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Reduced access structures with four minimal qualified subsets on six participants

Gharahi, M ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.3934/amc.2018014
  3. Publisher: American Institute of Mathematical Sciences , 2018
  4. Abstract:
  5. In this paper, we discuss a point about applying known decomposition techniques in their most general form. Three versions of these methods, which are useful for obtaining upper bounds on the optimal information ratios of access structures, are known as: Stinson’s λ-decomposition, (λ, ω)decomposition and λ-weighted-decomposition, where the latter two are generalizations of the first one. We continue by considering the problem of determining the exact values of the optimal information ratios of the reduced access structures with exactly four minimal qualified subsets on six participants, which remained unsolved in Martí-Farré et al.’s paper [Des. Codes Cryptogr. 61 (2011), 167-186]. We improve the known upper bounds for all the access structures, except four cases, determining the exact values of the optimal information ratios. All three decomposition techniques are used while some cases are handled by taking full advantage of the generality of decompositions. © 2018 AIMS
  6. Keywords:
  7. Decomposition techniques ; Optimal information ratio ; Secret sharing scheme
  8. Source: Advances in Mathematics of Communications ; Volume 12, Issue 1 , February , 2018 , Pages 199-214 ; 19305346 (ISSN)
  9. URL: https://aimsciences.org/article/doi/10.3934/amc.2018014