From non-adaptive to adaptive pseudorandom functions

Abstract

Unlike the standard notion of pseudorandom functions (PRF), a non-adaptive PRF is only required to be indistinguishable from random in the eyes of a non-adaptive distinguisher (i.e., one that prepares its oracle calls in advance). A recent line of research has studied the possibility of a direct construction of adaptive PRFs from non-adaptive ones, where direct means that the constructed adaptive PRF uses only few (ideally, constant number of) calls to the underlying non-adaptive PRF. Unfortunately, this study has only yielded negative results, showing that "natural" such constructions are unlikely to exist (e.g., Myers [EUROCRYPT '04], Pietrzak [CRYPTO '05, EUROCRYPT '06]).. We give an affirmative answer to the above question, presenting a direct construction of adaptive PRFs from non-adaptive ones. Our construction is extremely simple, a composition of the non-adaptive PRF with an appropriate pairwise independent hash function. © 2012 Springer-Verlag.