Mostra el registre d'ítem simple
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 | 2017-07-04T05:40:29Z |
dc.date.available | 2017-07-04T05:40:29Z |
dc.date.issued | 2010 |
dc.identifier.citation | Farràs Ventura, O., Padro, C. Ideal hierarchical secret sharing schemes. A: Theory of Cryptography Conference. "Theory of Cryptography: 7th Theory of Cryptography Conference, TCC 2010: Zurich, Switzerland: february 9-11, 2010: proceedings". Zurich: Springer, 2010, p. 219-236. |
dc.identifier.isbn | 978-3-642-11799-2 |
dc.identifier.uri | http://hdl.handle.net/2117/106120 |
dc.description.abstract | Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention from 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 deals with the properties of the hierarchically minimal sets of the access structure, which are the minimal qualified sets whose participants are in the lowest possible levels in the hierarchy. By using our characterization, it can be efficiently checked whether any given hierarchical access structure that is defined by its hierarchically minimal sets is ideal. We use the well known connection between ideal secret sharing and matroids and, in particular, the fact that every ideal access structure is a matroid port. In addition, we use recent results on ideal multipartite access structures and the connection between multipartite matroids and integer polymatroids. We prove that every ideal hierarchical access structure is the port of a representable matroid and, more specifically, we prove that every ideal structure in this family admits ideal linear secret sharing schemes over fields of all characteristics. In addition, methods to construct such ideal schemes can be derived from the results in this paper and the aforementioned ones on ideal multipartite secret sharing. Finally, we use our results to find a new proof for the characterization of the ideal weighted threshold access structures that is simpler than the existing one. |
dc.format.extent | 18 p. |
dc.language.iso | eng |
dc.publisher | Springer |
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::Estadística matemàtica::Anàlisi multivariant |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
dc.subject.lcsh | Sequences (Mathematics) |
dc.subject.lcsh | Coding theory |
dc.subject.other | Secret sharing |
dc.subject.other | Ideal secret sharing schemes |
dc.subject.other | Hierarchical secret sharing |
dc.subject.other | Weighted threshold secret sharing |
dc.subject.other | Multipartite secret sharing |
dc.subject.other | Multipartite matroids |
dc.subject.other | Integer polymatroids |
dc.title | Ideal hierarchical secret sharing schemes |
dc.type | Conference report |
dc.subject.lemac | Seqüències (Matemàtica) |
dc.subject.lemac | Codificació, Teoria de la |
dc.contributor.group | Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia |
dc.identifier.doi | 10.1007/978-3-642-11799-2_14 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::62 Statistics::62L Sequential methods |
dc.subject.ams | Classificació AMS::94 Information And Communication, Circuits::94A Communication, information |
dc.relation.publisherversion | https://link.springer.com/chapter/10.1007%2F978-3-642-11799-2_14 |
dc.rights.access | Open Access |
local.identifier.drac | 18547379 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Farràs Ventura, O.; Padro, C. |
local.citation.contributor | Theory of Cryptography Conference |
local.citation.pubplace | Zurich |
local.citation.publicationName | Theory of Cryptography: 7th Theory of Cryptography Conference, TCC 2010: Zurich, Switzerland: february 9-11, 2010: proceedings |
local.citation.startingPage | 219 |
local.citation.endingPage | 236 |