Multi-Prover Interactive Proof Systems with Leakage

2026-05-10

AI Summary

This work investigates the robustness of multi-prover interactive proof systems under bounded information leakage among provers. To address this challenge, the authors introduce two key techniques: a protocol transformation method leveraging the parallel repetition theorem and low-soundness PCPs, enabling the first systematic construction of protocols resilient to leakage of any polynomial number of bits $p(n)$. The paper establishes a theoretical framework for MIP and MIP* under leakage, extending their power to capture NEXP and RE, respectively. It also constructs leakage-resilient two-prover protocols for NP and uncovers a deep connection between this robustness problem and the sliding-scale conjecture for PCPs.

Abstract

It is known that there exist multi-prover interactive protocols ($\mathsf{MIP}$ protocols) for the complexity class $\mathsf{NEXP}$, succinct $\mathsf{MIP}$ protocols for $\mathsf{NP}$ and multi-prover interactive protocols with shared entanglement ($\mathsf{MIP}^\ast$ protocols) for $\mathsf{RE}$. This extraordinary power of multi-prover interactive proof systems comes from the assumption that provers do not communicate with each other during the protocols. If they are allowed to communicate freely, the setting is the same as in the single-prover case, and the computational power of the system becomes significantly weaker. In this paper, we investigate for the first time the setting where communication (i.e., leakage of information) between provers is allowed but bounded. We introduce two techniques to approach this question and show that multi-prover interactive proof systems are robust against some amount of leakage. Our first technique is based on parallel repetition theorems. We apply it to show that for any polynomial $p$, we can construct two-prover one-round $\mathsf{MIP}$ and $\mathsf{MIP}^\ast$ protocols for $\mathsf{NEXP}$ and $\mathsf{RE}$, respectively, that are robust against $p(n)$ bits of leakage. We further derive our second technique to convert any low-soundness PCP construction to a two-prover one-round $\mathsf{MIP}$ protocol for $\mathsf{NP}$ robust against leakage. We also discuss the relation between robustness against leakage in multi-prover interactive proof systems and the Sliding Scale Conjecture in the PCP literature.

Problem

• multi-prover interactive proofs
• information leakage
• bounded communication
• computational robustness
• MIP protocols

Innovation

• multi-prover interactive proofs
• information leakage
• parallel repetition
• PCP
• robustness