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Finding lower bounds on the complexity of secret sharing schemes by linear programming
dc.contributor.author | Padró Laimon, Carles |
dc.contributor.author | Vázquez González, Leonor |
dc.contributor.author | Yang, An |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2017-06-29T07:37:30Z |
dc.date.available | 2017-06-29T07:37:30Z |
dc.date.issued | 2013-05-01 |
dc.identifier.citation | Padro, C., Vázquez, L., Yang, A. Finding lower bounds on the complexity of secret sharing schemes by linear programming. "Discrete applied mathematics", 1 Maig 2013, vol. 161, núm. 7-8, p. 1072-1084. |
dc.identifier.issn | 0166-218X |
dc.identifier.uri | http://hdl.handle.net/2117/105967 |
dc.description.abstract | Optimizing the maximum, or average, length of the shares in relation to the length of the secret for every given access structure is a difficult and long-standing open problem in cryptology. Most of the known lower bounds on these parameters have been obtained by implicitly or explicitly using that every secret sharing scheme defines a polymatroid related to the access structure. The best bounds that can be obtained by this combinatorial method can be determined by using linear programming, and this can be effectively done for access structures on a small number of participants. By applying this linear programming approach, we improve some of the known lower bounds for the access structures on five participants and the graph access structures on six participants for which these parameters were still undetermined. Nevertheless, the lower bounds that are obtained by this combinatorial method are not tight in general. For some access structures, they can be improved by adding to the linear program non-Shannon information inequalities as new constraints. We obtain in this way new separation results for some graph access structures on eight participants and for some ports of non-representable matroids. Finally, we prove that, for two access structures on five participants, the combinatorial lower bound cannot be attained by any linear secret sharing scheme |
dc.format.extent | 13 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::Matemàtica discreta::Combinatòria |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica |
dc.subject.lcsh | Combinatorial probabilities |
dc.subject.lcsh | Numerical analysis |
dc.subject.other | Secret sharing |
dc.subject.other | linear programming |
dc.subject.other | polymatroid |
dc.subject.other | non-Shannon information inequalities |
dc.title | Finding lower bounds on the complexity of secret sharing schemes by linear programming |
dc.type | Article |
dc.subject.lemac | Combinacions (Matemàtica) |
dc.subject.lemac | Anàlisi numèrica |
dc.contributor.group | Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia |
dc.identifier.doi | 10.1016/j.dam.2012.10.020 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::60 Probability theory and stochastic processes::60C05 Combinatorial probability |
dc.subject.ams | Classificació AMS::65 Numerical analysis::65K Mathematical programming, optimization and variational techniques |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0166218X12004003?via%3Dihub |
dc.rights.access | Open Access |
local.identifier.drac | 18547224 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Padro, C.; Vázquez, L.; Yang, A. |
local.citation.publicationName | Discrete applied mathematics |
local.citation.volume | 161 |
local.citation.number | 7-8 |
local.citation.startingPage | 1072 |
local.citation.endingPage | 1084 |
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