Cumulative arrays and geometric secret sharing schemes

  • Wen-Ai Jackson
  • Keith M. Martin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 718)


Cumulative secret sharing schemes were introduced by Simmons et al (1991) based on the generalised secret sharing scheme of Ito et al (1987). A given monotone access structure together with a security level is associated with a unique cumulative scheme. Geometric secret sharing schemes form a wide class of secret sharing schemes which have many desirable properties including good information rates. We show that every non-degenerate geometric secret sharing scheme is ‘contained’ in the corresponding cumulative scheme. As there is no known practical algorithm for constructing efficient secret sharing schemes, the significance of this result is that, at least theoretically, a geometric scheme can be constructed from the corresponding cumulative scheme.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Wen-Ai Jackson
    • 1
  • Keith M. Martin
    • 2
  1. 1.Department of MathematicsRoyal HollowayEgham Hill, EghamUK
  2. 2.Department of Pure MathematicsThe University of AdelaideAdelaideAustralia

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