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Non-interactive Zero-Knowledge Functional Proofs

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Advances in Cryptology – ASIACRYPT 2023 (ASIACRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14442))

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Abstract

In this paper, we consider to generalize NIZK by empowering a prover to share a witness in a fine-grained manner with verifiers. Roughly, the prover is able to authorize a verifier to obtain extra information of witness, i.e., besides verifying the truth of the statement, the verifier can additionally obtain certain function of the witness from the accepting proof using a secret functional key provided by the prover.

To fulfill these requirements, we introduce a new primitive called non-interactive zero-knowledge functional proofs (fNIZKs), and formalize its security notions. We provide a generic construction of fNIZK for any \({\textsf{NP}}\) relation \(\mathcal {R}\), which enables the prover to share any function of the witness with a verifier. For a widely-used relation about set membership proof (implying range proof), we construct a concrete and efficient fNIZK, through new building blocks (set membership encryption and dual inner-product encryption), which might be of independent interest.

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Notes

  1. 1.

    A commitment scheme supports Sigma protocols, if there exists a Sigma protocol to prove the well-formedness of a commitment.

  2. 2.

    In this scenario, the authority generates a public key and a secret key, and all users utilize the public key to generate or verify proofs. The secret functional keys are generated by the authority, using the secret key.

  3. 3.

    For each \(x\in \mathcal {L}_{\mathcal {R}_{sm }}\), its witness is in the form of \((w,r_{\text {com} })\). In fSMP, we are only interested in functions of w (rather than \(r_{\text {com} }\)). So we define \(\mathbb {F}\) as family of functions whose domain is \(\mathcal {W}\) (rather than \(\mathcal {W}\times \mathcal{R}\mathcal{S}_{\textsf {Commit} .\textsf {Com} }\)).

  4. 4.

    Note that the Sigma protocol \(\mathrm{\Sigma }^{\mathcal {R}''}_{clause }\) supports that the verifier can recover the commitment via the responses and the challenge, so we can save the proof size by only sending the responds to the verifier as the proof.

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Acknowledgements

We would like to express our sincere appreciation to Junqing Gong for his valuable suggestions on the inner-product encryption! We also want to express our sincere appreciation to the anonymous reviewers for their valuable comments and suggestions! Gongxian Zeng and Zhengan Huang was supported by The Major Key Project of PCL (PCL2023A09). Junzuo Lai was supported by National Natural Science Foundation of China under Grant No. U2001205, Guangdong Basic and Applied Basic Research Foundation (Grant No. 2023B1515040020), Industrial project No. TC20200930001. Jian Weng was supported by National Natural Science Foundation of China under Grant Nos. 61825203, 62332007 and U22B2028, Major Program of Guangdong Basic and Applied Research Project under Grant No. 2019B030302008, Guangdong Provincial Science and Technology Project under Grant No. 2021A0505030033, Science and Technology Major Project of Tibetan Autonomous Region of China under Grant No. XZ202201ZD0006G, National Joint Engineering Research Center of Network Security Detection and Protection Technology, Guangdong Key Laboratory of Data Security and Privacy Preserving, Guangdong Hong Kong Joint Laboratory for Data Security and Privacy Protection, and Engineering Research Center of Trustworthy AI, Ministry of Education. This research is supported by the National Research Foundation, Singapore under its Strategic Capability Research Centres Funding Initiative. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore.

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Authors and Affiliations

  1. Peng Cheng Laboratory, Shenzhen, China

    Gongxian Zeng & Zhengan Huang

  2. College of Information Science and Technology, Jinan University, Guangzhou, China

    Junzuo Lai & Jian Weng

  3. Nanyang Technological University, Singapore, Singapore

    Linru Zhang, Xiangning Wang, Kwok-Yan Lam & Huaxiong Wang

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  1. Gongxian Zeng
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Correspondence to Junzuo Lai , Zhengan Huang , Linru Zhang or Xiangning Wang .

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Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Jian Guo

  2. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

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Zeng, G. et al. (2023). Non-interactive Zero-Knowledge Functional Proofs. In: Guo, J., Steinfeld, R. (eds) Advances in Cryptology – ASIACRYPT 2023. ASIACRYPT 2023. Lecture Notes in Computer Science, vol 14442. Springer, Singapore. https://doi.org/10.1007/978-981-99-8733-7_8

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  • DOI: https://doi.org/10.1007/978-981-99-8733-7_8

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