Properties of Hash Functions

A hash function is a function that takes a relatively arbitrary amount of input and
produces an output of fixed size. The properties of some hash functions can be
used to greatly increase the security of a system administrator’s network; when
implemented correctly they can verify the integrity and source of a file, network
packet, or any arbitrary data.
Good hash functions, in the original sense of the term, are usually required to satisfy certain properties listed below :

- A hash is a one-way function.
- The cost of computing a hash function must be small enough to make a hashing-based solution advantageous with regard to alternative approaches.
- A hash procedure must be deterministic — meaning that for a given input value it must always generate the same hash value. In other words, it must be a function of the hashed data, in the mathematical sense of the term.
- A good hash function should map the expected inputs as evenly as possible over its output range i.e. every hash value in the output range should be generated with roughly the same probability.
- The range of hash values may be different for each run of the program, or may change along the same run. In those situations, one needs a hash function which takes two parameters — the input data z, and the number n of allowed hash values.
- A hash function that is used to search for similar (as opposed to equivalent) data must be as continuous as possible; two inputs that differ by a little should be mapped to equal or nearly equal hash values.