A characterisation of ideal weighted secret sharing schemes

Beimel, Tassa and Weinreb [SIAM J. Discrete Math. 22 (2008), 360–397] and Farràs and Padró [Lecture Notes in Comput. Sci. 5978, Springer, 2010, 219–236] partially characterised access structures of ideal weighted secret sharing schemes in terms of the operation of composition. They proved that any w...

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Main Authors: Hameed Ali, Slinko Arkadii
Format: Article
Language:English
Published: De Gruyter 2015-12-01
Series:Journal of Mathematical Cryptology
Subjects:
Online Access:https://doi.org/10.1515/jmc-2015-0002
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spelling doaj-f1482083f341446893f22a706d88c9812021-09-06T19:40:44ZengDe GruyterJournal of Mathematical Cryptology1862-29761862-29842015-12-019422724410.1515/jmc-2015-0002A characterisation of ideal weighted secret sharing schemesHameed Ali0Slinko Arkadii1Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New ZealandDepartment of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1142, New ZealandBeimel, Tassa and Weinreb [SIAM J. Discrete Math. 22 (2008), 360–397] and Farràs and Padró [Lecture Notes in Comput. Sci. 5978, Springer, 2010, 219–236] partially characterised access structures of ideal weighted secret sharing schemes in terms of the operation of composition. They proved that any weighted ideal access structure is a composition of indecomposable ones. Farràs and Padró gave a list of seven classes of access structures – one unipartite, three bipartite and three tripartite – to which all weighted ideal indecomposable access structures may belong. In this paper we determine exactly which access structures from those classes are indecomposable. We also determine which compositions of indecomposable weighted access structures are again weighted and obtain an if-and-only-if characterisation of ideal weighted secret sharing schemes. We use game-theoretic techniques to achieve this.https://doi.org/10.1515/jmc-2015-0002secret sharing schemeaccess structuresimple gamecomposition of games94a6291a8091a12
collection DOAJ
language English
format Article
sources DOAJ
author Hameed Ali
Slinko Arkadii
spellingShingle Hameed Ali
Slinko Arkadii
A characterisation of ideal weighted secret sharing schemes
Journal of Mathematical Cryptology
secret sharing scheme
access structure
simple game
composition of games
94a62
91a80
91a12
author_facet Hameed Ali
Slinko Arkadii
author_sort Hameed Ali
title A characterisation of ideal weighted secret sharing schemes
title_short A characterisation of ideal weighted secret sharing schemes
title_full A characterisation of ideal weighted secret sharing schemes
title_fullStr A characterisation of ideal weighted secret sharing schemes
title_full_unstemmed A characterisation of ideal weighted secret sharing schemes
title_sort characterisation of ideal weighted secret sharing schemes
publisher De Gruyter
series Journal of Mathematical Cryptology
issn 1862-2976
1862-2984
publishDate 2015-12-01
description Beimel, Tassa and Weinreb [SIAM J. Discrete Math. 22 (2008), 360–397] and Farràs and Padró [Lecture Notes in Comput. Sci. 5978, Springer, 2010, 219–236] partially characterised access structures of ideal weighted secret sharing schemes in terms of the operation of composition. They proved that any weighted ideal access structure is a composition of indecomposable ones. Farràs and Padró gave a list of seven classes of access structures – one unipartite, three bipartite and three tripartite – to which all weighted ideal indecomposable access structures may belong. In this paper we determine exactly which access structures from those classes are indecomposable. We also determine which compositions of indecomposable weighted access structures are again weighted and obtain an if-and-only-if characterisation of ideal weighted secret sharing schemes. We use game-theoretic techniques to achieve this.
topic secret sharing scheme
access structure
simple game
composition of games
94a62
91a80
91a12
url https://doi.org/10.1515/jmc-2015-0002
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