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Cheater Identifiable Secret Sharing Schemes via Multi-Receiver Authentication

  • Rui Xu
  • Kirill Morozov
  • Tsuyoshi Takagi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Cheater identifiable secret sharing multi-receiver authentication code Shamir secret sharing rushing adversary 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Rui Xu
    • 1
  • Kirill Morozov
    • 2
  • Tsuyoshi Takagi
    • 2
  1. 1.Graduate School of MathematicsKyushu UniversityJapan
  2. 2.Institute of Mathematics for IndustryKyushu UniversityJapan

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