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Fine-Grained Verifier NIZK and Its Applications

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Public-Key Cryptography – PKC 2023 (PKC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13941))

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Abstract

In this paper, we propose a new type of non-interactive zero-knowledge (NIZK), called Fine-grained Verifier NIZK (FV-NIZK), which provides more flexible and more fine-grained verifiability of proofs than standard NIZK that supports public verifiability and designated-verifier NIZK (DV-NIZK) that supports private verifiability. FV-NIZK has two statistically equivalent verification approaches:

  • a master verification using the master secret key msk;

  • a fine-grained verification using a derived secret key \(sk_d\), which is derived from msk w.r.t. d (which may stand for user identity, email address, vector, etc.).

We require unbounded simulation soundness (USS) of FV-NIZK to hold, even if an adversary obtains derived secret keys \(sk_d\) with d of its choices, and define proof pseudorandomness which stipulates the pseudorandomness of proofs for adversaries that are not given any secret key.

We present two instantiations of FV-NIZK for linear subspace languages, based on the matrix decisional Diffie-Hellman (MDDH) assumption. One of the FV-NIZK instantiations is pairing-free and achieves almost tight USS and proof pseudorandomness.

We illustrate the usefulness of FV-NIZK by showing two applications and obtain the following pairing-free schemes:

  • the first almost tightly multi-challenge CCA (mCCA)-secure inner-product functional encryption (IPFE) scheme without pairings;

  • the first public-key encryption (PKE) scheme that reconciles the inherent contradictions between public verifiability and anonymity. We formalize such PKE as Fine-grained Verifiable PKE (FV-PKE), which derives a special key from the decryption secret key, such that for those who obtain the derived key, they can check the validity of ciphertexts but the anonymity is lost from their views (CCA-security still holds for them), while for others who do not get the derived key, they cannot do the validity check but the anonymity holds for them.

    Our FV-PKE scheme achieves almost tight mCCA-security for adversaries who obtain the derived keys, and achieves almost tight ciphertext pseudorandomness (thus anonymity) for others who do not get any derived key.

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Notes

  1. 1.

    Note that the CRS of NIZK is contained in the public key of PKE, since the encryption algorithm of PKE involves NIZK proof generation which requires the CRS.

  2. 2.

    This entropy requirement is necessary to achieve verification equivalence, see Remark 1 in Sect. 3 for more discussions.

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Acknowledgments

We would like to thank the anonymous reviewers for their valuable comments and suggestions. Shengli Liu and Xiangyu Liu were partially supported by National Natural Science Foundation of China (NSFC No. 61925207), Guangdong Major Project of Basic and Applied Basic Research (2019B030302008), and the National Key R &D Program of China under Grant 2022YFB2701500. Shuai Han was partially supported by National Natural Science Foundation of China (Grant No. 62002223), Shanghai Sailing Program (20YF1421100), Young Elite Scientists Sponsorship Program by China Association for Science and Technology (YESS20200185), and Ant Group through CCF-Ant Research Fund (CCF-AFSG RF20220224). Dawu Gu is partially supported by the National Key Research and Development Project (Grant No. 2020YFA0712302).

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Authors and Affiliations

  1. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Xiangyu Liu, Shengli Liu, Shuai Han & Dawu Gu

  2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    Xiangyu Liu, Shengli Liu & Shuai Han

  3. Westone Cryptologic Research Center, Beijing, 100070, China

    Shengli Liu

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  1. Xiangyu Liu
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Correspondence to Shengli Liu or Shuai Han .

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Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. Georgia Institute of Technology, Atlanta, GA, USA

    Vladimir Kolesnikov

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Liu, X., Liu, S., Han, S., Gu, D. (2023). Fine-Grained Verifier NIZK and Its Applications. In: Boldyreva, A., Kolesnikov, V. (eds) Public-Key Cryptography – PKC 2023. PKC 2023. Lecture Notes in Computer Science, vol 13941. Springer, Cham. https://doi.org/10.1007/978-3-031-31371-4_17

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  • DOI: https://doi.org/10.1007/978-3-031-31371-4_17

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