CRC-32 Hash Generator

About

A cyclic redundancy check, or CRC, is a code used to detect accidental changes to digital data. Blocks of data entering a system are given a short check value, based on the remainder of a polynomial division of their contents. When the data is retrieved, the calculation is repeated, and if the check values do not match, corrective action can be taken against data corruption. CRCs can also be used for error correction.

CRC stands for cyclic redundancy check. It is a popular error-detection method used in digital networks and storage devices. The check value is a redundancy that expands the message without adding information, and the algorithm is based on cyclic codes. CRCs are particularly good at detecting common errors caused by noise in transmission channels. The check value has a fixed length, so the function that generates it can be used as a hash function.

CRCs are based on the theory of cyclic error-correcting codes. The use of systematic cyclic codes, which encode messages by adding a fixed-length check value, for the purpose of error detection in communication networks, was first proposed by W. Wesley Peterson in 1961. Cyclic codes are not only simple to implement but have the benefit of being particularly well suited for the detection of burst errors: contiguous sequences of erroneous data symbols in messages. This is important because burst errors are common transmission errors in many communication channels, including magnetic and optical storage devices. Typically, an n-bit CRC applied to a data block of arbitrary length will detect any single error burst not longer than n bits, and the fraction of all longer error bursts that it will detect is (1 − 2−n).

A CRC code requires the definition of a generator polynomial, which becomes the divisor in a polynomial long division. The message is the dividend in this division, and the quotient is discarded while the remainder becomes the result. It's important to note that the polynomial coefficients are calculated according to the arithmetic of a finite field, so the addition operation can be performed bitwise-parallel (without carry between digits).

All CRCs commonly used employ the Galois field of two elements, GF(2), which are usually called 0 and 1 to match computer architecture.

A CRC is an error-detecting code used in digital networks and storage devices to detect accidental changes to raw data. A CRC is calculated by dividing the data by a predetermined polynomial and using the remainder as the CRC.

The parity bit is a 1-bit CRC that uses the generator polynomial x + 1 (two terms). It has the name CRC-1.

The device calculates a short, fixed-length binary sequence (the check value or CRC) for each block of data to be sent or stored, and appends it to the data. This forms a codeword.