On basing private information retrieval on NP-hardness

Abstract

The possibility of basing the security of cryptographic objects on the (minimal) assumption that NP BPP is at the very heart of complexity-theoretic cryptography. Most known results along these lines are negative, showing that assuming widely believed complexity-theoretic conjectures, there are no reductions from an NPhard problem to the task of breaking certain cryptographic schemes. We make progress along this line of inquiry by showing that the security of single-server single-round private information retrieval schemes cannot be based on NP-hardness, unless the polynomial hierarchy collapses. Our main technical contribution is in showing how to break the security of a PIR protocol given an SZK oracle. Our result is tight in terms of both the correctness and the privacy parameter of the PIR scheme.