On the optimization of bipartite secret sharing schemes

Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participa...

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Detalhes bibliográficos
Autores: Farras Ventura, Oriol, Metcalf-Burton, Jessica Ruth, Padró Laimon, Carles|||0000-0002-8644-5929, Vázquez González, Leonor
Formato: artículo
Fecha de publicación:2010
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/12185
Acesso em linha:https://hdl.handle.net/2117/12185
https://dx.doi.org/10.1007/978-3-642-14496-7_8
Access Level:acceso abierto
Palavra-chave:Cryptography
Matroids
Linear programming
Criptografia
Matroides
Programació lineal
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica
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repository_id_str
spelling On the optimization of bipartite secret sharing schemesFarras Ventura, OriolMetcalf-Burton, Jessica RuthPadró Laimon, Carles|||0000-0002-8644-5929Vázquez González, LeonorCryptographyMatroidsLinear programmingCriptografiaMatroidesProgramació linealÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàticaOptimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the bipartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.20102010-01-0120112011-03-31journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/12185https://dx.doi.org/10.1007/978-3-642-14496-7_8reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/121852026-05-27T15:37:01Z
dc.title.none.fl_str_mv On the optimization of bipartite secret sharing schemes
title On the optimization of bipartite secret sharing schemes
spellingShingle On the optimization of bipartite secret sharing schemes
Farras Ventura, Oriol
Cryptography
Matroids
Linear programming
Criptografia
Matroides
Programació lineal
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica
title_short On the optimization of bipartite secret sharing schemes
title_full On the optimization of bipartite secret sharing schemes
title_fullStr On the optimization of bipartite secret sharing schemes
title_full_unstemmed On the optimization of bipartite secret sharing schemes
title_sort On the optimization of bipartite secret sharing schemes
dc.creator.none.fl_str_mv Farras Ventura, Oriol
Metcalf-Burton, Jessica Ruth
Padró Laimon, Carles|||0000-0002-8644-5929
Vázquez González, Leonor
author Farras Ventura, Oriol
author_facet Farras Ventura, Oriol
Metcalf-Burton, Jessica Ruth
Padró Laimon, Carles|||0000-0002-8644-5929
Vázquez González, Leonor
author_role author
author2 Metcalf-Burton, Jessica Ruth
Padró Laimon, Carles|||0000-0002-8644-5929
Vázquez González, Leonor
author2_role author
author
author
dc.subject.none.fl_str_mv Cryptography
Matroids
Linear programming
Criptografia
Matroides
Programació lineal
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica
topic Cryptography
Matroids
Linear programming
Criptografia
Matroides
Programació lineal
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica
description Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the bipartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.
publishDate 2010
dc.date.none.fl_str_mv 2010
2010-01-01
2011
2011-03-31
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/12185
https://dx.doi.org/10.1007/978-3-642-14496-7_8
url https://hdl.handle.net/2117/12185
https://dx.doi.org/10.1007/978-3-642-14496-7_8
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,228081

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