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dc.contributor.authorFarràs Ventura, Oriol
dc.contributor.authorPadró Laimon, Carles
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.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.
dc.description.abstractHierarchical 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.
dc.format.extent14 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa
dc.subject.lcshProgramming (Mathematics)
dc.subject.lcshOperations research
dc.subject.othersecret sharing
dc.subject.otherideal secret sharing schemes
dc.subject.otherhierarchical secret sharing
dc.subject.otherweighted secret sharing schemes
dc.subject.othermultipartite secret sharing
dc.titleIdeal hierarchical secret sharing schemes
dc.subject.lemacProgramació (Matemàtica)
dc.subject.lemacInvestigació operativa
dc.contributor.groupUniversitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::90 Operations research, mathematical programming::90C Mathematical programming
dc.subject.amsClassificació AMS::90 Operations research, mathematical programming::90B Operations research and management science
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
local.citation.authorFarràs Ventura, O.; Padro, C.
local.citation.publicationNameIEEE transactions on information theory

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