42, MPEG-2)	0x04C11DB7 or 0xEDB88320 (0xDB710641)
CRC-32C (Castagnoli)	${\displaystyle x^{32}+x^{28}+x^{27}+x^{26}+x^{25}+x^{23}+x^{22}+x^{20}+x^{19}+x^{18}+x^{14}+x^{13}+x^{11}+x^{10}+x^{9}+x^{8}+x^{6}+1}$	0x1EDC6F41 or 0x82F63B78 (0x05EC76F1)
CRC-32K (Koopman)	${\displaystyle x^{32}+x^{30}+x^{29}+x^{28}+x^{26}+x^{20}+x^{19}+x^{17}+x^{16}+x^{15}+x^{11}+x^{10}+x^{7}+x^{6}+x^{4}+x^{2}+x+1}$	0x741B8CD7 or 0xEB31D82E (0xD663B05D)
CRC-64-ISO	${\displaystyle x^{64}+x^{4}+x^{3}+x+1}$ (HDLC — ISO 3309)	0x000000000000001B or 0xD800000000000000 (0xB000000000000001)
CRC-64-ECMA-182	${\displaystyle x^{64}+x^{62}+x^{57}+x^{55}+x^{54}+x^{53}+x^{52}+x^{47}+x^{46}+x^{45}+x^{40}+x^{39}+x^{38}+x^{37}+x^{35}+x^{33}+}$ ${\displaystyle x^{32}+x^{31}+x^{29}+x^{27}+x^{24}+x^{23}+x^{22}+x^{21}+x^{19}+x^{17}+x^{13}+x^{12}+x^{10}+x^{9}+x^{7}+x^{4}+x+1}$ (as described in ECMA-182 p.63)	0x42F0E1EBA9EA3693 or 0xC96C5795D7870F42 (0x92D8AF2BAF0E1E85)

Known to exist, but technologically defunct -- mainly replaced by

• CRC-128 (IEEE)
• CRC-256 (IEEE)