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A Multi-Group Signature Scheme from Lattices

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Information and Communications Security (ICICS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11999))

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Abstract

Group signature allows group members to sign on behalf of the group anonymously, and incorporate some tracing mechanism to identify the actual signer. Multi-group signature (MGS), introduced by Ateniese and Tsudik (FC’99), is a proper generalization of group signature. It allows signers to sign messages anonymously on behalf of multiple groups and has extensive applications in electronic commerce. However, all existing MGS schemes are from classical assumptions and will be insecure once quantum computers come true.

In this paper, we propose the first MGS scheme in the lattice setting which is also the first quantum-resistant proposal. The keystone of our work is a zero-knowledge argument of knowledge (\( \mathsf {ZKAoK} \)) system of different syndromes of the same vector based on the work by Libert et al. (Asiacrypt’16) and Ling et al. (PKC’18). With additional signing and encryption layers, our \( \mathsf {ZKAoK} \) allows the signer to prove memberships in multiple groups simultaneously, which is the key issue on the MGS construction, and it can be of independent interest. For security proofs, we formalize the MGS model in the framework of Bellare et al. (CT-RSA’05).

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Notes

  1. 1.

    In this work, the post-quantum security is only considered in the classical random oracle model, rather than quantum random oracle model. This is in the same spirit as in many other work, such as [16, 17, 27].

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Acknowledgments

The authors would like to thank the anonymous reviewers of ICICS 2019 for helpful comments. This work is supported by the National Natural Science Foundation of China (Grant No. 61872359 and Grant No. 61936008).

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Tian Qiu, Lin Hou & Dongdai Lin

  2. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

    Tian Qiu, Lin Hou & Dongdai Lin

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  1. Tian Qiu
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  2. Lin Hou
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Correspondence to Lin Hou .

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Editors and Affiliations

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

    Jianying Zhou

  2. The Hong Kong Polytechnic University, Kowloon, Hong Kong

    Xiapu Luo

  3. Peking University, Beijing, China

    Qingni Shen

  4. Institute of Information Engineering, Beijing, China

    Zhen Xu

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Qiu, T., Hou, L., Lin, D. (2020). A Multi-Group Signature Scheme from Lattices. In: Zhou, J., Luo, X., Shen, Q., Xu, Z. (eds) Information and Communications Security. ICICS 2019. Lecture Notes in Computer Science(), vol 11999. Springer, Cham. https://doi.org/10.1007/978-3-030-41579-2_21

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