Towards Practical Zero-Knowledge Proof for PSPACE

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 $\mathbf{7 2 \%}$ 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.