Extending Brickell–Davenport theorem to non-perfect secret sharing schemes

One important result in secret sharing is the Brickell–Davenport theorem: every ideal perfect secret sharing scheme defines a matroid that is uniquely determined by the access structure. We present a generalization of the Brickell–Davenport theorem to the general case, in which non-perfect schemes a...

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Bibliographic Details
Published in:Designs, codes, and cryptography Vol. 74; no. 2; pp. 495 - 510
Main Authors: Farràs, Oriol, Padró, Carles
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2015
Subjects:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
Non-perfect secret sharing scheme
94A62
05B35
Secret sharing
Matroid
Polymatroid
ISSN:0925-1022, 1573-7586
Online Access:Get full text
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Summary:One important result in secret sharing is the Brickell–Davenport theorem: every ideal perfect secret sharing scheme defines a matroid that is uniquely determined by the access structure. We present a generalization of the Brickell–Davenport theorem to the general case, in which non-perfect schemes are also considered. After analyzing that result under a new point of view and identifying its combinatorial nature, we present a characterization of the (not necessarily perfect) secret sharing schemes that are associated with matroids. Some optimality properties of such schemes are discussed.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-013-9858-8