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Ideal hierarchical secret sharing schemes

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10.1109/TIT.2011.2182034
 
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Farràs Ventura, Oriol
Padró Laimon, CarlesMés informacióMés informacióMés informació
Document typeArticle
Defense date2012-01-24
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
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.
CitationFarràs Ventura, O., Padro, C. Ideal hierarchical secret sharing schemes. "IEEE transactions on information theory", 24 Gener 2012, vol. 58, núm. 5, p. 3273-3286. 
URIhttp://hdl.handle.net/2117/105968
DOI10.1109/TIT.2011.2182034
ISSN0018-9448
Publisher versionhttp://ieeexplore.ieee.org/document/6138912/
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  • MAK - Matemàtica Aplicada a la Criptografia - Articles de revista [48]
  • Departament de Matemàtiques - Articles de revista [2.895]
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