Tests for Poly-Random Function Collections

Poly-random function collections (a.k.a. pseudorandom function collections) are an important cryptographic primitive, rst introduced by Goldreich, Goldwasser and Micali in 1986. Pseudorandom functions provide simple solutions to problems in private key cryptography, including encryption and message authentication. In this paper we are interested in the resources required by a test to distinguish between a function collection and a collection of truly random functions. We deene the level of interactiveness of a test for function collections as the number of rounds of queries it asks about the values of a function from the collection. We introduce a hierarchy of function collections, parameterized by the number of rounds required by some test to break them. We show that if there exists a one-way function, the hierarchy is proper.