Computation of cyclic redundancy checks

Overview of the computation of cyclic redundancy checks

Computation of a cyclic redundancy check is derived from the mathematics of polynomial division, modulo two. In practice, it resembles long division of the binary message string, with a fixed number of zeroes appended, by the "generator polynomial" string except that exclusive or operations replace subtractions. Division of this type is efficiently realised in hardware by a modified shift register, and in software by a series of equivalent algorithms, starting with simple code close to the mathematics and becoming faster through byte-wise parallelism and space–time tradeoffs.

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