# Pseudorandom function family

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Pseudorandom function family

In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in the following way: No efficient algorithm can distinguish (with significant advantage) between a function chosen randomly from the PRF family and a random oracle (a function whose outputs are fixed completely at random). Pseudorandom functions are vital tools in the construction of cryptographic primitives, especially secure encryption schemes.

Pseudorandom functions are not to be confused with pseudorandom generators (PRGs). The guarantee of a PRG is that a "single" output appears random if the input was chosen at random. On the other hand, the guarantee of a PRF is that "all its outputs" appear random, regardless of how the corresponding inputs were chosen, as long as the "function" was drawn at random from the PRF family.

A pseudorandom function family can be constructed from any pseudorandom generator, using, for example, the construction given by Goldreich, Goldwasser, and Micali. [Oded Goldreich, Shafi Goldwasser, Silvio Micali (1986) "How to Construct Random Functions", "Journal of the ACM", vol.33, no.4, p.792-807. doi|10.1145/6490.6503; [http://theory.lcs.mit.edu/~cis/pubs/shafi/1986-jacm.pdf preprint] ; [http://www.math.weizmann.ac.il/~/oded/ggm.html web page and preprint] ]

ee also

*Pseudorandom permutation

References

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