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Graph Decompositions and Secret Sharing Schemes

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 658)

Abstract

In this paper, we continue a study of secret sharing schemes for access structures based on graphs. Given a graph G, we require that a subset of participants can compute a secret key if they contain an edge of G; otherwise, they can obtain no information regarding the key. We study the information rate of such schemes, which measures how much information is being distributed as shares as compared to the size of the secret key, and the average information rate, which is the ratio between the secret size and the arithmetic mean of the size of the shares. We give both upper and lower bounds on the optimal information rate and average information rate that can be obtained. Upper bounds arise by applying entropy arguments due to Capocelli et al [10]. Lower bounds come from constructions that are based on graph decompositions. Application of these constructions requires solving a particular linear programming problem. We prove some general results concerning the information rate and average information rate for paths, cycles and trees. Also, we study the 30 (connected) graphs on at most five vertices, obtaining exact values for the optimal information rate in 26 of the 30 cases, and for the optimal average information rate in 28 of the 30 cases.

Keywords

Bipartite Graph Connected Graph Linear Programming Problem Secret Sharing Vertex Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di SalernoBaronissi, SAItaly
  2. 2.Computer Science and Engineering Department and Center for Communication and Information ScienceUniversity of NebraskaLincolnUSA

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