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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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 |
work_keys_str_mv |
AT hameedali acharacterisationofidealweightedsecretsharingschemes AT slinkoarkadii acharacterisationofidealweightedsecretsharingschemes AT hameedali characterisationofidealweightedsecretsharingschemes AT slinkoarkadii characterisationofidealweightedsecretsharingschemes |
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