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Cheating Detectable Secret Sharing Schemes Supporting an Arbitrary Finite Field

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Advances in Information and Computer Security (IWSEC 2014)

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Abstract

In this paper, we present k-out-of-n threshold secret sharing scheme which can detect share forgery by at most k − 1 cheaters. Though, efficient schemes with such a property are presented so far, some schemes cannot be applied when a secret is an element of \(\mathbb{F}_{2^N}\) and some schemes require a secret to be an element of a multiplicative group. The schemes proposed in the paper possess such a merit that a secret can be an element of arbitrary finite field. Let \(|\mathcal{S}|\) and ε be the size of secret and successful cheating probability of cheaters, respectively. Then the sizes of share \(|\mathcal{V}_i|\) of two proposed schemes respectively satisfy \(|\mathcal{V}_i|=(2\cdot|\mathcal{S}|)/\epsilon\) and \(|\mathcal{V}_i|=(4\cdot|\mathcal{S}|)/\epsilon\) which are only 2 and 3 bits longer than the existing lower bound.

This work was supported by JSPS KAKENHI Grant Number 24800064.

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Authors and Affiliations

  1. Hosei University, Japan

    Satoshi Obana & Kazuya Tsuchida

Authors
  1. Satoshi Obana
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  2. Kazuya Tsuchida
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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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Obana, S., Tsuchida, K. (2014). Cheating Detectable Secret Sharing Schemes Supporting an Arbitrary Finite Field. 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_7

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  • DOI: https://doi.org/10.1007/978-3-319-09843-2_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09842-5

  • Online ISBN: 978-3-319-09843-2

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