Cyclic redundancy check
Acyclic redundancy check(CRC) is anerror-detecting codecommonly used in digitalnetworksand storage devices to detect accidental changes to digital data.[1][2]Blocks of data entering these systems get a shortcheck valueattached, based on the remainder of apolynomial divisionof their contents. On retrieval, the calculation is repeated and, in the event the check values do not match, corrective action can be taken against data corruption. CRCs can be used forerror correction(seebitfilters).[3]
CRCs are so called because thecheck(data verification) value is aredundancy(it expands the message without addinginformation) and thealgorithmis based oncycliccodes.CRCs are popular because they are simple to implement in binaryhardware,easy to analyze mathematically, and particularly good at detecting common errors caused bynoisein transmission channels. Because the check value has a fixed length, thefunctionthat generates it is occasionally used as ahash function.
Introduction
[edit]CRCs are based on the theory ofcyclicerror-correcting codes.The use ofsystematiccyclic codes, which encode messages by adding a fixed-length check value, for the purpose of error detection in communication networks, was first proposed byW. Wesley Petersonin 1961.[4] Cyclic codes are not only simple to implement but have the benefit of being particularly well suited for the detection ofburst errors:contiguous sequences of erroneous data symbols in messages. This is important because burst errors are common transmission errors in manycommunication channels,including magnetic and optical storage devices. Typically ann-bit CRC applied to a data block of arbitrary length will detect any single error burst not longer thannbits, and the fraction of all longer error bursts that it will detect is approximately(1 − 2−n).
Specification of a CRC code requires definition of a so-calledgenerator polynomial.This polynomial becomes thedivisorin apolynomial long division,which takes the message as thedividendand in which thequotientis discarded and theremainderbecomes the result. The important caveat is that the polynomialcoefficientsare calculated according to the arithmetic of afinite field,so the addition operation can always be performed bitwise-parallel (there is no carry between digits).
In practice, all commonly used CRCs employ the finite field of two elements,GF(2).The two elements are usually called 0 and 1, comfortably matching computer architecture.
A CRC is called ann-bit CRC when its check value isnbits long. For a givenn,multiple CRCs are possible, each with a different polynomial. Such a polynomial has highest degreen,which means it hasn+ 1terms. In other words, the polynomial has a length ofn+ 1;its encoding requiresn+ 1bits. Note that most polynomial specifications either drop theMSBorLSB,since they are always 1. The CRC and associated polynomial typically have a name of the form CRC-n-XXX as in thetablebelow.
The simplest error-detection system, theparity bit,is in fact a 1-bit CRC: it uses the generator polynomialx+ 1(two terms),[5]and has the name CRC-1.
Application
[edit]A CRC-enabled device calculates a short, fixed-length binary sequence, known as thecheck valueorCRC,for each block of data to be sent or stored and appends it to the data, forming acodeword.
When a codeword is received or read, the device either compares its check value with one freshly calculated from the data block, or equivalently, performs a CRC on the whole codeword and compares the resulting check value with an expectedresidueconstant.
If the CRC values do not match, then the block contains a data error.
The device may take corrective action, such as rereading the block or requesting that it be sent again. Otherwise, the data is assumed to be error-free (though, with some small probability, it may contain undetected errors; this is inherent in the nature of error-checking).[6]
Data integrity
[edit]CRCs are specifically designed to protect against common types of errors on communication channels, where they can provide quick and reasonable assurance of theintegrityof messages delivered. However, they are not suitable for protecting against intentional alteration of data.
Firstly, as there is no authentication, an attacker can edit a message and recompute the CRC without the substitution being detected. When stored alongside the data, CRCs and cryptographic hash functions by themselves do not protect againstintentionalmodification of data. Any application that requires protection against such attacks must use cryptographic authentication mechanisms, such asmessage authentication codesordigital signatures(which are commonly based oncryptographic hashfunctions).
Secondly, unlike cryptographic hash functions, CRC is an easily reversible function, which makes it unsuitable for use in digital signatures.[7]
Thirdly, CRC satisfies a relation similar to that of alinear function(or more accurately, anaffine function):[8]
wheredepends on the length ofand.This can be also stated as follows, where,andhave the same length
as a result, even if the CRC is encrypted with astream cipherthat usesXORas its combining operation (ormodeofblock cipherwhich effectively turns it into a stream cipher, such as OFB or CFB), both the message and the associated CRC can be manipulated without knowledge of the encryption key; this was one of the well-known design flaws of theWired Equivalent Privacy(WEP) protocol.[9]
Computation
[edit]To compute ann-bit binary CRC, line the bits representing the input in a row, and position the (n+ 1)-bit pattern representing the CRC's divisor (called a "polynomial") underneath the left end of the row.
In this example, we shall encode 14 bits of message with a 3-bit CRC, with a polynomialx3+x+ 1.The polynomial is written in binary as the coefficients; a 3rd-degree polynomial has 4 coefficients (1x3+ 0x2+ 1x+ 1). In this case, the coefficients are 1, 0, 1 and 1. The result of the calculation is 3 bits long, which is why it is called a 3-bit CRC. However, you need 4 bits to explicitly state the polynomial.
Start with the message to be encoded:
11010011101100
This is first padded with zeros corresponding to the bit lengthnof the CRC. This is done so that the resulting code word is insystematicform. Here is the first calculation for computing a 3-bit CRC:
11010011101100 000 <--- input right padded by 3 bits 1011 <--- divisor (4 bits) = x³ + x + 1 ------------------ 01100011101100 000 <--- result
The algorithm acts on the bits directly above the divisor in each step. The result for that iteration is the bitwise XOR of the polynomial divisor with the bits above it. The bits not above the divisor are simply copied directly below for that step. The divisor is then shifted right to align with the highest remaining 1 bit in the input, and the process is repeated until the divisor reaches the right-hand end of the input row. Here is the entire calculation:
11010011101100 000 <--- input right padded by 3 bits 1011 <--- divisor 01100011101100 000 <--- result (note the first four bits are the XOR with the divisor beneath, the rest of the bits are unchanged) 1011 <--- divisor... 00111011101100 000 1011 00010111101100 000 1011 00000001101100 000 <--- note that the divisor moves over to align with the next 1 in the dividend (since quotient for that step was zero) 1011 (in other words, it doesn't necessarily move one bit per iteration) 00000000110100 000 1011 00000000011000 000 1011 00000000001110 000 1011 00000000000101 000 101 1 ----------------- 00000000000000 100 <--- remainder (3 bits). Division algorithm stops here as dividend is equal to zero.
Since the leftmost divisor bit zeroed every input bit it touched, when this process ends the only bits in the input row that can be nonzero are the n bits at the right-hand end of the row. Thesenbits are the remainder of the division step, and will also be the value of the CRC function (unless the chosen CRC specification calls for some postprocessing).
The validity of a received message can easily be verified by performing the above calculation again, this time with the check value added instead of zeroes. The remainder should equal zero if there are no detectable errors.
11010011101100 100 <--- input with check value 1011 <--- divisor 01100011101100 100 <--- result 1011 <--- divisor... 00111011101100 100 ...... 00000000001110 100 1011 00000000000101 100 101 1 ------------------ 00000000000000 000 <--- remainder
The followingPythoncode outlines a function which will return the initial CRC remainder for a chosen input and polynomial, with either 1 or 0 as the initial padding. Note that this code works with string inputs rather than raw numbers:
defcrc_remainder(input_bitstring,polynomial_bitstring,initial_filler):
"""Calculate the CRC remainder of a string of bits using a chosen polynomial.
initial_filler should be '1' or '0'.
"""
polynomial_bitstring=polynomial_bitstring.lstrip('0')
len_input=len(input_bitstring)
initial_padding=(len(polynomial_bitstring)-1)*initial_filler
input_padded_array=list(input_bitstring+initial_padding)
while'1'ininput_padded_array[:len_input]:
cur_shift=input_padded_array.index('1')
foriinrange(len(polynomial_bitstring)):
input_padded_array[cur_shift+i]\
=str(int(polynomial_bitstring[i]!=input_padded_array[cur_shift+i]))
return''.join(input_padded_array)[len_input:]
defcrc_check(input_bitstring,polynomial_bitstring,check_value):
"""Calculate the CRC check of a string of bits using a chosen polynomial." ""
polynomial_bitstring=polynomial_bitstring.lstrip('0')
len_input=len(input_bitstring)
initial_padding=check_value
input_padded_array=list(input_bitstring+initial_padding)
while'1'ininput_padded_array[:len_input]:
cur_shift=input_padded_array.index('1')
foriinrange(len(polynomial_bitstring)):
input_padded_array[cur_shift+i]\
=str(int(polynomial_bitstring[i]!=input_padded_array[cur_shift+i]))
return('1'notin''.join(input_padded_array)[len_input:])
>>>crc_remainder('11010011101100','1011','0')
'100'
>>>crc_check('11010011101100','1011','100')
True
Mathematics
[edit]This sectionneeds additional citations forverification.(July 2016) |
Mathematical analysis of this division-like process reveals how to select a divisor that guarantees good error-detection properties. In this analysis, the digits of the bit strings are taken as the coefficients of a polynomial in some variablex—coefficients that are elements of the finite fieldGF(2)(the integers modulo 2, i.e. either a zero or a one), instead of more familiar numbers. The set of binary polynomials is a mathematicalring.
Designing polynomials
[edit]The selection of the generator polynomial is the most important part of implementing the CRC algorithm. The polynomial must be chosen to maximize the error-detecting capabilities while minimizing overall collision probabilities.
The most important attribute of the polynomial is its length (largest degree(exponent) +1 of any one term in the polynomial), because of its direct influence on the length of the computed check value.
The most commonly used polynomial lengths are 9 bits (CRC-8), 17 bits (CRC-16), 33 bits (CRC-32), and 65 bits (CRC-64).[5]
A CRC is called ann-bit CRC when its check value isn-bits. For a givenn,multiple CRCs are possible, each with a different polynomial. Such a polynomial has highest degreen,and hencen+ 1terms (the polynomial has a length ofn+ 1). The remainder has lengthn.The CRC has a name of the form CRC-n-XXX.
The design of the CRC polynomial depends on the maximum total length of the block to be protected (data + CRC bits), the desired error protection features, and the type of resources for implementing the CRC, as well as the desired performance. A common misconception is that the "best" CRC polynomials are derived from eitherirreducible polynomialsor irreducible polynomials times the factor1 +x,which adds to the code the ability to detect all errors affecting an odd number of bits.[10]In reality, all the factors described above should enter into the selection of the polynomial and may lead to a reducible polynomial. However, choosing a reducible polynomial will result in a certain proportion of missed errors, due to the quotient ring havingzero divisors.
The advantage of choosing aprimitive polynomialas the generator for a CRC code is that the resulting code has maximal total block length in the sense that all 1-bit errors within that block length have different remainders (also calledsyndromes) and therefore, since the remainder is a linear function of the block, the code can detect all 2-bit errors within that block length. Ifis the degree of the primitive generator polynomial, then the maximal total block length is,and the associated code is able to detect any single-bit or double-bit errors.[11]We can improve this situation. If we use the generator polynomial,whereis a primitive polynomial of degree,then the maximal total block length is,and the code is able to detect single, double, triple and any odd number of errors.
A polynomialthat admits other factorizations may be chosen then so as to balance the maximal total blocklength with a desired error detection power. TheBCH codesare a powerful class of such polynomials. They subsume the two examples above. Regardless of the reducibility properties of a generator polynomial of degreer,if it includes the "+1" term, the code will be able to detect error patterns that are confined to a window ofrcontiguous bits. These patterns are called "error bursts".
Specification
[edit]The concept of the CRC as an error-detecting code gets complicated when an implementer or standards committee uses it to design a practical system. Here are some of the complications:
- Sometimes an implementationprefixes a fixed bit patternto the bitstream to be checked. This is useful when clocking errors might insert 0-bits in front of a message, an alteration that would otherwise leave the check value unchanged.
- Usually, but not always, an implementationappendsn0-bits(nbeing the size of the CRC) to the bitstream to be checked before the polynomial division occurs. Such appending is explicitly demonstrated in theComputation of CRCarticle. This has the convenience that the remainder of the original bitstream with the check value appended is exactly zero, so the CRC can be checked simply by performing the polynomial division on the received bitstream and comparing the remainder with zero. Due to the associative and commutative properties of the exclusive-or operation, practical table driven implementations can obtain a result numerically equivalent to zero-appending without explicitly appending any zeroes, by using an equivalent,[10]faster algorithm that combines the message bitstream with the stream being shifted out of the CRC register.
- Sometimes an implementationexclusive-ORs a fixed bit patterninto the remainder of the polynomial division.
- Bit order:Some schemes view the low-order bit of each byte as "first", which then during polynomial division means "leftmost", which is contrary to our customary understanding of "low-order". This convention makes sense whenserial-porttransmissions are CRC-checked in hardware, because some widespread serial-port transmission conventions transmit bytes least-significant bit first.
- Byte order:With multi-byte CRCs, there can be confusion over whether the byte transmitted first (or stored in the lowest-addressed byte of memory) is the least-significant byte (LSB) or the most-significant byte (MSB). For example, some 16-bit CRC schemes swap the bytes of the check value.
- Omission of the high-order bitof the divisor polynomial: Since the high-order bit is always 1, and since ann-bit CRC must be defined by an (n+ 1)-bit divisor whichoverflowsann-bitregister,some writers assume that it is unnecessary to mention the divisor's high-order bit.
- Omission of the low-order bitof the divisor polynomial: Since the low-order bit is always 1, authors such as Philip Koopman represent polynomials with their high-order bit intact, but without the low-order bit (theor 1 term). This convention encodes the polynomial complete with its degree in one integer.
These complications mean that there are three common ways to express a polynomial as an integer: the first two, which are mirror images in binary, are the constants found in code; the third is the number found in Koopman's papers.In each case, one term is omitted.So the polynomialmay be transcribed as:
- 0x3 = 0b0011, representing(MSB-first code)
- 0xC = 0b1100, representing(LSB-first code)
- 0x9 = 0b1001, representing(Koopman notation)
In the table below they are shown as:
Name | Normal | Reversed | Reversed reciprocal |
---|---|---|---|
CRC-4 | 0x3 | 0xC | 0x9 |
Obfuscation
[edit]CRCs inproprietary protocolsmight beobfuscatedby using a non-trivial initial value and a final XOR, but these techniques do not add cryptographic strength to the algorithm and can bereverse engineeredusing straightforward methods.[12]
Standards and common use
[edit]Numerous varieties of cyclic redundancy checks have been incorporated intotechnical standards.By no means does one algorithm, or one of each degree, suit every purpose; Koopman and Chakravarty recommend selecting a polynomial according to the application requirements and the expected distribution of message lengths.[13]The number of distinct CRCs in use has confused developers, a situation which authors have sought to address.[10]There are three polynomials reported for CRC-12,[13]twenty-two conflicting definitions of CRC-16, and seven of CRC-32.[14]
The polynomials commonly applied are not the most efficient ones possible. Since 1993, Koopman, Castagnoli and others have surveyed the space of polynomials between 3 and 64 bits in size,[13][15][16][17]finding examples that have much better performance (in terms ofHamming distancefor a given message size) than the polynomials of earlier protocols, and publishing the best of these with the aim of improving the error detection capacity of future standards.[16]In particular,iSCSIandSCTPhave adopted one of the findings of this research, the CRC-32C (Castagnoli) polynomial.
The design of the 32-bit polynomial most commonly used by standards bodies, CRC-32-IEEE, was the result of a joint effort for theRome Laboratoryand the Air Force Electronic Systems Division by Joseph Hammond, James Brown and Shyan-Shiang Liu of theGeorgia Institute of Technologyand Kenneth Brayer of theMitre Corporation.The earliest known appearances of the 32-bit polynomial were in their 1975 publications: Technical Report 2956 by Brayer for Mitre, published in January and released for public dissemination throughDTICin August,[18]and Hammond, Brown and Liu's report for the Rome Laboratory, published in May.[19]Both reports contained contributions from the other team. During December 1975, Brayer and Hammond presented their work in a paper at the IEEE National Telecommunications Conference: the IEEE CRC-32 polynomial is the generating polynomial of aHamming codeand was selected for its error detection performance.[20]Even so, the Castagnoli CRC-32C polynomial used in iSCSI or SCTP matches its performance on messages from 58 bits to 131 kbits, and outperforms it in several size ranges including the two most common sizes of Internet packet.[16]TheITU-TG.hnstandard also uses CRC-32C to detect errors in the payload (although it uses CRC-16-CCITT forPHY headers).
CRC-32C computation is implemented in hardware as an operation (CRC32
) ofSSE4.2instruction set, first introduced inIntelprocessors'Nehalemmicroarchitecture.ARMAArch64architecture also provides hardware acceleration for both CRC-32 and CRC-32C operations.
Polynomial representations
[edit]The table below lists only the polynomials of the various algorithms in use. Variations of a particular protocol can impose pre-inversion, post-inversion and reversed bit ordering as described above. For example, the CRC32 used in Gzip and Bzip2 use the same polynomial, but Gzip employs reversed bit ordering, while Bzip2 does not.[14] Note that even parity polynomials inGF(2)with degree greater than 1 are never primitive. Even parity polynomial marked as primitive in this table represent a primitive polynomial multiplied by.The most significant bit of a polynomial is always 1, and is not shown in the hex representations.
Name | Uses | Polynomial representations | Parity[21] | Primitive[22] | Maximum bits of payload byHamming distance[23][16][22] | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Normal | Reversed | Reciprocal | Reversed reciprocal | ≥ 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2[24] | ||||
CRC-1 | most hardware; also known asparity bit | 0x1 | 0x1 | 0x1 | 0x1 | even | ||||||||||||||||
CRC-3-GSM | mobile networks[25] | 0x3 | 0x6 | 0x5 | 0x5 | odd | yes[26] | – | – | – | – | – | – | – | – | – | – | – | – | – | 4 | ∞ |
CRC-4-ITU | ITU-TG.704,p. 12 | 0x3 | 0xC | 0x9 | 0x9 | odd | ||||||||||||||||
CRC-5-EPC | Gen 2 RFID[27] | 0x09 | 0x12 | 0x05 | 0x14 | odd | ||||||||||||||||
CRC-5-ITU | ITU-TG.704,p. 9 | 0x15 | 0x15 | 0x0B | 0x1A | even | ||||||||||||||||
CRC-5-USB | USBtoken packets | 0x05 | 0x14 | 0x09 | 0x12 | odd | ||||||||||||||||
CRC-6-CDMA2000-A | mobile networks[28] | 0x27 | 0x39 | 0x33 | 0x33 | odd | ||||||||||||||||
CRC-6-CDMA2000-B | mobile networks[28] | 0x07 | 0x38 | 0x31 | 0x23 | even | ||||||||||||||||
CRC-6-DARC | Data Radio Channel[29] | 0x19 | 0x26 | 0x0D | 0x2C | even | ||||||||||||||||
CRC-6-GSM | mobile networks[25] | 0x2F | 0x3D | 0x3B | 0x37 | even | yes[30] | – | – | – | – | – | – | – | – | – | – | 1 | 1 | 25 | 25 | ∞ |
CRC-6-ITU | ITU-TG.704,p. 3 | 0x03 | 0x30 | 0x21 | 0x21 | odd | ||||||||||||||||
CRC-7 | telecom systems, ITU-TG.707,ITU-TG.832,MMC,SD | 0x09 | 0x48 | 0x11 | 0x44 | odd | ||||||||||||||||
CRC-7-MVB | Train Communication Network,IEC 60870-5[31] | 0x65 | 0x53 | 0x27 | 0x72 | odd | ||||||||||||||||
CRC-8 | DVB-S2[32] | 0xD5 | 0xAB | 0x57 | 0xEA[13] | even | no[33] | – | – | – | – | – | – | – | – | – | – | 2 | 2 | 85 | 85 | ∞ |
CRC-8-AUTOSAR | automotive integration,[34]OpenSafety[35] | 0x2F | 0xF4 | 0xE9 | 0x97[13] | even | yes[33] | – | – | – | – | – | – | – | – | – | – | 3 | 3 | 119 | 119 | ∞ |
CRC-8-Bluetooth | wireless connectivity[36] | 0xA7 | 0xE5 | 0xCB | 0xD3 | even | ||||||||||||||||
CRC-8-CCITT | ITU-TI.432.1 (02/99);ATMHEC,ISDNHEC and cell delineation,SMBus PEC | 0x07 | 0xE0 | 0xC1 | 0x83 | even | ||||||||||||||||
CRC-8-Dallas/Maxim | 1-Wirebus[37] | 0x31 | 0x8C | 0x19 | 0x98 | even | ||||||||||||||||
CRC-8-DARC | Data Radio Channel[29] | 0x39 | 0x9C | 0x39 | 0x9C | odd | ||||||||||||||||
CRC-8-GSM-B | mobile networks[25] | 0x49 | 0x92 | 0x25 | 0xA4 | even | ||||||||||||||||
CRC-8-SAE J1850 | AES3;OBD | 0x1D | 0xB8 | 0x71 | 0x8E | odd | ||||||||||||||||
CRC-8-WCDMA | mobile networks[28][38] | 0x9B | 0xD9 | 0xB3 | 0xCD[13] | even | ||||||||||||||||
CRC-10 | ATM; ITU-TI.610 | 0x233 | 0x331 | 0x263 | 0x319 | even | ||||||||||||||||
CRC-10-CDMA2000 | mobile networks[28] | 0x3D9 | 0x26F | 0x0DF | 0x3EC | even | ||||||||||||||||
CRC-10-GSM | mobile networks[25] | 0x175 | 0x2BA | 0x175 | 0x2BA | odd | ||||||||||||||||
CRC-11 | FlexRay[39] | 0x385 | 0x50E | 0x21D | 0x5C2 | even | ||||||||||||||||
CRC-12 | telecom systems[40][41] | 0x80F | 0xF01 | 0xE03 | 0xC07[13] | even | ||||||||||||||||
CRC-12-CDMA2000 | mobile networks[28] | 0xF13 | 0xC8F | 0x91F | 0xF89 | even | ||||||||||||||||
CRC-12-GSM | mobile networks[25] | 0xD31 | 0x8CB | 0x197 | 0xE98 | odd | ||||||||||||||||
CRC-13-BBC | Time signal,Radio teleswitch[42][43] | 0x1CF5 | 0x15E7 | 0x0BCF | 0x1E7A | even | ||||||||||||||||
CRC-14-DARC | Data Radio Channel[29] | 0x0805 | 0x2804 | 0x1009 | 0x2402 | even | ||||||||||||||||
CRC-14-GSM | mobile networks[25] | 0x202D | 0x2D01 | 0x1A03 | 0x3016 | even | ||||||||||||||||
CRC-15-CAN | 0xC599[44][45] | 0x4CD1 | 0x19A3 | 0x62CC | even | |||||||||||||||||
CRC-15-MPT1327 | [46] | 0x6815 | 0x540B | 0x2817 | 0x740A | odd | ||||||||||||||||
CRC-16-Chakravarty | Optimal for payloads ≤64 bits[31] | 0x2F15 | 0xA8F4 | 0x51E9 | 0x978A | odd | ||||||||||||||||
CRC-16-ARINC | ACARSapplications[47] | 0xA02B | 0xD405 | 0xA80B | 0xD015 | odd | ||||||||||||||||
CRC-16-CCITT | X.25,V.41,HDLCFCS,XMODEM,Bluetooth,PACTOR,SD,DigRF,many others; known asCRC-CCITT | 0x1021 | 0x8408 | 0x811 | 0x8810[13] | even | ||||||||||||||||
CRC-16-CDMA2000 | mobile networks[28] | 0xC867 | 0xE613 | 0xCC27 | 0xE433 | odd | ||||||||||||||||
CRC-16-DECT | cordless telephones[48] | 0x0589 | 0x91A0 | 0x2341 | 0x82C4 | even | ||||||||||||||||
CRC-16-T10-DIF | SCSIDIF | 0x8BB7[49] | 0xEDD1 | 0xDBA3 | 0xC5DB | odd | ||||||||||||||||
CRC-16-DNP | DNP,IEC 870,M-Bus | 0x3D65 | 0xA6BC | 0x4D79 | 0x9EB2 | even | ||||||||||||||||
CRC-16-IBM | Bisync,Modbus,USB,ANSIX3.28,SIA DC-07, many others; also known asCRC-16andCRC-16-ANSI | 0x8005 | 0xA001 | 0x4003 | 0xC002 | even | ||||||||||||||||
CRC-16-OpenSafety-A | safety fieldbus[35] | 0x5935 | 0xAC9A | 0x5935 | 0xAC9A[13] | odd | ||||||||||||||||
CRC-16-OpenSafety-B | safety fieldbus[35] | 0x755B | 0xDAAE | 0xB55D | 0xBAAD[13] | odd | ||||||||||||||||
CRC-16-Profibus | fieldbus networks[50] | 0x1DCF | 0xF3B8 | 0xE771 | 0x8EE7 | odd | ||||||||||||||||
Fletcher-16 | Used inAdler-32A & B Checksums | Often confused to be a CRC, but actually a checksum; seeFletcher's checksum | ||||||||||||||||||||
CRC-17-CAN | CAN FD[51] | 0x1685B | 0x1B42D | 0x1685B | 0x1B42D | even | ||||||||||||||||
CRC-21-CAN | CAN FD[51] | 0x102899 | 0x132281 | 0x064503 | 0x18144C | even | ||||||||||||||||
CRC-24 | FlexRay[39] | 0x5D6DCB | 0xD3B6BA | 0xA76D75 | 0xAEB6E5 | even | ||||||||||||||||
CRC-24-Radix-64 | OpenPGP,RTCM104v3 | 0x864CFB | 0xDF3261 | 0xBE64C3 | 0xC3267D | even | ||||||||||||||||
CRC-24-WCDMA | Used inOS-9 RTOS.Residue = 0x800FE3.[52] | 0x800063 | 0xC60001 | 0x8C0003 | 0xC00031 | even | yes[53] | – | – | – | – | – | – | – | – | – | – | 4 | 4 | 8388583 | 8388583 | ∞ |
CRC-30 | CDMA | 0x2030B9C7 | 0x38E74301 | 0x31CE8603 | 0x30185CE3 | even | ||||||||||||||||
CRC-32 | ISO3309 (HDLC),ANSIX3.66 (ADCCP),FIPSPUB 71, FED-STD-1003,ITU-T V.42,ISO/IEC/IEEE 802-3 (Ethernet),SATA,MPEG-2,PKZIP,Gzip,Bzip2,POSIXcksum,[54]PNG,[55]ZMODEM,many others | 0x04C11DB7 | 0xEDB88320 | 0xDB710641 | 0x82608EDB[16] | odd | yes | – | 10 | – | – | 12 | 21 | 34 | 57 | 91 | 171 | 268 | 2974 | 91607 | 4294967263 | ∞ |
CRC-32C(Castagnoli) | iSCSI,SCTP,G.hnpayload,SSE4.2,Btrfs,ext4,Ceph | 0x1EDC6F41 | 0x82F63B78 | 0x05EC76F1 | 0x8F6E37A0[16] | even | yes | 6 | – | 8 | – | 20 | – | 47 | – | 177 | – | 5243 | – | 2147483615 | – | ∞ |
CRC-32K(Koopman {1,3,28}) | Excellent at Ethernet frame length, poor performance with long files[citation needed] | 0x741B8CD7 | 0xEB31D82E | 0xD663B05D | 0xBA0DC66B[16] | even | no | 2 | – | 4 | – | 16 | – | 18 | – | 152 | – | 16360 | – | 114663 | – | ∞ |
CRC-32K2(Koopman {1,1,30}) | Excellent at Ethernet frame length, poor performance with long files[citation needed] | 0x32583499 | 0x992C1A4C | 0x32583499 | 0x992C1A4C[16] | even | no | – | – | 3 | – | 16 | – | 26 | – | 134 | – | 32738 | – | 65506 | – | ∞ |
CRC-32Q | aviation;AIXM[56] | 0x814141AB | 0xD5828281 | 0xAB050503 | 0xC0A0A0D5 | even | ||||||||||||||||
Adler-32 | Often confused to be a CRC, but actually a checksum; seeAdler-32 | |||||||||||||||||||||
CRC-40-GSM | GSM control channel[57][58][59] | 0x0004820009 | 0x9000412000 | 0x2000824001 | 0x8002410004 | even | ||||||||||||||||
CRC-64-ECMA | ECMA-182p. 51,XZ Utils | 0x42F0E1EBA9EA3693 | 0xC96C5795D7870F42 | 0x92D8AF2BAF0E1E85 | 0xA17870F5D4F51B49 | even | ||||||||||||||||
CRC-64-ISO | ISO 3309 (HDLC),Swiss-Prot/TrEMBL;considered weak for hashing[60] | 0x000000000000001B | 0xD800000000000000 | 0xB000000000000001 | 0x800000000000000D | odd | ||||||||||||||||
Implementations
[edit]- Implementation of CRC32 in GNU Radio up to 3.6.1 (ca. 2012)
- C class code for CRC checksum calculation with many different CRCs to choose from
CRC catalogues
[edit]See also
[edit]- Checksum
- Computation of cyclic redundancy checks
- Information security
- List of checksum algorithms
- List of hash functions
- LRC
- Mathematics of cyclic redundancy checks
- Simple file verification
References
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Cyclic Redundancy Check (CRC) mechanism is used to protect the data and provide protection of integrity from error bits when data is transmitted from sender to receiver.
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Cyclic Redundancy Check (CRC) is an efficient method to ensure a low probability of undetected errors in data transmission using a checksum as a result of polynomial division.
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Further reading
[edit]- Warren Jr., Henry S. (2013)."14. Cyclic Redundancy Check".Hacker's Delight(2nd ed.).Addison Wesley.pp. 319–330.ISBN978-0-321-84268-8.
- Koopman, Philip (2024).Understanding Checksums and Cyclic Redundancy Checks.ASINB0CVXWDZ99.
External links
[edit]- Mitra, Jubin; Nayak, Tapan (January 2017). "Reconfigurable very high throughput low latency VLSI (FPGA) design architecture of CRC 32".Integration, the VLSI Journal.56:1–14.doi:10.1016/j.vlsi.2016.09.005.
- Cyclic Redundancy Checks,MathPages, overview of error-detection of different polynomials
- Williams, Ross(1993)."A Painless Guide to CRC Error Detection Algorithms".Archived fromthe originalon 3 September 2011.Retrieved15 August2011.
- Black, Richard (1994)."Fast CRC32 in Software".The Blue Book.Systems Research Group, Computer Laboratory, University of Cambridge.Algorithm 4 was used in Linux and Bzip2.
- Kounavis, M.; Berry, F. (2005)."A Systematic Approach to Building High Performance, Software-based, CRC generators"(PDF).Intel.Archived(PDF)from the original on 16 December 2006.Retrieved4 February2007.,Slicing-by-4 and slicing-by-8 algorithms
- Kowalk, W. (August 2006)."CRC Cyclic Redundancy Check Analysing and Correcting Errors"(PDF).Universität Oldenburg.Archived(PDF)from the original on 11 June 2007.Retrieved1 September2006.— Bitfilters
- Warren, Henry S. Jr."Cyclic Redundancy Check"(PDF).Hacker's Delight.Archived fromthe original(PDF)on 3 May 2015.— theory, practice, hardware, and software with emphasis on CRC-32.
- Reverse-Engineering a CRC AlgorithmArchived7 August 2011 at theWayback Machine
- Cook, Greg."Catalogue of parameterised CRC algorithms".CRC RevEng.Archivedfrom the original on 1 August 2020.Retrieved18 September2020.
- Koopman, Phil."Blog: Checksum and CRC Central".— includes links to PDFs giving 16 and 32-bit CRCHamming distances
- — (April 2023)."Why Life Critical Networks Tend To Provide HD=6".
- Koopman, Philip; Driscoll, Kevin; Hall, Brendan (March 2015)."Cyclic Redundancy Code and Checksum Algorithms to Ensure Critical Data Integrity"(PDF).Federal Aviation Administration. DOT/FAA/TC-14/49.Archived(PDF)from the original on 18 May 2015.Retrieved9 May2015.
- Koopman, Philip (January 2023).Mechanics of Cyclic Redundancy Check Calculations– via YouTube.