Pseudorandom functions and lattices

Abstract

We give direct constructions of pseudorandom function (PRF) families based on conjectured hard lattice problems and learning problems. Our constructions are asymptotically efficient and highly parallelizable in a practical sense, i.e., they can be computed by simple, relatively small low-depth arithmetic or boolean circuits (e.g., in NC1 or even TC0). In addition, they are the first low-depth PRFs that have no known attack by efficient quantum algorithms. Central to our results is a new "derandomization" technique for the learning with errors (LWE) problem which, in effect, generates the error terms deterministically. © 2012 International Association for Cryptologic Research.