A New Algorithm for Searching a Consistent Set of Shares in a Threshold Scheme with Cheaters

  • Raylin Tso
  • Ying Miao
  • Eiji Okamoto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2971)


In a (k,n) Shamir’s threshold scheme, if one or more of the n shares are fake, then the secret may not be reconstructed correctly by some sets of k shares. Supposing that at most t of the n shares are fake, Rees et al. (1999) described two algorithms to determine consistent sets of shares so that the secret can be reconstructed correctly from k shares in any of these consistent sets. In their algorithms, no honest participant can be absent and at least n-t shares should be pooled during the secret reconstruction phase. In this paper, we propose a modified algorithm for this problem so that the number of participants taking part in the secret reconstruction can be reduced to k+2t and the shares need to be pooled can be reduced to, in the best case, k+t, and less than or equal to k+2t in the others. Its efficiency is also investigated.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Raylin Tso
    • 1
  • Ying Miao
    • 2
  • Eiji Okamoto
    • 3
  1. 1.Risk Engineering Major Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukubaJapan
  2. 2.Institute of Policy and Planning SciencesUniversity of TsukubaTsukubaJapan
  3. 3.Institute of Information Sciences and ElectronicsUniversity of TsukubaTsukubaJapan

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