Three-level secret sharing schemes from the twisted cubic

Giulietti, Massimo; Vincenti, Rita

doi:10.1016/j.disc.2009.11.040

Cited by 27 publications

(31 citation statements)

References 7 publications

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“…This problem is studied by Beutelspacher and Wettl [10] and by Giuletti and Vincenti [27] for particular cases of multilevel access structures. They present upper and lower bounds on the minimum size of the field for several multilevel access structures with two and three levels.…”

Section: Constructing and Characterizingmentioning

confidence: 99%

Ideal Secret Sharing Schemes for Useful Multipartite Access Structures

Farràs¹,

Padrö²

2011

Lecture Notes in Computer Science

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Abstract. This paper is a survey of the main results and open problems in a line of work that was initiated shortly after secret sharing was introduced. Namely, the construction of ideal linear secret sharing schemes for access structures that are natural generalizations of the threshold ones and have interesting properties for the applications. Some of them have hierarchical properties, while other ones are suitable for situations requiring the agreement of several parties. These access structures are multipartite, that is, the participants are distributed into several parts and all participants in the same part play an equivalent role in the structure. This line of work has received an impulse from a recently discovered connection between ideal multipartite secret sharing schemes and integer polymatroids.

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Section: Constructing and Characterizingmentioning

confidence: 99%

Ideal Secret Sharing Schemes for Useful Multipartite Access Structures

Farràs¹,

Padrö²

2011

Lecture Notes in Computer Science

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“…Some issues related to the efficiency of the constructions of ideal schemes for several particular families of multipartite access structures have been considered [3], [7], [10], [17], [38], [39]. We describe in the following a unified framework, derived from the general results in [14], in which those open problems can be more precisely stated.…”

Section: Efficiency Of the Constructions Of Ideal Multipartite Smentioning

confidence: 99%

“…Other related solutions appeared in [7], [17] for very particular cases of hierarchical threshold access structures. To better understand these methods, let us consider first the case of the threshold access structures.…”

Section: Efficiency Of the Constructions Of Ideal Multipartite Smentioning

confidence: 99%

“…An efficient method to construct vector space secret sharing schemes for DHTAS was given by Brickell [10]. For some particular DHTAS, the minimum size of the field over which such schemes can be constructed have been analyzed in [7], [17]. Conjunctive hierarchical threshold access structures (CHTAS), which are dual to DHTAS, were introduced by Tassa [38].…”

Section: Summary: a Taxonomy Of Ideal Multipartite Access Strucmentioning

confidence: 99%

“…We discuss in the following some general construction methods that can be derived from the techniques introduced in previous works [7], [10], [17], [30], [38], [39] for particular families of multipartite access structures. The first method, which was used in [10], [30] and other works, consists basically in constructing the matrix M column by column, checking at every step that all submatrices that must be nonsingular are so.…”

Section: Efficiency Of the Constructions Of Ideal Multipartite Smentioning

confidence: 99%

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Natural Generalizations of Threshold Secret Sharing

Farràs

Padrö

Xing

et al. 2011

Lecture Notes in Computer Science

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Abstract-We present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit an ideal linear secret sharing schemes over every large enough finite field, they can be described by a small number of parameters, and they have useful properties for the applications of secret sharing. The use of integer polymatroids makes it possible to find many new such families and it simplifies in great measure the proofs for the existence of ideal secret sharing schemes for them.

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A new multi‐use multi‐secret sharing scheme based on the duals of minimal linear codes

Song

et al. 2014

Security Comm Networks

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There are several methods to construct multi‐secret sharing schemes, one of which is based on coding theory. Generally, however, it is very hard to determine the minimal access structures of the schemes based on linear codes. In this paper, we first propose the concept of minimal linear codes so as to make it easier to determine the access structures of the schemes based on the duals of minimal linear codes. It is proved that the shortening codes of minimal linear codes are also minimal ones. Then we present the algorithm to determine whether a class of linear codes are minimal. On the basis of our aforementioned studies, we further devise a new multi‐use multi‐secret sharing scheme based on the dual code of a minimal linear code, where each participant has to carry only one share. Furthermore, we study the minimal access structures of the multi‐secret sharing scheme and present specific examples through programming. Copyright © 2014 John Wiley & Sons, Ltd.

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Three-level secret sharing schemes from the twisted cubic

Cited by 27 publications

References 7 publications

Ideal Secret Sharing Schemes for Useful Multipartite Access Structures

Ideal Secret Sharing Schemes for Useful Multipartite Access Structures

Natural Generalizations of Threshold Secret Sharing

A new multi‐use multi‐secret sharing scheme based on the duals of minimal linear codes

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