Polynomial representations of cyclic redundancy checks

These are polynomial representations of cyclic redundancy checks CRCs.

Name	Polynomial	Representations: normal / reversed / reverse of reciprocal
CRC-1	$x+1$ (most hardware; also known as parity bit)	0x1 / 0x1 / 0x1
CRC-4-ITU	$x^{4}+x+1$ (ITU-T G.704, p. 12)	0x3 / 0xC / 0x9
CRC-5-EPC	$x^{5}+x^{3}+1$ (Gen 2 RFID^[1])	0x09 / 0x12 / 0x14
CRC-5-ITU	$x^{5}+x^{4}+x^{2}+1$ (ITU-T G.704, p. 9)	0x15 / 0x15 / 0x1A
CRC-5-USB	$x^{5}+x^{2}+1$ (USB token packets)	0x05 / 0x14 / 0x12
CRC-6-ITU	$x^{6}+x+1$ (ITU-T G.704, p. 3)	0x03 / 0x30 / 0x21
CRC-7	$x^{7}+x^{3}+1$ (telecom systems, ITU-T G.707, ITU-T G.832, MMC, SD)	0x09 / 0x48 / 0x44
CRC-8-CCITT	$x^{8}+x^{2}+x+1$ (ATM HEC), ISDN Header Error Control and Cell Delineation ITU-T I.432.1 (02/99)	0x07 / 0xE0 / 0x83
CRC-8-Dallas/Maxim	$x^{8}+x^{5}+x^{4}+1$ (1-Wire bus)	0x31 / 0x8C / 0x98
CRC-8	$x^{8}+x^{7}+x^{6}+x^{4}+x^{2}+1$	0xD5 / 0xAB / 0xEA^[2]
CRC-8-SAE J1850	$x^{8}+x^{4}+x^{3}+x^{2}+1$	0x1D / 0xB8 / 0x8E
CRC-8-WCDMA	$x^{8}+x^{7}+x^{4}+x^{3}+x+1$ ^[3]	0x9B / 0xD9 / 0xCD^[2]
CRC-10	$x^{{10}}+x^{9}+x^{5}+x^{4}+x+1$ (ATM; ITU-T I.610)	0x233 / 0x331 / 0x319
CRC-11	$x^{{11}}+x^{9}+x^{8}+x^{7}+x^{2}+1$ (FlexRay^[4])	0x385 / 0x50E / 0x5C2
CRC-12	$x^{{12}}+x^{{11}}+x^{3}+x^{2}+x+1$ (telecom systems^[5]^[6])	0x80F / 0xF01 / 0xC07^[2]
CRC-13-BBC	$x^{{13}}+x^{{12}}+x^{{11}}+x^{{10}}+x^{7}+x^{6}+x^{5}+x^{4}+x^{2}+1$	0x1CF5 / 0x15E7 / 0x1E7A
CRC-15-CAN	$x^{{15}}+x^{{14}}+x^{{10}}+x^{8}+x^{7}+x^{4}+x^{3}+1$	0x4599 / 0x4CD1 / 0x62CC
CRC-16-IBM	$x^{16} + x^{15} + x^2 + 1$ (Bisync, Modbus, USB, ANSI X3.28, many others; also known as CRC-16 and CRC-16-ANSI)	0x8005 / 0xA001 / 0xC002
CRC-16-CCITT	$x^{16} + x^{12} + x^5 + 1$ (X.25, V.41, HDLC, XMODEM, Bluetooth, SD, many others; known as CRC-CCITT)	0x1021 / 0x8408 / 0x8810^[2]
CRC-16-T10-DIF	$x^{{16}}+x^{{15}}+x^{{11}}+x^{{9}}+x^{8}+x^{7}+x^{5}+x^{4}+x^{2}+x+1$ (SCSI DIF)	0x8BB7^[7] / 0xEDD1 / 0xC5DB
CRC-16-DNP	$x^{{16}}+x^{{13}}+x^{{12}}+x^{{11}}+x^{{10}}+x^{8}+x^{6}+x^{5}+x^{2}+1$ (DNP, IEC 870, M-Bus)	0x3D65 / 0xA6BC / 0x9EB2
CRC-16-DECT	$x^{{16}}+x^{{10}}+x^{8}+x^{7}+x^{3}+1$ (cordless telephones)^[8]	0x0589 / 0x91A0 / 0x82C4
CRC-16-Fletcher	Not a CRC; see Fletcher's checksum	Used in Adler-32 A & B CRCs
CRC-24	$x^{{24}}+x^{{22}}+x^{{20}}+x^{{19}}+x^{{18}}+x^{{16}}+x^{{14}}+x^{{13}}+x^{{11}}+x^{{10}}+x^{8}+x^{7}+x^{6}+x^{3}+x+1$ (FlexRay^[4])	0x5D6DCB / 0xD3B6BA / 0xAEB6E5
CRC-24-Radix-64	$x^{{24}}+x^{{23}}+x^{{18}}+x^{{17}}+x^{{14}}+x^{{11}}+x^{{10}}+x^{7}+x^{6}+x^{5}+x^{4}+x^{3}+x+1$ (OpenPGP)	0x864CFB / 0xDF3261 / 0xC3267D
CRC-30	$x^{{30}}+x^{{29}}+x^{{21}}+x^{{20}}+x^{{15}}+x^{{13}}+x^{{12}}+x^{{11}}+x^{{8}}+x^{{7}}+x^{{6}}+x^{{2}}+x+1$ (CDMA)	0x2030B9C7 / 0x38E74301 / 0x30185CE3
CRC-32-Adler	Not a CRC; see Adler-32	See Adler-32
CRC-32	$x^{{32}}+x^{{26}}+x^{{23}}+x^{{22}}+x^{{16}}+x^{{12}}+x^{{11}}+x^{{10}}+x^{8}+x^{7}+x^{5}+x^{4}+x^{2}+x+1$ (ISO 3309, ANSI X3.66, FIPS PUB 71, FED-STD-1003, ITU-T V.42, Ethernet, SATA, MPEG-2, Gzip, PKZIP, POSIX cksum, PNG,^[9] ZMODEM)	0x04C11DB7 / 0xEDB88320 / 0x82608EDB^[10]
CRC-32C (Castagnoli)	$x^{{32}}+x^{{28}}+x^{{27}}+x^{{26}}+x^{{25}}+x^{{23}}+x^{{22}}+x^{{20}}+x^{{19}}+x^{{18}}+x^{{14}}+x^{{13}}+x^{{11}}+x^{{10}}+x^{9}+x^{8}+x^{6}+1$ (iSCSI & SCTP, G.hn payload, SSE4.2)	0x1EDC6F41 / 0x82F63B78 / 0x8F6E37A0^[10]
CRC-32K (Koopman)	$x^{{32}}+x^{{30}}+x^{{29}}+x^{{28}}+x^{{26}}+x^{{20}}+x^{{19}}+x^{{17}}+x^{{16}}+x^{{15}}+x^{{11}}+x^{{10}}+x^{{7}}+x^{{6}}+x^{{4}}+x^{{2}}+x+1$	0x741B8CD7 / 0xEB31D82E / 0xBA0DC66B^[10]
CRC-32Q	$x^{{32}}+x^{{31}}+x^{{24}}+x^{{22}}+x^{{16}}+x^{{14}}+x^{{8}}+x^{{7}}+x^{{5}}+x^{{3}}+x+1$ (aviation; AIXM^[11])	0x814141AB / 0xD5828281 / 0xC0A0A0D5
CRC-40-GSM	$x^{{40}}+x^{{26}}+x^{{23}}+x^{{17}}+x^{3}+1$ (GSM control channel^[12]^[13]^[14])	0x0004820009 / 0x9000412000 / 0x8002410004
CRC-64-ISO	$x^{{64}}+x^{4}+x^{3}+x+1$ (HDLC — ISO 3309, Swiss-Prot/TrEMBL; considered weak for hashing^[15])	0x000000000000001B / 0xD800000000000000 / 0x800000000000000D
CRC-64-ECMA-182	$x^{{64}}+x^{{62}}+x^{{57}}+x^{{55}}+x^{{54}}+x^{{53}}+x^{{52}}+x^{{47}}+x^{{46}}+x^{{45}}+x^{{40}}+x^{{39}}+x^{{38}}+x^{{37}}+x^{{35}}+x^{{33}}+$ $x^{{32}}+x^{{31}}+x^{{29}}+x^{{27}}+x^{{24}}+x^{{23}}+x^{{22}}+x^{{21}}+x^{{19}}+x^{{17}}+x^{{13}}+x^{{12}}+x^{{10}}+x^{9}+x^{7}+x^{4}+x+1$ (as described in ECMA-182 p. 51)	0x42F0E1EBA9EA3693 / 0xC96C5795D7870F42 / 0xA17870F5D4F51B49

External links

References

↑ "Class-1 Generation-2 UHF RFID Protocol" (PDF). 1.2.0. EPCglobal. 23 October 2008: 35. Retrieved 21 May 2009.
1 2 3 4 Koopman, Philip; Chakravarty, Tridib (28 June – 1 July 2004). "Cyclic Redundancy Code (CRC) Polynomial Selection For Embedded Networks" (PDF). 2004 International Conference on Dependable Systems and Networks: 145–154. ISBN 0-7695-2052-9. doi:10.1109/DSN.2004.1311885.
↑ Richardson, Andrew (17 March 2005). WCDMA Handbook. Cambridge, UK: Cambridge University Press. p. 223. ISBN 0521828155.
1 2 "FlexRay Protocol Specification". 2.1 Revision A. Flexray Consortium. 22 December 2005: 93.
↑ Perez A, Wismer & Becker (1983). "Byte-Wise CRC Calculations". IEEE Micro. 3 (3): 40–50. doi:10.1109/MM.1983.291120.
↑ Ramabadran, T.V.; Gaitonde, S.S. (1988). "A tutorial on CRC computations". IEEE Micro. 8 (4): 62–75. doi:10.1109/40.7773.
↑ Thaler, Pat (28 August 2003). "16-bit CRC polynomial selection" (PDF). INCITS T10. Retrieved 11 August 2009.
↑ "ETSI EN 300 175-3". V2.2.1. Sophia Antipolis, France: European Telecommunications Standards Institute. November 2008.
↑ Boutell, Thomas; Randers-Pehrson, Glenn; et al. (14 July 1998). "PNG (Portable Network Graphics) Specification, Version 1.2". Retrieved 3 February 2011.
1 2 3 Koopman, Philip (23–26 June 2002). "32-Bit Cyclic Redundancy Codes for Internet Applications" (PDF). 2002 International Conference on Dependable Systems and Networks: 459–468. ISBN 0-7695-1597-5. doi:10.1109/DSN.2002.1028931. Retrieved 14 January 2011.
↑ "AIXM Primer" (PDF). 4.5. European Organisation for the Safety of Air Navigation. 20 March 2006. Retrieved 29 April 2009.
↑ ETSI TS 100 909 version 8.9.0 (January 2005), Section 4.1.2 a
↑ Gammel, B.M. (31 October 2005). "Crypto - Codes". Retrieved 10 February 2011.
↑ Geremia, Patrick (April 1999). "Cyclic redundancy check computation: an implementation using the TMS320C54x" (PDF) (SPRA530). Texas Instruments: 5. Retrieved 10 February 2011.
↑ Jones, David T. "An Improved 64-bit Cyclic Redundancy Check for Protein Sequences" (PDF). University College London. Retrieved 15 December 2009.

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Polynomial representations of cyclic redundancy checks

See also

External links

References