Parallel Repetition for Post-Quantum Arguments

TL;DR

This paper demonstrates that parallel repetition exponentially reduces soundness error in post-quantum public-coin interactive arguments, including threshold verifiers, with simplified analysis for classical verifiers.

Contribution

It extends parallel repetition results to post-quantum settings for public-coin and threshold verifiers, with a simplified approach for classical verifiers.

Findings

Parallel repetition reduces soundness error exponentially in post-quantum settings.

Results apply to threshold verifiers accepting if a certain number of executions succeed.

Simplified analysis for protocols with classical verifiers compared to quantum protocol settings.

Abstract

In this work, we show that parallel repetition of public-coin interactive arguments reduces the soundness error at an exponential rate even in the post-quantum setting. Moreover, we generalize this result to hold for threshold verifiers, where the parallel repeated verifier accepts if and only if at least $t$ of the executions are accepted (for some threshold $t$). Prior to this work, these results were known only when the cheating prover was assumed to be classical. We also prove a similar result for three-message private-coin arguments. Previously, Bostanci, Qian, Spooner, and Yuen (STOC 2024) proved such a parallel repetition result in the more general setting of quantum protocols, where the verifier and communication may be quantum. We consider only protocols where the verifier is classical, but obtain a simplified analysis, and for the more general setting of threshold verifiers.