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Title: Ideal hierarchical secret sharing schemes
Authors: Farràs, Oriol
Padró, Carles
Issue Date: 2011
Source: Farràs, O., & Padró, C. (2012). Ideal Hierarchical Secret Sharing Schemes. IEEE Transactions on Information Theory, 58(5), 3273-3286.
Series/Report no.: IEEE transactions on information theory
Abstract: Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization is based on the well-known connection between ideal secret sharing schemes and matroids and, more specifically, on the connection between ideal multipartite secret sharing schemes and integer polymatroids. In particular, we prove that every hierarchical matroid port admits an ideal linear secret sharing scheme over every large enough finite field. Finally, we use our results to present a new proof for the existing characterization of the ideal weighted threshold access structures.
ISSN: 0018-9448
DOI: 10.1109/TIT.2011.2182034
Rights: © 2011 IEEE.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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