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On New Zero-Knowledge Proofs for Fully Anonymous Lattice-Based Group Signature Scheme with Verifier-Local Revocation

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Applied Cryptography and Network Security Workshops (ACNS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12418))

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Abstract

The first lattice-based verifier-local revocation group signature (GS-VLR) was introduced by Langlois et al. in 2014, and subsequently, a full and corrected version was proposed by Ling et al. in 2018. However, zero-knowledge proofs in both schemes are within a structure of Bonsai Tree, and thus have bit-sizes of the group public-key and member secret-key proportional to \(\log N\), where N is the group size. On the other hand, the revocation tokens in both schemes are related to the member secret-key and only obtain a weaker security, selfless-anonymity. For the tracing algorithms in both schemes, they just run in the linear time of N. Therefore, for a large group, the zero-knowledge proofs in lattice-based GS-VLR schemes are not that secure and efficient.

In this work, we firstly utilize a compact and scalable identity-encoding technique which only needs a constant number of public matrices to encode the member’s identity information and it saves a \(\mathcal {O}(\log N)\) factor in both bit-sizes for the group public-key and member secret-key. Secondly, separating from the member secret-key, we generate revocation token within some public matrix and a short Gaussian vector, and thus obtain the strongest security, full-anonymity. Moreover, the explicit-traceability, to trace the signer’s identity in a constant time, independent of N, for the tracing authority is also satisfied. In particular, a new Stern-type statistical zero-knowledge proof protocol for a fully anonymous lattice-based GS-VLR scheme enjoying the above three advantages is proposed.

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Acknowledgments

The authors would like to thank the anonymous reviewers of ACNS-SCI 2020 for their helpful comments, and this research is supported by the National Natural Science Foundation of China (No. 61772477) and Science and Technology Development of Henan Province (No. 20210222210356).

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Authors and Affiliations

  1. Zhengzhou University of Light Industry, Zhengzhou, 450001, China

    Yanhua Zhang, Yifeng Yin & Qikun Zhang

  2. Fuzhou University, Fuzhou, 350108, China

    Ximeng Liu

  3. Guangzhou University, Guangzhou, 510006, China

    Huiwen Jia

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  1. Yanhua Zhang
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  2. Ximeng Liu
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  3. Yifeng Yin
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  4. Qikun Zhang
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Correspondence to Yanhua Zhang .

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Editors and Affiliations

  1. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

  2. University of Padua, Padua, Italy

    Mauro Conti

  3. Singapore University of Technology and Design, Singapore, Singapore

    Chuadhry Mujeeb Ahmed

  4. The University of Hong Kong, Hong Kong, Hong Kong

    Man Ho Au

  5. ICIS, Radboud University Nijmegen, Nijmegen, The Netherlands

    Lejla Batina

  6. University of California, Irvine, CA, USA

    Zhou Li

  7. University of Science and Technology of China, Hefei, China

    Jingqiang Lin

  8. University of Padua, Padua, Italy

    Eleonora Losiouk

  9. University of Kansas, Lawrence, KS, USA

    Bo Luo

  10. CIISE, Concordia University, Montréal, QC, Canada

    Suryadipta Majumdar

  11. Technical University of Denmark, Lyngby, Denmark

    Weizhi Meng

  12. AppGate Inc., Bogotá, Colombia

    Martín Ochoa

  13. Delft University of Technology, Delft, The Netherlands

    Stjepan Picek

  14. Stevens Institute of Technology, Hoboken, NJ, USA

    Georgios Portokalidis

  15. City University of Hong Kong, Hong Kong, China

    Cong Wang

  16. Chinese University of Hong Kong, Shatin, Hong Kong

    Kehuan Zhang

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Zhang, Y., Liu, X., Yin, Y., Zhang, Q., Jia, H. (2020). On New Zero-Knowledge Proofs for Fully Anonymous Lattice-Based Group Signature Scheme with Verifier-Local Revocation. In: Zhou, J., et al. Applied Cryptography and Network Security Workshops. ACNS 2020. Lecture Notes in Computer Science(), vol 12418. Springer, Cham. https://doi.org/10.1007/978-3-030-61638-0_21

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  • DOI: https://doi.org/10.1007/978-3-030-61638-0_21

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