A '''random function''' is a function chosen at random from a finite family of functions. Typically, the family consists of the set of all maps from the [[Domain of a function|___domain]] to the [[codomain]]. Thus, a random function can be considered to map each input independently at random to any one of the possible outputs. Viewed this way it is an idealization of a [[cryptographic hash function]]. A special case of a random function is a '''[[random permutation]]'''.
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A random function is a useful building block in enabling [[cryptographic protocol]]s. However, there are scenarios where it is not possible for mutually distrustful parties to agree on a random function (i.e, [[coin flipping]] is impossible). Therefore, cryptographers study models which explicitly allow for the use of a random function or a related object. See [[random oracle model]], [[common reference string model]].
