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Security Analysis of a Multi-secret Sharing Scheme with Unconditional Security

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Security, Privacy, and Anonymity in Computation, Communication, and Storage (SpaCCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12383))

Abstract

Harn has introduced a (t, n) threshold secret sharing scheme recently, in which shareholders’ shares are not disclosed in the secret reconstruction phase. The benefit is that the outside adversary cannot learn the secret even if it is recovered by more than t shareholders. Moreover, Harn has further extended this scheme into a multi-secret sharing scheme so that multiple secrets can be recovered individually at different stagies. Both schemes are claimed to achieve the perfectness property using heuristic arguments. However, in this paper, we show that the above claim is false and these schemes are not perfect. In the first scheme, the coalition of \(t-1\) shareholders can conclude that the secret is not uniformly distributed. And in the multi-secret sharing scheme, when the public parameters satisfy some special conditions, the coalition of \(t-1\) shareholders can even use the recovered secrets to preclude some possible values for the unrecovered secrets.

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Notes

  1. 1.

    Note that similar technique has been used in [9] and this scheme was attacked by a novel cryptanalysis, called linear subspace attack [2]. But our work is different from the existing attack and it illustrates some other weaknesses of Harn’s work.

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Acknowledgement

This work was partially supported by the Guizhou Key Laboratory of Public Big Data (Grant No. 2019BDKFJJ005).

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Authors and Affiliations

  1. School of Computer Science, Wuhan University of Technology, Wuhan, 430070, China

    Min Xiao & Zhe Xia

  2. Guizhou Key Laboratory of Public Big Data, Guizhou University, Guiyang, 550025, China

    Zhe Xia

Authors
  1. Min Xiao
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  2. Zhe Xia
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Corresponding author

Correspondence to Zhe Xia .

Editor information

Editors and Affiliations

  1. Guangzhou University, Guangzhou, China

    Guojun Wang

  2. Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Bing Chen

  3. Computer Science, Georgia State University, Atlanta, GA, USA

    Wei Li

  4. College of Science and Engineering, Qatar Foundation Education City, Doha, Qatar

    Roberto Di Pietro

  5. Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Xuefeng Yan

  6. Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Hao Han

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Xiao, M., Xia, Z. (2021). Security Analysis of a Multi-secret Sharing Scheme with Unconditional Security. In: Wang, G., Chen, B., Li, W., Di Pietro, R., Yan, X., Han, H. (eds) Security, Privacy, and Anonymity in Computation, Communication, and Storage. SpaCCS 2020. Lecture Notes in Computer Science(), vol 12383. Springer, Cham. https://doi.org/10.1007/978-3-030-68884-4_44

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  • DOI: https://doi.org/10.1007/978-3-030-68884-4_44

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68883-7

  • Online ISBN: 978-3-030-68884-4

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