Certified-Everlasting Quantum NIZK Proofs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908828461694976 |
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| author | Pappu, Nikhil |
| author_facet | Pappu, Nikhil |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Certified-Everlasting Quantum NIZK Proofs Pappu, Nikhil Quantum Physics Cryptography and Security 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. |
| title | Certified-Everlasting Quantum NIZK Proofs |
| topic | Quantum Physics Cryptography and Security |
| url | https://arxiv.org/abs/2512.13628 |