The Detection of Cheaters in Threshold Schemes

  • E. F. Brickell
  • D. R. Stinson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 403)


Informally, a (t, w)-threshold scheme is a way of distributing partial information (shadows) to w participants, so that any t of them can easily calculate a key (or secret), but no subset of fewer than t participants can determine the key. In this paper, we present an unconditionally secure threshold scheme in which any cheating participant can be detected and identified with high probability by any honest participant, even if the cheater is in coalition with other participants. We also give a construction that will detect with high probability a dealer who distributes inconsistent shadows (shares) to the honest participants. Our scheme is not perfect; a set of t − 1 participants can rule out at most \( 1 + \left( {\begin{array}{*{20}c} {w - t + 1} \\ {t - 1} \\ \end{array} } \right) \) possible keys, given the information they have. In our scheme, the key will be an element of GF(q) for some prime power q. Hence, q can be chosen large enough so that the amount of information obtained by any t − 1 participants is negligible.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • E. F. Brickell
    • 1
  • D. R. Stinson
    • 2
  1. 1.Sandia National LaboratoriesAlbuquerque
  2. 2.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

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