Random function: Difference between revisions

Revision as of 12:11, 29 February 2012

Revision as of 10:27, 22 March 2012

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In probability and statistics, one important type of random function is studied under the name of [[stochastic process]]es, for which there are a variety of models describing systems where an observation is a random function of time or space. However, there are other applications where there is a need to describe the uncertainty with which a function is known and where the state of knowledge about the true function can be expressed by saying that it is an unknown realisation of a random function, for example in the [[Dirichlet process]].<ref>{{cite book

| title = Bayesian Nonparametrics

| isbn = 05215134640-521-51346-4

| publisher = Cambridge University Press

| authorlink1 =Nils Lid Hjort|first1=Nils Lid |last1=Hjort| first2= Chris|last2= Holmes|first3= Peter |last3= Müller|first4= Stephen G.|last4= Walker

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==Applications==

Thus, a random function can be considered to map each input independently at random to any one of the possible outputs.{{clarify|date=February 2012}} Viewed this way it is an idealization of a [[cryptographic hash function]].

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).{{cnCitation needed|date=December 2011}} 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]].

==Notes==