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Synopsis

spoof will assist you in modifying a message to make the CRC of that message equal to any desired value. spoof does not need the message itself, but just the length of the message, the exclusive-or of the message's current CRC and the desired new CRC, and a set of bit locations in the message to potentially modify. spoof will then deliver a subset of those locations whose bits should be inverted. The modified message will then have the desired CRC.

flip takes the output from spoof and flips the specified bits in the provided file.

ruse will modify a small number of bits in a file such that the specified CRC of the file is unchanged. The least number of bits possible will be changed, starting at a randomly chosen location in the file. To do this, ruse uses a provided dictionary of CRC codewords in the file codewords.txt, pulled from the work of Philip Koopman, which he makes available online. If the specified CRC is not covered in codewords.txt, then the CRC polynomial is used as the codeword.

Motivation

The purpose of spoof is to illustrate the extremely non-cryptographic nature of a Cyclic Redundancy Check (CRC) as a signature. Since a CRC is a linear operation on the message, it is easy to invert the operation to construct messages with any desired CRC. spoof runs in O(log(n)) time, where n is the length of the message. Similarly, ruse applies codewords found through brute-force searches for bit patterns that leave CRCs with given polynomials unchanged.

Installation

Compile and link spoof.c and fline.c with a standard C99 compiler, compile and link flip.c also with C99, and compile ruse.cc with a standard C++11 compiler. spoof.c is a command-line program that takes input from stdin and produces output on stdout. flip takes spoof's output from stdin, and flips bits in the named file. ruse is a command-line program that modifies the named file. The instructions for each are near the start of the respective source files.

Test

This spoof input, specifying a 4-bit CRC with polynomial x4+x+1 reflected, an exclusive-or of the current and desired CRC of 1111, a message length of 89 (decimal) bytes, and four candidate bit locations to change in byte offset and bit number:

4 3 1
f 89
37 0
41 0
45 0
49 0

will produce this output:

invert these bits in the sequence:
offset bit
    41 0

applying the spoof output to a file:

./spoof < spoof.input | flip tothisfile.txt

This ruse command:

./ruse 32 4c11db7 1 file

will modify some number of bits in file, leaving the standard CRC-32 unchanged. The script getcodes can be used to pull the latest codewords from Philip Koopman's website:

./getcodes > codewords.txt

License

This code is under the zlib license, permitting free commercial use.

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Modify a message to have a desired CRC signature.

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