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On New Zero-Knowledge Proofs for Lattice-Based Group Signatures with Verifier-Local Revocation

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Information Security (ISC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11723))

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Abstract

For lattice-based group signatures with verifier-local revocation (VLR), a group member who issues a signature on behalf of the whole group can validly prove to the verifiers with an efficient non-interactive zero-knowledge proof protocol, from which the verifiers only come to the conclusion that the signer is a certified group member who owns a valid secret signing key and its corresponding revocation token is out of the revocation list. The first such construction was introduced by Langlois et al. (PKC 2014), furthermore, a full and corrected version was proposed in TCS 2018. However, both schemes are within the structure of Bonsai Trees, and thus the bit-sizes of the group public-key and the group member secret-key are proportional to \(\log N\), where N is the maximum number of group members, therefore both constructions are not suitable for a large group.

In this work, we adopt a more efficient and compact identity-encoding technique which only needs a constant number of matrices to encode the group member’s identity information and it saves a \(\mathcal {O}(\log N)\) factor in both bit-sizes for the group public-key and the group member secret-key. In particular, a new Stern-type statistical zero-knowledge proof protocol allowing to prove the signer’s validity as a valid certified group member and its revocation token correctly committed via a one-way and injective Learning With Errors (\(\textsf {LWE}\)) function is proposed.

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Acknowledgments

The authors thank the anonymous reviewers of ISC 2019 for their helpful comments and this research is supported by the National Key R&D Program of China under Grant 2017YFB0802000 and the National Natural Science Foundation of China under Grant 61772477.

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Authors and Affiliations

  1. Zhengzhou University of Light Industry, Zhengzhou, 450002, China

    Yanhua Zhang & Qikun Zhang

  2. Xidian University, Xi’an, 710071, China

    Yupu Hu

  3. Guangzhou University, Guangzhou, 510006, China

    Huiwen Jia

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  1. Yanhua Zhang
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  2. Yupu Hu
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Correspondence to Yanhua Zhang .

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Editors and Affiliations

  1. The Ohio State University, Columbus, OH, USA

    Zhiqiang Lin

  2. University of Maryland, College Park, MD, USA

    Charalampos Papamanthou

  3. Stony Brook University, Stony Brook, NY, USA

    Michalis Polychronakis

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Zhang, Y., Hu, Y., Zhang, Q., Jia, H. (2019). On New Zero-Knowledge Proofs for Lattice-Based Group Signatures with Verifier-Local Revocation. In: Lin, Z., Papamanthou, C., Polychronakis, M. (eds) Information Security. ISC 2019. Lecture Notes in Computer Science(), vol 11723. Springer, Cham. https://doi.org/10.1007/978-3-030-30215-3_10

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  • DOI: https://doi.org/10.1007/978-3-030-30215-3_10

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