Cyclic redundancy check
<algorithm> (CRC or "cyclic redundancy code") A number derived from, and stored or transmitted with, a block of data in order to detect corruption.
By recalculating the CRC and comparing it to the value originally transmitted, the receiver can detect some types of transmission errors.
A CRC is more complicated than a checksum.
It is calculated using division either using shifts and exclusive ORs or table lookup (modulo 256 or 65536).
The CRC is "redundant" in that it adds no information.
A single corrupted bit in the data will result in a one bit change in the calculated CRC but multiple corrupted bits may cancel each other out.
CRCs treat blocks of input bits as coefficient-sets for polynomials.
E.g., binary 10100000 implies the polynomial: 1*x^7 + 0*x^6 + 1*x^5 + 0*x^4 + 0*x^3 + 0*x^2 + 0*x^1 + 0*x^0. This is the "message polynomial".
A second polynomial, with constant coefficients, is called the "generator polynomial". This is divided into the message polynomial, giving a quotient and remainder.
The coefficients of the remainder form the bits of the final CRC.
So, an order-33 generator polynomial is necessary to generate a 32-bit CRC.
The exact bit-set used for the generator polynomial will naturally affect the CRC that is computed.
Most CRC implementations seem to operate 8 bits at a time by building a table of 256 entries, representing all 256 possible 8-bit byte combinations, and determining the effect that each byte will have.
CRCs are then computed using an input byte to select a 16- or 32-bit value from the table.
This value is then used to update the CRC.
Ethernet packets have a 32-bit CRC.
Many disk formats include a CRC at some level.
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