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Warren, Henry S. Jr. "Cyclic Redundancy Check" (PDF). Hacker's Delight. Archived from the original (PDF) on 3 May 2015. — theory, practice, hardware, and software with emphasis on CRC-32. Reverse-Engineering a CRC Algorithm Archived 7 August 2011 at the Wayback Machine; Cook, Greg. "Catalogue of parameterised CRC algorithms". CRC RevEng.
For example, it would be entirely possible to compute a CRC 64 bits at a time using a slice-by-9 algorithm, using 9 128-entry lookup tables to handle 63 bits, and the 64th bit handled by the bit-at-a-time algorithm (which is effectively a 1-bit, 2-entry lookup table).
The checksum algorithms most used in practice, such as Fletcher's checksum, Adler-32, and cyclic redundancy checks (CRCs), address these weaknesses by considering not only the value of each word but also its position in the sequence. This feature generally increases the cost of computing the checksum.
Internet Checksum: 16 bits sum (ones' complement) sum24 24 bits sum sum32 32 bits sum fletcher-4: 4 bits sum fletcher-8: 8 bits sum fletcher-16: 16 bits sum fletcher-32: 32 bits sum Adler-32: 32 bits sum xor8: 8 bits sum Luhn algorithm: 1 decimal digit sum Verhoeff algorithm: 1 decimal digit sum Damm algorithm: 1 decimal digit Quasigroup operation
A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones'-complement operation prior to transmission to detect unintentional all-zero messages. Checksum schemes include parity bits, check digits, and longitudinal redundancy checks.
The Fletcher checksum is an algorithm for computing a position-dependent checksum devised by John G. Fletcher (1934–2012) at Lawrence Livermore Labs in the late 1970s. [1] The objective of the Fletcher checksum was to provide error-detection properties approaching those of a cyclic redundancy check but with the lower computational effort ...
The cyclic redundancy check (CRC) is a check of the remainder after division in the ring of polynomials over GF(2) (the finite field of integers modulo 2). That is, the set of polynomials where each coefficient is either zero or one, and arithmetic operations wrap around.
Adler-32 is a checksum algorithm written by Mark Adler in 1995, [1] modifying Fletcher's checksum. Compared to a cyclic redundancy check of the same length, it trades reliability for speed. Adler-32 is more reliable than Fletcher-16, and slightly less reliable than Fletcher-32. [2]