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Short Code-Based One-out-of-Many Proofs and Applications

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Public-Key Cryptography – PKC 2024 (PKC 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14602))

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Abstract

In this work, we propose two novel succinct one-out-of-many proofs from coding theory, which can be seen as extensions of the Stern’s framework and Veron’s framework from proving knowledge of a preimage to proving knowledge of a preimage for one element in a set, respectively. The size of each proof is short and scales better with the size of the public set than the code-based accumulator in [35]. Based on our new constructions, we further present a logarithmic-size ring signature scheme and a logarithmic-size group signature scheme. Our schemes feature short signature sizes, especially our group signature. To our best knowledge, it is the most compact code-based group signature scheme so far. At 128-bit security level, our group signature size is about 144 KB for a group with \(2^{20}\) members while the group signature size of the previously most compact code-based group signature constructed by the above accumulator exceeds 3200 KB.

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Acknowledgment

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions that substantially improved the quality of this paper. This research was supported by the National Natural Science Foundation of China under Grant No. 62372446, the National Key Research and Development Program of China under Grant No. 2018YFA0704703 and the Key Research Program of the Chinese Academy of Sciences, Grant No. ZDRW-XX-2022-1.

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Authors and Affiliations

  1. Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, CAS, Beijing, China

    Xindong Liu & Li-Ping Wang

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

    Xindong Liu & Li-Ping Wang

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  1. Xindong Liu
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Correspondence to Li-Ping Wang .

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Editors and Affiliations

  1. The University of Sydney, Sydney, NSW, Australia

    Qiang Tang

  2. The Australian National University, Acton, ACT, Australia

    Vanessa Teague

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Liu, X., Wang, LP. (2024). Short Code-Based One-out-of-Many Proofs and Applications. In: Tang, Q., Teague, V. (eds) Public-Key Cryptography – PKC 2024. PKC 2024. Lecture Notes in Computer Science, vol 14602. Springer, Cham. https://doi.org/10.1007/978-3-031-57722-2_12

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