Ideal secret sharing schemes with multipartite access structures

Ng, Siaw–Lynn

doi:10.1049/ip-com:20050073

Cited by 24 publications

(29 citation statements)

References 7 publications

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“…In addition, while these open problems have been previously studied for particular families of multipartite access structures [1,2,4,7,14,16,32,35,43,44], our approach makes it possible to state them in the most general possible way.…”

Section: Constructing Ideal Multipartite Secret Sharing Schemesmentioning

confidence: 99%

“…Constructions of ideal secret sharing schemes for variants of the compartmented and multilevel access structures, and also for some tripartite access structures, have been given in [1,2,16,32,43,44]. All these constructions provide vector space secret sharing schemes, but some interesting new techniques are introduced in the ones by Tassa [43] and Tassa and Dyn [44].…”

Section: On the Construction Of Ideal Multipartite Secret Sharing Schmentioning

confidence: 99%

“…The existence of such a matrix representing the matroid M is guaranteed by Theorem 6.1. The constructions of ideal multipartite secret sharing schemes in [1,2,7,16,32,35,43,44] follow a common strategy. Namely, such a matrix M is constructed in some way and then one has to check that, for every basis of the matroid M, the corresponding columns of M are linearly independent.…”

Section: Constructing Ideal Multipartite Secret Sharing Schemesmentioning

confidence: 99%

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Ideal Multipartite Secret Sharing Schemes

Farràs¹,

Martí-Farré²,

Padrö³

2007

Advances in Cryptology - EUROCRYPT 2007

108

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Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. In this work, the characterization of ideal multipartite access structures is studied with all generality. Our results are based on the well-known connections between ideal secret sharing schemes and matroids and on the introduction of a new combinatorial tool in secret sharing, integer polymatroids.Our results can be summarized as follows. First, we present a characterization of multipartite matroid ports in terms of integer polymatroids. As a consequence of this characterization, a necessary condition for a multipartite access structure to be ideal is obtained. Second, we use representations of integer polymatroids by collections of vector subspaces to characterize the representable multipartite matroids. In this way we obtain a sufficient condition for a multipartite access structure to be ideal, and also a unified framework to study the open problems about the efficiency of the constructions of ideal multipartite secret sharing schemes. Finally, we apply our general results to obtain a complete characterization of ideal tripartite access structures, which was until now an open problem.

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Section: Constructing Ideal Multipartite Secret Sharing Schemesmentioning

confidence: 99%

Section: On the Construction Of Ideal Multipartite Secret Sharing Schmentioning

confidence: 99%

Section: Constructing Ideal Multipartite Secret Sharing Schemesmentioning

confidence: 99%

See 1 more Smart Citation

Ideal Multipartite Secret Sharing Schemes

Farràs¹,

Martí-Farré²,

Padrö³

2007

Advances in Cryptology - EUROCRYPT 2007

108

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“…As an example we consider the quasi-threshold multipartite defining structures that were first described in [11]. Construction 4.6 Let P 1 , .…”

Section: Construction 45mentioning

confidence: 99%

The combinatorics of generalised cumulative arrays

Martin¹,

Ng²

2007

Mathematical Cryptology

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In this paper we present a combinatorial analysis of generalised cumulative arrays. These are structures that are associated with a monotone collections of subsets of a base set and have properties that find application in areas of information security. We propose a number of basic measures of efficiency of a generalised cumulative array and then study fundamental bounds on their parameters. We then look at a number of construction techniques and show that the problem of finding good generalised cumulative arrays is closely related to the problem of finding boolean expressions with special properties.

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“…By using different kinds of polynomial interpolation, Tassa [33], and Tassa and Dyn [34] proposed constructions of ideal secret sharing schemes for several families of multipartite access structures that contain the multilevel and compartmented ones. Other proposals of ideal multipartite secret sharing schemes have been given in [14,26]. All these constructions are based as well on the general linear algebra method by Brickell [6].…”

Section: Introductionmentioning

confidence: 99%

Ideal Hierarchical Secret Sharing Schemes

Farràs

Padrö

2010

Lecture Notes in Computer Science

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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.

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Ideal secret sharing schemes with multipartite access structures

Cited by 24 publications

References 7 publications

Ideal Multipartite Secret Sharing Schemes

Ideal Multipartite Secret Sharing Schemes

The combinatorics of generalised cumulative arrays

Ideal Hierarchical Secret Sharing Schemes

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