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secret sharing schemes on access structures with intersection number equal to one开题资料.pdf


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secret sharing schemes on access structures with intersection number equal to one开题资料.pdf
文档介绍:
Discrete Applied Mathematics 154 (2006) 552–563
www.elsevier.com/locate/dam
Secret sharing schemes on access structures with intersection
number equal to oneଁ
Jaume Martí-Farré, Carles Padró
Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C. Jordi Girona, 1-3, Mòdul C3, Campus Nord,
08034 Barcelona, Spain
Received 29 July 2002; received in revised form 17 March 2005; accepted 15 September 2005
Available online 24 October 2005
Abstract
The characterization of ideal access structures and the search for bounds on the optimal information rate are two important
problems in secret sharing. These problems are studied in this paper for access structures with intersection number equal to one, that
is, structures such that there is at most one participant in the intersection of any two different minimal qualified subsets. The main
result in this work is the complete characterization of the ideal access structures with intersection number equal to one. In addition,
bounds on the optimal information rate are provided for the non-ideal case.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Cryptography; Secret sharing schemes; Information rate; Ideal schemes
1. Introduction
A secret sharing scheme  is a method to distribute shares of a secret value k ∈ K among a set of participants P in
such a way that only the qualified subsets of P are able to reconstruct the value of k from their shares. Secret sharing
was introduced by Blakley [1] and Shamir [15]. A comprehensive introduction to this topic can be found in [17].A
secret sharing scheme is said to be perfect if no information about the value of the secret can be obtained from the
shares of all the participants in
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