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A General Decomposition Construction for Incomplete Secret Sharing Schemes

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Abstract

A secret sharing scheme for an incomplete access structure (Γ,Δ) is a method of distributing information about a secret among a group of participants in such a way that sets of participants in Γ can reconstruct the secret and sets of participants in Δ can not obtain any new information about the secret. In this paper we present a more precise definition of secret sharing schemes in terms of information theory, and a new decomposition theorem. This theorem generalizes previous decomposition theorems and also works for a more general class of access structures. We demonstrate some applications of the theorem.

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Authors and Affiliations

  1. Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA, Eindhoven, The Netherlands

    Marten van Dijk

  2. Department of Pure Mathematics, The University of Adelaide, Adelaide, SA, 5005, Australia

    Wen-Ai Jackson

  3. ESAT-COSIC, Katholieke Universiteit Leuven, Kard. Mercierlaan 94, B-3001, Heverlee, Belgium

    Keith M. Martin

Authors
  1. Marten van Dijk
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  2. Wen-Ai Jackson
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  3. Keith M. Martin
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Dijk, M.v., Jackson, WA. & Martin, K.M. A General Decomposition Construction for Incomplete Secret Sharing Schemes. Designs, Codes and Cryptography 15, 301–321 (1998). https://doi.org/10.1023/A:1008381427667

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