Parallel Repetition for Post-Quantum Arguments

2025-06-02

AI Summary

This work investigates parallel repetition of interactive arguments in the post-quantum setting, addressing three core questions: (1) whether the soundness error of public-coin protocols decays exponentially under parallel repetition; (2) whether this holds for threshold verifiers (i.e., *t*-accept rules); and (3) whether analogous guarantees extend to three-message private-coin protocols. Prior results were restricted to classical adversaries and did not handle threshold verification. We establish, for the first time in the post-quantum setting, a unified parallel repetition theorem for both public-coin and three-round private-coin arguments with classical verifiers. Our analysis shows that *k*-fold parallel repetition reduces soundness error from *ε* to *ε*^Ω(*k*), rigorously supporting arbitrary threshold acceptance rules. Technically, we integrate quantum information theory, game-theoretic reasoning, and probabilistic analysis within a clean, general framework—avoiding explicit modeling of quantum verifiers. This significantly simplifies and extends the STOC ’24 classical result, broadening its applicability to post-quantum cryptography.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Knowledge Representation and Reasoning: Argumentation
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

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.

Problem

• Reduces soundness error in post-quantum public-coin arguments
• Generalizes parallel repetition for threshold verifiers
• Simplifies analysis for classical-verifier private-coin arguments

Innovation

• Parallel repetition reduces post-quantum soundness error
• Generalized threshold verifiers accept t executions
• Simplified analysis for classical verifier protocols