Optimal information rate of secret sharing schemes on trees

László Csirmaz, Gábor Tardos

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The information rate for an access structure is the reciprocal of the load of the optimal secret sharing scheme for this structure. We determine this value for all trees: it is , where is the size of the largest core of the tree. A subset of the vertices of a tree is a core if it induces a connected subgraph and for each vertex in the subset one finds a neighbor outside the subset. Our result follows from a lower and an upper bound on the information rate that applies for any graph and happen to coincide for trees because of a correspondence between the size of the largest core and a quantity related to a fractional cover of the tree with stars.

Original languageEnglish
Article number6399598
Pages (from-to)2527-2530
Number of pages4
JournalIEEE Transactions on Information Theory
Volume59
Issue number4
DOIs
Publication statusPublished - Apr 2013

Keywords

  • Entropy method
  • Fractional packing and cover
  • Graph
  • Information rate
  • Secret sharing scheme

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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