Relativistic (or $2$-prover $1$-round) zero-knowledge protocol for $\mathsf{NP}$ secure against quantum adversaries

TL;DR

This paper demonstrates that a relativistic zero-knowledge protocol for NP problems remains secure against quantum adversaries by developing new tools for analyzing quantum measurements and applying them to various cryptographic protocols.

Contribution

It introduces a novel method for analyzing consecutive quantum measurements, proving security of relativistic zero-knowledge and commitment protocols against quantum attacks.

Findings

Security of Hamiltonian cycle zero-knowledge protocol against quantum adversaries

Security bounds for relativistic string and bit commitments in parallel against quantum attacks

Tight bounds on quantum knowledge error of certain $\

Abstract

In this paper, we show that the zero-knowledge construction for Hamiltonian cycle remains secure against quantum adversaries in the relativistic setting. Our main technical contribution is a tool for studying the action of consecutive measurements on a quantum state which in turn gives upper bounds on the value of some entangled games. This allows us to prove the security of our protocol against quantum adversaries. We also prove security bounds for the (single-round) relativistic string commitment and bit commitment in parallel against quantum adversaries. As an additional consequence of our result, we answer an open question from [Unr12] and show tight bounds on the quantum knowledge error of some $\Sigma$-protocols.