Collection of efficiently-computable functions which emulate a random oracle
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 "GGM" construction given by Goldreich, Goldwasser, and Micali.[1] While in practice, block ciphers are used in most instances where a pseudorandom function is needed, they do not, in general, constitute a pseudorandom function family, as block ciphers such as AES are defined for only limited numbers of input and key sizes.[2]
^Goldreich, Oded; Goldwasser, Shafi; Micali, Silvio (October 1986). "How to Construct Random Functions" (PDF). Journal of the ACM. 33 (4): 792–807. doi:10.1145/6490.6503. web page and preprint
^Lindell, Yehuda; Katz, Jonathan (2008). Introduction to Modern Cryptography. Chapman & Hall/CRC. p. 88. ISBN 978-1-58488-551-1.
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