A hash function is any well-defined procedure or mathematical function that converts a large, possibly variable-sized amount of data into a small datum, usually a single integer that may serve as an index to an array (cf. associative array). The values returned by a hash function are called hash values, hash codes, hash sums, checksums or simply hashes.
A cryptographically strong hash function exhibits two features: it is irreversible and it minimizes collisions. Irreversibility means that the original data cannot be reconstructed from its hash. Cf. encryption, which must be reversible (see write-only memory.) A collision occurs when two different sets of data generate the same hash.
Hash functions are related to (and often confused with) checksums, check digits, fingerprints, randomization functions, and error-correcting codes. Although these concepts overlap to some extent, each has its own uses and requirements and is designed and optimized differently.