Beating Classical Impossibility of Position Verification

TL;DR

This paper demonstrates that classical position verification is impossible without quantum assumptions, and introduces a protocol leveraging quantum hardness assumptions, specifically Learning with Errors, to achieve verifiable position proofs.

Contribution

It establishes the necessity of quantum proofs for classical verifiers and adapts a proof of quantumness protocol to create a new position verification scheme.

Findings

Classical position verification requires quantum assumptions.

A new position verification protocol based on Learning with Errors.

Development of the notion of 1-of-2 non-local soundness.

Abstract

Chandran et al. (SIAM J. Comput.'14) formally introduced the cryptographic task of position verification, where they also showed that it cannot be achieved by classical protocols. In this work, we initiate the study of position verification protocols with classical verifiers. We identify that proofs of quantumness (and thus computational assumptions) are necessary for such position verification protocols. For the other direction, we adapt the proof of quantumness protocol by Brakerski et al. (FOCS'18) to instantiate such a position verification protocol. As a result, we achieve classically verifiable position verification assuming the quantum hardness of Learning with Errors. Along the way, we develop the notion of 1-of-2 non-local soundness for a natural non-local game for 1-of-2 puzzles, first introduced by Radian and Sattath (AFT'19), which can be viewed as a computational unclonability property. We show that 1-of-2 non-local soundness follows from the standard 2-of-2 soundness (and therefore the adaptive hardcore bit property), which could be of independent interest.