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Zero-Knowledge Proofs for Improved Lattice-Based Group Signature Scheme with Verifier-Local Revocation

  • Yanhua ZhangEmail author
  • Yifeng Yin
  • Ximeng Liu
  • Qikun Zhang
  • Huiwen Jia
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1105)

Abstract

The first lattice-based group signature scheme with verifier-local revocation (GS-VLR) was introduced by Langlois et al. in PKC 2014, and subsequently, a full and corrected version was designed by Ling et al. in TCS 2018. However, zero-knowledge proofs in both schemes are within a structure of Bonsai Tree, and have bit-sizes of the group public-key and the 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 some public matrix and the group member secret-key, and thus 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, zero-knowledge proofs in lattice-based GS-VLR schemes are not that secure and efficient.

In this work, we firstly utilize an efficient and compact 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 the group member secret-key. Secondly, separating from the member secret-key, we generate revocation token within some secret Gaussian vector and thus obtain a stronger security, almost-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 proofs protocol for an improved lattice-based GS-VLR scheme enjoying the above three advantages is proposed.

Keywords

Lattice-based group signatures Verifier-local revocation Zero-knowledge proofs Explicit traceability Almost-full anonymity 

Notes

Acknowledgments

The authors would like to thank the anonymous reviewers of FCS 2019 for their helpful comments and this research is supported by the National Natural Science Foundation of China under Grant 61772477.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Yanhua Zhang
    • 1
    Email author
  • Yifeng Yin
    • 1
  • Ximeng Liu
    • 2
  • Qikun Zhang
    • 1
  • Huiwen Jia
    • 3
  1. 1.Zhengzhou University of Light IndustryZhengzhouChina
  2. 2.Fuzhou UniversityFuzhouChina
  3. 3.Guangzhou UniversityGuangzhouChina

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