Post-Quantum Perfect Zero-Knowledge Arguments for NP From Any One-Way Permutation

Overview & Synopsis

In this paper, we show for the first time that post-quantum one-way permutations are sufficient for perfect zero-knowledge classical arguments for all of NP with security guaranteed against quantum adversaries. We first establish that Naor, Ostrovsky,Venkatesen, and Yung's bit commitment scheme built from any permutation using interactive hashing, called the NOVY scheme, is sum-binding and collapse-binding against quantum polynomial-time committers provided the permutation is post-quantum one-way. We then show that the collapse-binding property of the NOVY scheme allows for Blum's perfect zero-knowledge argument for HAMCYCLE to remain so exactly as it stands against quantum adversaries.