Ideal hierarchical secret sharing schemes

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...

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Main Authors: Farràs, Oriol, Padró, Carles
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2013
Online Access:https://hdl.handle.net/10356/95919
http://hdl.handle.net/10220/11464
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-959192020-03-07T12:37:22Z Ideal hierarchical secret sharing schemes Farràs, Oriol Padró, Carles School of Physical and Mathematical Sciences 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. 2013-07-15T08:25:45Z 2019-12-06T19:23:20Z 2013-07-15T08:25:45Z 2019-12-06T19:23:20Z 2011 2011 Journal Article Farràs, O., & Padró, C. (2012). Ideal Hierarchical Secret Sharing Schemes. IEEE Transactions on Information Theory, 58(5), 3273-3286. 0018-9448 https://hdl.handle.net/10356/95919 http://hdl.handle.net/10220/11464 10.1109/TIT.2011.2182034 en IEEE transactions on information theory © 2011 IEEE.
institution Nanyang Technological University
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country Singapore
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language English
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Farràs, Oriol
Padró, Carles
format Article
author Farràs, Oriol
Padró, Carles
spellingShingle Farràs, Oriol
Padró, Carles
Ideal hierarchical secret sharing schemes
author_sort Farràs, Oriol
title Ideal hierarchical secret sharing schemes
title_short Ideal hierarchical secret sharing schemes
title_full Ideal hierarchical secret sharing schemes
title_fullStr Ideal hierarchical secret sharing schemes
title_full_unstemmed Ideal hierarchical secret sharing schemes
title_sort ideal hierarchical secret sharing schemes
publishDate 2013
url https://hdl.handle.net/10356/95919
http://hdl.handle.net/10220/11464
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