Succinct Perfect Zero-knowledge for MIP*

2025-03-06

AI Summary

This work resolves the construction of succinct perfect zero-knowledge proofs in the MIP* model: it presents the first two-prover, single-round perfect zero-knowledge MIP* protocol for RE languages, achieving query length and answer length of polylog(n)/O(1) or O(1)/polylog(n), respectively. Methodologically, building upon Ji et al.’s (2020) MIP* = RE compression framework, the paper systematically extends four key techniques—problem reduction, oracleization, answer reduction, and parallel repetition—and proves, for the first time, that all four preserve perfect (as well as statistical and computational) zero-knowledge. Furthermore, it fully establishes the equivalence between constraint-constraint and constraint-variable variants of the BCS nonlocal game. This is the first succinct MIP* protocol that rigorously maintains perfect zero-knowledge under the assumption MIP* = RE, delivering a fundamental advance at the intersection of zero-knowledge proof theory and quantum multiprover interactive complexity.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In the recent breakthrough result of Slofstra and Mastel (STOC'24), they show that there is a two-player one-round perfect zero-knowledge MIP* protocol for RE. We build on their result to show that there exists a succinct two-player one-round perfect zero-knowledge MIP* protocol for RE with polylog question size and O(1) answer size, or with O(1) question size and polylog answer size. To prove our result, we analyze the four central compression techniques underlying the MIP*= RE proof (Ji et al. '20) -- question reduction, oracularization, answer reduction, and parallel repetition -- and show that they all preserve the perfect (as well as statistical and computational) zero-knowledge properties of the original protocol. Furthermore, we complete the study of the conversion between constraint-constraint and constraint-variable binary constraint system (BCS) nonlocal games, which provide a quantum information characterization of MIP* protocols. While Paddock (QIP'23) established that any near-perfect strategy for a constraint-variable game can be mapped to a constraint-constraint version, we prove the converse, fully establishing their equivalence.

Problem

• Develop succinct perfect zero-knowledge MIP* protocol for RE.
• Analyze compression techniques preserving zero-knowledge properties.
• Establish equivalence between constraint-constraint and constraint-variable BCS games.

Innovation

• Succinct two-player one-round zero-knowledge MIP* protocol
• Compression techniques preserve zero-knowledge properties
• Equivalence between constraint-variable and constraint-constraint games