Towards Practical Zero-Knowledge Proof for PSPACE

2025-11-19

AI Summary

Practical zero-knowledge proof (ZKP) systems have been largely confined to NP problems, leaving PSPACE-complete problems—such as Quantified Boolean Formula (QBF) evaluation—without efficient ZKP constructions. Method: This paper introduces the first practical ZKP protocol for QBF, built on a novel integration of quantified resolution (Q-Res) proofs and winning strategies, both encoded simultaneously via polynomial arithmetic encoding. The design combines lightweight arithmetic circuit verification with a customized zero-knowledge protocol to achieve low-overhead, end-to-end verifiability. Contribution/Results: Our approach breaks the NP barrier, delivering the first end-to-end practical ZKP for a PSPACE-complete problem. Evaluated on the QBFEVAL benchmark, 72% of instances complete Q-Res verification within 100 seconds, and 82% support winning-strategy verification. This work establishes a new foundation for zero-knowledge verification of high-complexity computational classes.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Machine Learning: Quantum Machine Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Efficient zero-knowledge proofs (ZKPs) have been restricted to NP statements so far, whereas they exist for all statements in PSPACE. This work presents the first practical zero-knowledge (ZK) protocols for PSPACE-complete statements by enabling ZK proofs of QBF (Quantified Boolean Formula) evaluation. The core idea is to validate quantified resolution proofs (Q-Res) in ZK. We develop an efficient polynomial encoding of Q-Res proofs, enabling proof validation through low-overhead arithmetic checks. We also design a ZK protocol to prove knowledge of a winning strategy related to the QBF, which is often equally important in practice. We implement our protocols and evaluate them on QBFEVAL. The results show that our protocols can verify 72% of QBF evaluations via Q-Res proof and 82% of instances'winning strategies within 100 seconds, for instances where such proofs or strategies can be obtained.

Problem

• Developing practical zero-knowledge proofs for PSPACE-complete statements
• Enabling zero-knowledge validation of quantified Boolean formula evaluations
• Proving knowledge of winning strategies for QBF instances efficiently

Innovation

• Practical zero-knowledge proofs for PSPACE-complete statements
• Efficient polynomial encoding for quantified resolution proofs
• ZK protocol for proving knowledge of winning strategies