Certified-Everlasting Quantum NIZK Proofs

TL;DR

This paper introduces certified-everlasting non-interactive zero-knowledge proofs (CE-NIZKs) for NP, enabling proof revocation and certification, with constructions based on LWE assumptions and quantum EPR pairs.

Contribution

It presents the first CE-NIZK constructions for NP in the CRS and shared EPR models, overcoming known barriers and leveraging LWE and quantum techniques.

Findings

CE-NIZKs for NP are achievable in the CRS model based on LWE.

CE-NIZKs in the shared EPR model can be constructed using quantum EPR pairs.

The barrier to CE-NIZKs in the CRS model is identified and circumvented.

Abstract

We study non-interactive zero-knowledge proofs (NIZKs) for NP satisfying: 1) statistical soundness, 2) computational zero-knowledge and 3) certified-everlasting zero-knowledge (CE-ZK). The CE-ZK property allows a verifier of a quantum proof to revoke the proof in a way that can be checked (certified) by the prover. Conditioned on successful certification, the verifier's state can be efficiently simulated with only the statement, in a statistically indistinguishable way. Our contributions regarding these certified-everlasting NIZKs (CE-NIZKs) are as follows: - We identify a barrier to obtaining CE-NIZKs in the CRS model via generalizations of known interactive zero-knowledge proofs that satisfy CE-ZK. - We circumvent this by constructing CE-NIZK from black-box use of NIZK for NP satisfying certain properties, along with OWFs. As a result, we obtain CE-NIZKs for NP in the CRS model, based on polynomial hardness of the learning with errors (LWE) assumption. - In addition, we observe that the aforementioned barrier does not apply to the shared EPR model. We leverage this fact to construct a CE-NIZK for NP in this model based on any statistical binding hidden-bits generator, which can be based on LWE. The only quantum computation in this protocol involves single-qubit measurements of the shared EPR pairs.