Source: Wikipedia. Pages: 68. Chapters: Cryptographic hash functions, Cyclic redundancy check, SHA-1, MD5, RIPEMD, Pearson hashing, Collision, Random oracle, One-way compression function, SHA-2, NIST hash function competition, Universal hashing, Fast Syndrome Based Hash, GOST, VEST, MinHash, Very smooth hash, SWIFFT, Merkle¿Damgård construction, Provably secure cryptographic hash function, Elliptic curve only hash, LM hash, Comparison of file verification software, Comparison of cryptographic hash functions, Whirlpool, Keccak, MD2, Tiger, Hash tree, MD4, Hash function security summary, Java hashCode(), RadioGatún, Perfect hash function, Skein, Rolling hash, BLAKE, Fowler¿Noll¿Vo hash function, MD6, Identicon, MDC-2, List of hash functions, Md5sum, Zobrist hashing, Grøstl, MurmurHash, Hash list, Examples of SHA digests, Jenkins hash function, SMASH, Universal one-way hash function, JH, HAVAL, Sha1sum, SANDstorm hash, Bitstate hashing, Locality preserving hashing, N-Hash, FORK-256, MASH-1, Hash filter, HAS-V, Morton number, Quantum fingerprinting, HAS-160. Excerpt: A cyclic redundancy check (CRC) is an error-detecting code designed to detect accidental changes to raw computer data, and is commonly used in digital networks and storage devices such as hard disk drives. A CRC-enabled device calculates a short, fixed-length binary sequence, known as the check value or improperly the CRC, for each block of data to be sent or stored and appends it to the data, forming a codeword. When a codeword is received or read, the device either compares its check value with one freshly calculated from the data block, or equivalently, performs a CRC on the whole codeword and compares the resulting check value with an expected residue constant. If the check values do not match, then the block contains a data error and the device may take corrective action such as rereading or requesting the block be sent again, otherwise the data is assumed to be error-free (though, with some small probability, it may contain undetected errors; this is the fundamental nature of error-checking). CRCs are so called because the check (data verification) code is a redundancy (it adds zero information to the message) and the algorithm is based on cyclic codes. CRCs are popular because they are simple to implement in binary hardware, are easy to analyze mathematically, and are particularly good at detecting common errors caused by noise in transmission channels. As the check value has a fixed length, the function that generates it is occasionally used as a hash function. The CRC was invented by W. Wesley Peterson in 1961; the 32-bit polynomial used in the CRC function of Ethernet and many other standards is the work of several researchers and was published in 1975. 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 im
