A General Decomposition Construction for Incomplete SecretSharing Schemes

  • Authors:
  • Marten Van Dijk;Wen-Ai Jackson;Keith M. Martin

  • Affiliations:
  • Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands;Department of Pure Mathematics, The University of Adelaide, Adelaide SA 5005, Australia;Katholieke Universiteit Leuven, ESAT-COSIC, Kard. Mercierlaan 94, B-3001, Heverlee, Belgium

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 1998

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Abstract

A secret sharing schemefor an incomplete access structure (\G,\D) is amethod of distributing information about a secret among a groupof participants in such a way that sets of participants in \Gcan reconstruct the secret and sets of participants in \Dcan not obtain any new information about the secret. In thispaper we present a more precise definition of secret sharingschemes in terms of information theory, and a new decompositiontheorem. This theorem generalizes previous decomposition theoremsand also works for a more general class of access structures.We demonstrate some applications of the theorem.