Certified-Everlasting Quantum NIZK Proofs

Abstract:We study non-interactive zero-knowledge proofs (NIZKs) for NP satisfying: 1) statistical soundness, 2) computational zero-knowledge (ZK) 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 ZK proofs that satisfy CE-ZK. - We circumvent this by constructing CE-NIZK using non-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 to construct CE-NIZK for NP in this model based on any statistical binding hidden bits generator, which is known from LWE. The only quantum computation here involves single-qubit measurements of the EPR pairs.

Quantum Physics (quant-ph); Cryptography and Security (cs.CR)

arXiv:2512.13628 [quant-ph]

(or arXiv:2512.13628v4 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2512.13628 Focus to learn more arXiv-issued DOI via DataCite

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