A sophisticated checksum (often abbreviated CRC), which is based on the algebra of polynomials over the integers (mod 2). It is substantially
more reliable in detecting transmission errors, and is one common error-checking
protocol used in modems. The CRC is a form of hash function.

To compare large data blocks using the CRC, first precalculate the CRCs for each block. Two blocks can then be rapidly compared by seeing if their CRCs are equal,
saving a great deal of calculation time in most cases. The method is not infallible
since for an -bit
checksum,
of random blocks will have the same checksum for inequivalent data blocks. However,
if
is large, the probability that two inequivalent blocks have the same CRC can be made
very small.