Computationally Private Information Retrieval with Polylogarithmic Communication

Abstract

We present a single-database computationally private information retrieval scheme with polylogarithmic communication complexity. Our construction is based on a new, but reasonable intractability assumption, which we call the Φ-Hiding Assumption (ΦHA): essentially the difficulty of deciding whether a small prime divides Φ(m), where m is a composite integer of unknown factorization.