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Cheating Detectable Secret Sharing Schemes Supporting an Arbitrary Finite Field

  • Satoshi Obana
  • Kazuya Tsuchida
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8639)

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.

Keywords

Secret Sharing Cheating Detection Arbitrary Finite Field 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Satoshi Obana
    • 1
  • Kazuya Tsuchida
    • 1
  1. 1.Hosei UniversityJapan

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