From Non-adaptive to Adaptive Pseudorandom Functions

Unlike the standard notion of pseudorandom functions (PRF), a non-adaptive PRF is only required to be indistinguishable from a random function 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 (e.g., Myers in Advances in Cryptology – EUROCRYPT 2004, pp. 189–206, 2004; Pietrzak in Advances in Cryptology – CRYPTO 2005, pp. 55–65, 2005).

We give an affirmative answer to the above question, presenting a direct construction of adaptive PRFs from non-adaptive ones. The suggested construction is extremely simple, a composition of the non-adaptive PRF with an appropriate pairwise independent hash function.