CRCs

Cyclic redundancy checks (CRCs) are error-detecting codes used to identify accidental changes to digital data. They are widely used in networks and storage systems to verify integrity of frames, packets, or blocks. A CRC is derived from the data using a fixed polynomial and a set of parameters.

In the CRC calculation, the data is treated as a binary polynomial. It is divided by a fixed generator polynomial over GF(2). The nonzero remainder is appended to the data before transmission. On reception, the same division is performed; a zero remainder indicates no detectable error.

CRCs are particularly effective at detecting common error patterns. They can detect all single-bit and most burst errors, and any odd number of bit errors with appropriate polynomials. The exact detection capabilities depend on the chosen generator polynomial and initialization/finalization settings.

Several standard CRCs exist, differing in generator polynomial and parameters. Common ones include CRC-32 (used in Ethernet and PNG), CRC-16-CCITT and CRC-16-IBM, and CRC-8 variants. Implementations may use bitwise computation or lookup tables to improve performance.

CRCs are not cryptographic hash functions and do not provide security against intentional tampering. They detect accidental corruption well but are vulnerable to deliberate modification if not paired with other integrity measures. They are widely used in data transmission, storage formats, and file checksums.