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International Workshop on Security

IWSEC 2014: Advances in Information and Computer Security pp 72–87Cite as

Cheater Identifiable Secret Sharing Schemes via Multi-Receiver Authentication

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8639))

Abstract

We introduce two publicly cheater identifiable secret sharing (CISS) schemes with efficient reconstruction, tolerating t < k/2 cheaters. Our constructions are based on (k,n) threshold Shamir scheme, and they feature a novel application of multi-receiver authentication codes to ensure integrity of shares.

The first scheme, which tolerates rushing cheaters, has the share size |S|(n − t)n + t + 2/ε n + t + 2 in the general case, that can be ultimately reduced to |S|(k − t)k + t + 2/ε k + t + 2 assuming that all the t cheaters are among the k reconstructing players. The second scheme, which tolerates non-rushing cheaters, has the share size |S|(n − t)2t + 2/ε 2t + 2. These two constructions have the smallest share size among the existing CISS schemes of the same category, when the secret is a single field element.

In addition, we point out that an improvement in the share size to \(|S|/\epsilon^{n-\lfloor (k-1)/3\rfloor +1}\) can be achieved for a CISS tolerating t < k/3 rushing cheaters presented by Xu et al. at IWSEC 2013.

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Author information

Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, Japan

    Rui Xu

  2. Institute of Mathematics for Industry, Kyushu University, Japan

    Kirill Morozov & Tsuyoshi Takagi

Authors
  1. Rui Xu
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  2. Kirill Morozov
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  3. Tsuyoshi Takagi
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Editor information

Editors and Affiliations

  1. Network Security Research Institute, National Institute of Information and Communications Technology (NICT), 4-2-1 Nukui-Kitamachi, 184-8795, Koganei, Tokyo, Japan

    Maki Yoshida

  2. College of Information Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, 525-8577, Kusatsu, Shiga, Japan

    Koichi Mouri

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© 2014 Springer International Publishing Switzerland

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Xu, R., Morozov, K., Takagi, T. (2014). Cheater Identifiable Secret Sharing Schemes via Multi-Receiver Authentication. In: Yoshida, M., Mouri, K. (eds) Advances in Information and Computer Security. IWSEC 2014. Lecture Notes in Computer Science, vol 8639. Springer, Cham. https://doi.org/10.1007/978-3-319-09843-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-09843-2_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09842-5

  • Online ISBN: 978-3-319-09843-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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