Post-quantum Zero Knowledge in Constant Rounds

Abstract

We construct the first constant-round zero-knowledge classical argument for NP secure against quantum attacks. We assume the existence of quantum fully homomorphic encryption and other standard primitives, known based on the Learning with Errors Assumption for quantum algorithms. As a corollary, we also obtain the first constant-round zero-knowledge quantum argument for QMA.At the heart of our protocol is a new no-cloning non-black-box simulation technique.