Tight Parallel Repetition for Private-Coin Arguments

2026-09-30

AI Summary

This study addresses the challenge of achieving tight exponential soundness error reduction via parallel repetition of interactive arguments in post-quantum settings. To overcome classical cheating strategies, the proposed method leverages homomorphic encryption to establish tight parallel repetition for all interactive arguments, further generalizing this framework to threshold verifier scenarios. By integrating quantum computational theory with interactive proof systems, this work constructs the first constant-round succinct argument for QMA based on quantum homomorphic encryption. The primary contributions include achieving the first tight bounds under post-quantum assumptions while supporting threshold verification, thereby reducing argument errors to negligible levels. Ultimately, this research establishes a novel paradigm for efficient verification within post-quantum cryptography.

Abstract

We show that assuming the existence of homomorphic encryption, parallel repetition of all interactive arguments (after being run under homomorphic encryption) reduces the soundness error at a tight 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, and it was not known how to achieve tight bounds. As a corollary, we construct the first constant-round succinct argument for $\mathsf{QMA}$ with negligible completeness and soundness errors assuming only the existence of quantum homomorphic encryption.

Problem

• parallel repetition
• interactive arguments
• soundness error
• post-quantum
• succinct argument

Innovation

• Parallel Repetition
• Homomorphic Encryption
• Post-Quantum Security
• Threshold Verifiers
• Succinct Arguments for QMA