CRC RevEng

CRC RevEng

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README for CRC RevEng 1.5.1

CRC RevEng: arbitrary-precision CRC calculator and algorithm finder
Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017 Gregory Cook

This file is part of CRC RevEng.

CRC RevEng is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

CRC RevEng is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with CRC RevEng. If not, see <https://www.gnu.org/licenses/>.

THIRD-PARTY SOFTWARE

CRC RevEng incorporates source code from ASPEX under the terms of version 3 of the GNU General Public License (GPLv3). ASPEX is:

Copyright (C) 1998, 2003 by David A. Hinds -- All Rights Reserved

Homepage: <http://aspex.sourceforge.net/>

ASPEX is licensed under version 2 and all later versions of the GNU General Public License, therefore CRC RevEng remains licensed under version 3 and all later versions.

Depending on one's interpretation of the License, the author created a modified copy of ASPEX as a whole by extracting files getopt.c and getopt.h verbatim on 19 December 2010. These are found in the contrib/ directory. A compatible getopt module is available as standard in many environments and will work just as well, but this copy is included for those ANSI C environments that lack one.

A copy of the RISC OS Shared C Library (CLib), and a patch to make certain versions of RISC OS compatible with this version of CLib, are supplied with the RISC OS binary under licence from Castle Technology Limited for distribution to end users for the purpose of upgrading, if required. These are found in the bin/riscos/ directory. The ARM Tube OS binary, located in the bin/armtubeos/ directory, is statically linked with (that is, it incorporates) the RISC OS Shared C Library. CLib qualifies as a "System Library" and GPLv3 permits licensees to "combine GPLed software with GPL-incompatible System Libraries, [...] and distribute them both together." See Sections 1, 5 and 6 and A Quick Guide to GPLv3, <https://www.gnu.org/licenses/quick-guide-gplv3.html> The patch is an independent program and is not bound by GPLv3 by mere inclusion. See Section 5.

CRC REVENG

CRC RevEng is an arbitrary-precision, machine word length-independent, byte order-independent CRC calculator and algorithm finder in ANSI C. It is a port and expansion of the author's crcbfs.pl script from 2007, and runs up to 200 times faster on equivalent problems. It is also a reference implementation of the author's "Catalogue of parametrised CRC algorithms", with the 99 currently listed models available as presets.

To the author's knowledge CRC RevEng is the first published compiled application to address the general case of CRC algorithm reversal and reverse engineering, its predecessor crcbfs.pl being the first published application of any type to do so. Greg Ewing of Canterbury University in New Zealand solved a CRC algorithm manually on similar principles in 2010, but partly by feeding chosen plaintexts into an implementation at hand.

CRC RevEng is hosted by SourceForge, from where the latest version can be downloaded and documentation browsed:

        <http://reveng.sourceforge.net/>

COMPILING

Compiling CRC RevEng is straightforward: in the i386 GNU/Linux, MinGW and Raspbian environments, simply cd to the directory containing the source files, and enter

        make

A special makefile can also be used in MinGW to make a Windows executable with version information and an icon:

        make -f Mk.Win32

In RISC OS, with the Acorn Desktop Development Environment (DDE) installed, click Menu on the file RISCOSify, and set its type to Obey. Double-click Select first on RISCOSify, then on Mk/RISCOS.

In non-ASCII compatible environments, the array aliases[] in file preset.c may need to be reordered to suit the local string collation order. The correct order of models[] and aliases[] can be verified at compile time by the error-free completion of this command:

        make clean pretst

Otherwise, enter commands similar to the following to compile CRC RevEng on any ANSI C compliant compiler:

        gcc -O3 -Wall -ansi -c bmpbit.c cli.c model.c poly.c preset.c \
                reveng.c
        cd contrib
        gcc -O3 -Wall -ansi -c getopt.c
        cd ..
        gcc -o reveng bmpbit.o cli.o model.o poly.o preset.o reveng.o \
                contrib/getopt.o

The platform-independent method does not compile the preset models. To compile them, you will need to edit the configuration options in config.h to suit your architecture. Having done so, define the macro PRESETS in config.h and recompile as above.

Some enterprise users may wish to disable the -F switch to minimise CPU usage. To do this, define the macro NOFORCE in config.h or on the command line.

SYNOPSIS

Usage:  reveng  -cdDesvhu? [-bBfFGlLMrStVXyz]
                [-a BITS] [-A OBITS] [-i INIT] [-k KPOLY] [-m MODEL]
                [-p POLY] [-P RPOLY] [-q QPOLY] [-w WIDTH] [-x XOROUT]
                [STRING...]
Options:
        -a BITS         bits per character (1 to n)
        -A OBITS        bits per output character (1 to n)
        -i INIT         initial register value
        -k KPOLY        generator in Koopman notation (implies WIDTH)
        -m MODEL        preset CRC algorithm
        -p POLY         generator or search range start polynomial
        -P RPOLY        reversed generator polynomial (implies WIDTH)
        -q QPOLY        search range end polynomial
        -w WIDTH        register size, in bits
        -x XOROUT       final register XOR value
Modifier switches:
        -b big-endian CRC               -B big-endian CRC output
        -f read files named in STRINGs  -F skip preset model check pass
        -G skip brute force search pass -l little-endian CRC
        -L little-endian CRC output     -M non-augmenting algorithm
        -r right-justified output       -S print spaces between characters
        -t left-justified output        -V reverse algorithm only
        -X print uppercase hexadecimal  -y low bytes first in files
        -z raw binary STRINGs
Mode switches:
        -c calculate CRCs               -d dump algorithm parameters
        -D list preset algorithms       -e echo (and reformat) input
        -s search for algorithm         -v calculate reversed CRCs
        -h | -u | -? show this help

SPECIFYING A MODEL

You can use one of the preset models or specify your own.

        reveng -m crc-32

selects the CRC-32 algorithm used in PKZIP and elsewhere. You can dump any preset model as an extended Williams model record using -d:

        reveng -m crc-32 -d
        width=32  poly=0x04c11db7  init=0xffffffff  refin=true
        refout=true  xorout=0xffffffff  check=0xcbf43926
        residue=0xdebb20e3  name="CRC-32"

You can specify the parameters of the model instead:

        reveng -w 32 -p 04c11db7 -i ffffffff -l -x ffffffff

This is equivalent to

        reveng -m crc-32

except the model will have no name when dumped. (The -l switch sets both RefIn = True and RefOut = True. To set RefOut separately, use switches -L and -B.)

The options and switches for specifying a model are:

-b
Big-endian input and output (RefIn = False, RefOut = False). Implies -B and -r. This is the default.
-B
Big-endian output (RefOut = False). Implies -r.
-i INIT
A hexadecimal digit string specifying the initial value to set in the shift register before computing the CRC.
The width must be specified with -k, -m, -P or -w before -i.
-k KPOLY
The generator polynomial (see -p), written in the hexadecimal, reversed-reciprocal notation found in Philip Koopman's papers. The highest-order term is included and the lowest-order term is omitted, shifting the other terms to the right. Thus 0x18005 is specified as C002. This automatically provides the Width value.
-l
Little-endian input and output (RefIn = True, RefOut = True). Implies -L and -t.
-L
Little-endian output (RefOut = True). Implies -t.
-M
Specifies that the algorithm does not multiply the message polynomial by xn before division. The resulting algorithm does not comply with the Williams model, and cannot be dumped with -d.
-m MODEL
Set the Width, Poly, Init, RefIn, RefOut and XorOut values to the preset named MODEL. MODEL is matched case-insensitively with the Name and Alias fields in the author's "Catalogue of parametrised CRC algorithms", as of the date of this release. The preset models can be listed with -D.
-M, -r, -S, -t, -X, -y and -z must not precede -m MODEL.
-p POLY
The Poly value, that is, the generator polynomial that sets the feedback tap positions of the shift register. POLY is written in the hexadecimal, direct notation found in MSB-first code. The highest-order term is omitted, thus 0x18005 is specified as 8005.
-p also sets the start of the range for polynomial range searching, see -q.
The width must be specified with -k, -m, -P or -w before -p.
-P RPOLY
The generator polynomial (see -p), written in the hexadecimal, reversed notation found in LSB-first code. The highest-order term is omitted before reversal, thus 0x18005 is specified as A001. This automatically provides the Width value.
-V
Reverse the current model. If RefOut = True, the Init value is reversed otherwise the XorOut value is reversed. Then the Init and XorOut values are swapped, the generator polynomial is reciprocated and the RefIn and RefOut values are negated.
This switch is distinct from -v, see below.
-w WIDTH
The width, that is, the number of bits in the shift register.
-x XOROUT
A hexadecimal digit string specifying the value to be added to the final shift register value before output.
The width must be specified with -k, -m, -P or -w before -x.

Other model-related options:

-d
Dump an extended Williams model record of the specified model on standard output. Though formatted differently, this single-line record has identical semantics to the multi-line records presented in "A Painless Guide to CRC Error Detection Algorithms", with the addition of a Residue field. Disabled for the non-compliant models created by -M.
-D
Dump extended Williams model records of all preset models on standard output.

INPUT AND OUTPUT

Messages for CRC RevEng to process can be specified as files, as raw binary strings, or as numerical (typically hexadecimal) string arguments on the command line. Output from CRC RevEng is either as extended Williams model records (having their own fixed format) or as numerical string arguments printed one per line on standard output.

When passing numerical arguments on the command line, each argument is conceptually divided into characters, each character consisting of one or more hexadecimal digits. For each character, enough hex digits to specify it are read then a number of bits (specified by the -a option) are taken from the least significant end, reversed (if RefIn = True) and appended to the binary representation of the argument; any excess bits are discarded. The -a option (q.v.) permits a number of useful representations of a given underlying binary sequence.

When passing messages as files or as raw binary strings, the same division into characters applies; bytes of the message are read until enough bits have been collected, then a specified number of bits are taken from the specified least significant end of the collection (see -y), reflected (if RefIn = True) and added to the binary representation.

When printing CRCs, the binary representation is again divided into characters, each of which is reversed (if RefOut = True) and printed with the minimum sufficient number of hex digits.

Output model records conform to the Williams model set out in "A Painless Guide to CRC Error Detection Algorithms". To recap, the model consists of a linear feedback shift register (LFSR) having the number of cells defined in the width parameter, and shifting from right to left. The init parameter defines the settings of the bit cells at the start of each calculation, before reading the first message bit. The refin parameter, if equal to false, specifies that the characters of the message (whose size is specified by -a) are read bit-by-bit, most significant bit (MSB) first; if equal to true, the characters are read bit-by-bit, least significant bit (LSB) first. Each sampled message bit is then XORed with the bit being simultaneously shifted out of the register at the most significant end. The poly parameter specifies the feedback taps of the register – it is the result of initialising the register to all zeroes, then reading a single one bit.

The refout parameter, if equal to false, specifies that the contents of the register after reading the last message bit are unreflected before presentation; if equal to true, it specifies that they are reflected, character-by-character, before presentation. For the purpose of this definition, the reflection is performed by swapping the content of each cell with that of the cell an equal distance from the opposite end of the register; CRC output characters are then true images of parts of the reflected register. The xorout parameter defines the XOR value applied to the contents of the register after the last message bit has been read and after the optional reflection. The check parameter defines the contents of the register after initialising, reading the UTF-8 string "123456789" (as 8-bit characters), optionally reflecting, and applying the final XOR. The residue parameter defines the contents of the register after initialising, reading an error-free codeword and optionally reflecting the register, but not applying the final XOR. This is mathematically equivalent to initialising the register with the xorout parameter, reflecting it as described (if refout=true), calculating a CRC on a message of as many zero bits as there are cells in the register, and reflecting the result (if refin=true). The residue of a crossed-endian model is calculated assuming that the characters of the received CRC are specially reflected before submitting the codeword.

width is printed as a decimal integer. poly, init, xorout, check and residue are true images of the shift register at various times, printed as hexadecimal integers. refin and refout are Boolean values, displayed as either "true" or "false". The name parameter is the name assigned to a preset model, enclosed in double quotes, otherwise "(none)" (without quotes).

INPUT/OUTPUT OPTIONS

There are a few more options for controlling the presentation of input and output:

-a BITS
Specifies the number of bits per character in input and output. Implies -A BITS. Raw input messages are selected by -f or -z, otherwise messages are numerical arguments. Particular values of BITS cause the input to be interpreted as a sequence of:
-a 16
16-bit words, raw or as quartets of hex digits. When RefIn or RefOut are True, this is equivalent to swapping the bytes of each pair before input to an 8-bit calculator.
-a 8
8-bit characters, raw or as pairs of hex digits. This is the default.
-a 7
7-bit characters, one per 8-bit byte (raw) or as pairs of hex digits.
-a 4
Single hex digits (numerical arguments only).
-a 3
Single octal digits 0–7.
-a 1
Single binary digits 0–1.
Note that raw messages (files or arguments) consisting of digits will only be read as digit values if there are no characters except digits (not even a final newline or other whitespace), and if the digits are maskable in the system character encoding, as digits 0–9 are in ASCII, EBCDIC and Unicode. This is because the lowest bits of each byte are extracted as described above.
-A OBITS
Specifies the number of bits per character in output.
-f
Arguments are file names; input binary messages from the file data.
-r
Right-justified output. If a binary output message does not consist of a whole number of characters, this switch arranges for padding zeroes to be added to the start of the message. The padding will appear in the MSB of the first character (RefOut = False) or the LSB of the first character (RefOut = True). -r is the default when RefOut = False.
-S
Print spaces between the characters of the output string(s).
-t
Left-justified output. If a binary output message does not consist of a whole number of characters, this switch arranges for padding zeroes to be added to the end of the message. The padding will appear in the LSB of the last character (RefOut = False) or the MSB of the last character (RefOut = True). -t is the default when RefOut = True.
-X
Print uppercase hexadecimal characters.
-y
When reading binary messages from files or arguments, and the -a option is more than 8, this option specifies that the first byte of each character contains the LSB.
-z
Arguments are raw binary strings; input binary messages from the arguments.

CALCULATING AND REVERSING CRCs

When a model has been specified, use -c or -v to calculate CRCs for input messages.

-c
Calculate a CRC for each argument and print it on standard output, one per line.
-v
Reverse the current model (as for -V) AND the order of characters in each argument, calculate a CRC for each reversed argument, reverse the order of characters in each CRC and print it on standard output, one per line.

If -V and -v are given together, their respective model reversals cancel out. CRC RevEng then calculates an ordinary CRC for each argument, processing the characters from right to left and likewise emitting the CRC characters in reverse order.
Correspondingly, to obtain the same effect as -v using a model reversed by -V, the user must present the characters of his or her message, and process those of the returned CRC, in reverse order.

Take care when the CRC width (-w) is not a multiple of the character width (-a). If the result of a calculation is not what you expect, try selecting left-justification (with -t) or right-justification (with -r).

The -c mode is, of course, useful for creating a checksum to append to a message so that the combination will pass a particular CRC check. The -v mode, on the other hand, is useful for editing a message so as to force its checksum to a desired or at least predetermined value. In order to do this there must be some part of the message's data that can be modified freely without observable effect; many network protocols and file formats, including executables, images and word processor documents, have (or can be altered to have) reserved fields or comment sections that cannot be easily viewed, and whose contents are entirely ignored.

Among the simplest ways to control a CRC calculation is to find one such unused space that is both contiguous and large enough to hold a checksum. For example, suppose we have an existing message with an X.25 CRC:

  0: 44 6F 67 73 2F 2A 12 34  2A 2F 72 6F 63 6B 4E 47 | Dogs/*.4*/rockNG

Here, 4E 47 is the X.25 checksum, and we wish to alter the message without either changing the checksum or failing the CRC. We notice that the 7th and 8th bytes can be replaced at will, and these can contain a calculated value to force the CRC. Firstly we change the text as we wish:

  0: 43 61 74 73 2F 2A 12 34  2A 2F 72 75 6C 65 4E 47 | Cats/*.4*/ruleNG

Calculate the CRC of the part on the left of the unused space with XorOut = 0:

        reveng -m x-25 -x 0 -c 436174732f2a
        9dc5

Then reverse-calculate the CRC of the part on the right, including the old CRC, with Init = 0:

        reveng -m x-25 -i 0 -v 2a2f72756c654e47
        1505

Now exclusive-OR the two returned CRCs together, and insert the result in the unused space. CRC RevEng can be used to do the exclusive-OR if a hex calculator is not to hand:

        reveng -w 16 -p 0001 -c 9dc51505
        88c0

Our edited message now looks like this:

  0: 43 61 74 73 2F 2A 88 C0  2A 2F 72 75 6C 65 4E 47 | Cats/*.A*/ruleNG

To confirm that it still passes the X.25 CRC:

        reveng -m x-25 -c 436174732f2a88c02a2f72756c65
        4e47

For more flexible editing options, see Mark Adler's source file spoof.c (2014). "spoof.c takes an abbreviated description of the CRC, the exclusive-or of the current CRC of the message and the desired CRC, the length of the message, and a list of bit locations in a message, and tells you which of those bits should be inverted in the message to get the desired CRC. Note that it does not need the message itself, due to the linearity property of CRCs."

* * *

In Stigge et al. (section 4.1) a polynomial q(x) is calculated as the multiplicative inverse of xN such that (xN) q(x) = 1 (mod pCRC(x)). The authors promote the extended Euclidean algorithm as a means of calculating q(x), however any CRC calculator can also produce it. The reciprocal of the CRC-32 polynomial is 0xdb710641, as output by:

        reveng -w 32 -p 04c11db7 -V -d

The authors' constant CRCINV, a reflected representation of q(x), is the CRC of the reversal of the desired remainder, 0x00000001:

        reveng -w 32 -p db710641 -c 80000000
        5b358fd3

Equivalently, the -v function returns q(x) in direct order from the unreflected parameters:

        reveng -w 32 -p 04c11db7 -v 00000001
        cbf1acda

SEARCHING FOR CRC MODELS

The most important feature of CRC RevEng is the ability to recover the parameters of a CRC algorithm from a handful of codewords created by that algorithm. In general at least four data points are needed, either as known parameters or as message-CRC pairs. Extra data points help to eliminate false results and to confirm models that are found.

Known parameters are specified using -w, -p, -i and -x (see SPECIFYING A MODEL above). The width, -w, is a required parameter for all searches and counts as one of the data points. The size of characters (words) in the protocol must also be known and set with -a if this is not 8 bits.

The search function is selected with -s, and message-CRC pairs are given as arguments, each message and CRC combined into one argument. There must not be any non-participating characters between each message and its CRC, or the search will not work. Typically, end-of-message markers do not participate in the CRC.

As non-standard algorithms are comparatively rare, the program first tries all the preset models of the given width, reporting and exiting if one is found. Otherwise it commences a full search. As it proceeds it prints a progress message from time to time, allowing the search to be restarted from that point:

        reveng: searching: width=32  poly=0x50000001  refin=false
        refout=false

If -b or -l are specified, CRC RevEng only searches for algorithms with that bit ordering. Otherwise, it tries RefIn = False, RefOut = False then RefIn = True, RefOut = True. Crossed-endian algorithms are also uncommon and the program will not search for them.

To find the Poly value when Init is not known, at least two arguments must have the same length.

To find both the Init and XorOut values, at least two arguments must have different lengths; otherwise there is only enough information to determine one value, given the other. If all arguments have the same length then, by default, CRC RevEng fixes XorOut at zero and calculates Init accordingly. (In hardware it is easier to set a non-zero Init than to apply a non-zero XorOut.) To set XorOut to another value, specify -x XOROUT; to fix Init and calculate XorOut instead, use -i INIT.

When bit strings are input with -a 1, there is no information on endianness. In such cases -s returns the big- and little-endian forms of each algorithm found. The Check values of these forms will differ, as they are always calculated on the 8-bit UTF-8 string "123456789".

POLYNOMIAL RANGE SEARCHING

To restart a stopped search, or to divide a search between several processors, CRC RevEng can be instructed to search within a specified range of generator polynomial values.

The full search space comprises all 'odd' polynomials of the specified WIDTH, that is, polynomials of the form xn + ... + 1. Treating the concatenated coefficients as a binary integer, the range can be up to (but excluding) a specified polynomial, from a specified polynomial upwards, or from one polynomial up to (but excluding) another.

Polynomial range searching is enabled using [-p POLY] -q QPOLY, where POLY and QPOLY are hex strings. -p POLY, if given, must precede -q QPOLY. To start searching at a polynomial, use -p POLY -q 0. To stop searching at a polynomial (exclusive), use -q QPOLY. To search between two polynomial values, use -p POLY -q QPOLY.

Range limiting does not apply to the initial check against the preset models, or to Init or XorOut values, which are computed using a fast, efficient algorithm.

For example, to split a 32-bit search into four processes:

        reveng -w 32 -q 40000000 -s c98964f6b9 a5fa49f2fd 13370aee7df0
        reveng -w 32 -p 40000000 -q 80000000 \
                -s c98964f6b9 a5fa49f2fd 13370aee7df0
        reveng -w 32 -p 80000000 -q c0000000 \
                -s c98964f6b9 a5fa49f2fd 13370aee7df0
        reveng -w 32 -p c0000000 -q 0 \
                -s c98964f6b9 a5fa49f2fd 13370aee7df0

To continue an interrupted search:
NB: If an either-endian search is stopped while RefIn/RefOut = False then it takes two further command lines to complete the search: one big-endian range search, and one little-endian full search.

        reveng -w 32 -p 50000001 -q 0 -b \
                -s c98964f6b9 a5fa49f2fd 13370aee7df0
        reveng -w 32 -l -s c98964f6b9 a5fa49f2fd 13370aee7df0

The full list of search options is as follows:

-F
Skip the preset model check pass. (Not recommended.)
-G
Skip the brute force search pass. Ignored if a generator polynomial has been specified, so that the brute force search pass may return results on the polynomial.
-p POLY
When followed by -q QPOLY, sets the start of the range (inclusive) for polynomial range searching. POLY is written in hexadecimal direct notation. The LSB is forced to 1 as only 'odd' polynomials, with a +1 term, are tested.
-q QPOLY
Enables polynomial range searching and sets the end of the range (exclusive). A previous -p POLY is no longer treated as a known generator polynomial and is taken as the start of the range; if there is no previous -p POLY, the start of the range defaults to the lowest odd polynomial.
QPOLY is written in hexadecimal direct notation. If QPOLY is zero, the range extends up to (and including) the highest odd polynomial. Unlike -p POLY, the LSB is significant.
-s
Search for and display Williams model records of CRC models matching the arguments and given parameters.

OTHER FEATURES

CRC RevEng provides a few additional options for convenience:

-e
Echo arguments to standard output. Useful to check that files are being read correctly and, together with -a, -A, -b, -B, -l, -L, -r, -S, -t, -X and -y, to reformat argument strings.
The Init value is exclusive-ORed with the beginning of each argument, so that when the argument is not a whole number of bytes long, an equivalent string can be produced for input to a bytewise calculator (which has Init set to 0).
-h
-u
-?
Print a summary of options and switches to standard error, and exit.

SEARCH EXAMPLES

        reveng -w 16 -l -F -s 31816b 32c16a 31326a0a
        reveng -w 32 -p 04c11db7 -l -s c98964f6b9 a5fa49f2fd 13370aee7df0
        reveng -w 32 -l -s c98964f6b9 a5fa49f2fd 13370aee7df0

A comprehensive list is being compiled.

CAVEATS

In addition to the disclaimers listed at the top of this file and in the GNU General Public License (see file COPYING), remember that CRC RevEng is merely a search tool, and not authoritative. Searching is only statistical and any particular result may be a fluke, especially from a small number of samples. Also any output is only as accurate as the input.

Model reversal (-V, -v) makes little sense on crossed-endian models.

CRC RevEng lacks a facility to generate code to implement specified algorithms. Pycrc by Thomas Pircher (2014) is one suitable code generator; Mark Adler's crcany source package (2014) also produces source code when compiled and run, and references the author's CRC catalogue.

REFERENCES

Adler, Mark (15 January 2017). "zlib Home Site" (section "CRC (Cyclic Redundancy Check) Bonus Information"). Contains links to spoof.c.gz and crcany.tar.gz.

Bies, Lammert; et al. "Computer Interfacing Forum" (section "Error detection and correction").

Cook, Greg (6 February 2017). "Catalogue of parametrised CRC algorithms".

Ewing, Gregory C. (March 2010). "Reverse-Engineering a CRC Algorithm". Christchurch: University of Canterbury.

Koopman, Philip (July 2002). "32-Bit Cyclic Redundancy Codes for Internet Applications". The International Conference on Dependable Systems and Networks: 459–468. doi:10.1109/DSN.2002.1028931.

Koopman, Philip (23 January 2017). "Best CRC Polynomials". Pittsburgh: Carnegie Mellon University.

Koopman, Philip; Chakravarty, Tridib (June 2004). "Cyclic Redundancy Code (CRC) Polynomial Selection For Embedded Networks". The International Conference on Dependable Systems and Networks: 145–154. doi:10.1109/DSN.2004.1311885.

Pircher, Thomas (12 December 2016). pycrc. Python based parametrised CRC calculator and C code generator.

Stigge, Martin; Plötz, Henryk; Müller, Wolf; Redlich, Jens-Peter (May 2006). "Reversing CRC – Theory and Practice". Berlin: Humboldt University Berlin.

Williams, Ross N. (24 September 1996). "A Painless Guide to CRC Error Detection Algorithms V3.00".

INSPIRATION

CRC RevEng came about from the coincidence of four events:

THANKS

The author would like to thank Dr. Mark Adler, Lammert Bies, Wolfgang Ehrhardt, Greg Ewing, Prof. Philip Koopman, Thomas Pircher, Dr. Ross Williams, and all contributors to CRC RevEng and the CRC Catalogue.

AUTHOR

Greg Cook
<[email address]>
<http://regregex.bbcmicro.net/>

–END–


Greg Cook, [email address]
http://reveng.sourceforge.net/readme.htm Last updated 19 February 2017

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