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Ideal hierarchical secret sharing schemes
dc.contributor.author | Farràs Ventura, Oriol |
dc.contributor.author | Padró Laimon, Carles |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2017-06-29T08:18:46Z |
dc.date.available | 2017-06-29T08:18:46Z |
dc.date.issued | 2012-01-24 |
dc.identifier.citation | Farràs 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.identifier.issn | 0018-9448 |
dc.identifier.uri | http://hdl.handle.net/2117/105968 |
dc.description.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. |
dc.format.extent | 14 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa |
dc.subject.lcsh | Programming (Mathematics) |
dc.subject.lcsh | Operations research |
dc.subject.other | secret sharing |
dc.subject.other | ideal secret sharing schemes |
dc.subject.other | hierarchical secret sharing |
dc.subject.other | weighted secret sharing schemes |
dc.subject.other | multipartite secret sharing |
dc.title | Ideal hierarchical secret sharing schemes |
dc.type | Article |
dc.subject.lemac | Programació (Matemàtica) |
dc.subject.lemac | Investigació operativa |
dc.contributor.group | Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia |
dc.identifier.doi | 10.1109/TIT.2011.2182034 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming |
dc.subject.ams | Classificació AMS::90 Operations research, mathematical programming::90B Operations research and management science |
dc.relation.publisherversion | http://ieeexplore.ieee.org/document/6138912/ |
dc.rights.access | Open Access |
local.identifier.drac | 18547258 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Farràs Ventura, O.; Padro, C. |
local.citation.publicationName | IEEE transactions on information theory |
local.citation.volume | 58 |
local.citation.number | 5 |
local.citation.startingPage | 3273 |
local.citation.endingPage | 3286 |
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