Post-Quantum Zero Knowledge, Revisited or: How to Do Quantum Rewinding Undetectably

Abstract

When do classical zero-knowledge protocols remain secure against quantum attacks? In this work, we develop the techniques, tools, and abstractions necessary to answer this question for foundational protocols:1)We prove that the Goldreich-Micali-Wigderson protocol for graph non-isomorphism and the Feige-Shamir protocol for NP remain zero-knowledge against quantum adversaries. At the heart of our proof is a new quantum rewinding technique that enables extracting information from multiple invocations of a quantum adversary without disturbing its state.2)We prove that the Goldreich-Kahan protocol for NP is post-quantum zero knowledge using a simulator that can be seen as a natural quantum extension of the classical simulator.Our results achieve negligible simulation error, appearing to contradict a recent impossibility result due to Chia-Chung-Liu-Yamakawa (FOCS 2021). This brings us to our final contribution:3.We introduce coherent-runtime expected quantum polynomial time, a simulation notion that (a) precisely captures all of our zero-knowledge simulators, (b) cannot break any polynomial hardness assumptions, (c) implies strict polynomial-time ε-simulation and (d) is not subject to the CCLY impossibility. In light of our positive results and the CCLY negative results, we propose coherent-runtime simulation to be the appropriate quantum analogue of classical expected polynomial-time simulation.