Decomposition Construction for Secret Sharing Schemes with Graph Access Structures in Polynomial Time

Sun, Hung–Min; Wang, Huaxiong; Ku, Bying-He; Pieprzyk, Josef

doi:10.1137/080733802

Cited by 9 publications

(8 citation statements)

References 32 publications

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“…That is, if the size of each share is at least as large as the size of the secret. It is ideal if the size of each share is the same as that of the secret [18].…”

Section: Introductionmentioning

confidence: 99%

Perfect secret sharing scheme based on vertex domination set

Al-Saidi

Rajab

Said

et al. 2014

International Journal of Computer Mathematics

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“…That is, if the size of each share is at least as large as the size of the secret. It is ideal if the size of each share is the same as that of the secret [18].…”

Section: Introductionmentioning

confidence: 99%

Perfect secret sharing scheme based on vertex domination set

Al-Saidi

Rajab

Said

et al. 2014

International Journal of Computer Mathematics

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“…There are also another approaches based on graph access structure that have received a considerable attention. In the most of these approaches, many researchers have proposed different constructions of a perfect secret sharing scheme based on uniform access structures which contains qualified subsets all of the same cardinality m. In these constructions, participants are represented by the vertices of a graph G, the uniform access structure Γ is based on the concept of adjacent vertices and represented by the edges, for more details see for instance [4,18,3,14,6,13]. In [2] a novel approach to design a graph access structure, which is based on the concept of non-adjacent vertices, was proposed.…”

Section: Introductionmentioning

confidence: 99%

An ideal hierarchical secret sharing scheme

Meriem,

Sadek

2020

Preprint

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One of the methods used in order to protect a secret K is a secret sharing scheme. In this scheme the secret K is distributed among a finite set of participants P by a special participant called the dealer, in such a way that only predefined subsets of participants can recover the secret after collaborating with their secret shares. The construction of secret sharing schemes has received a considerable attention of many searchers whose main goal was to improve the information rate. In this paper, we propose a novel construction of a secret sharing scheme which is based on the hierarchical concept of companies illustrated through its organization chart and represented by a tree. We proof that the proposed scheme is ideal by showing that the information rate equals 1. In order to show the efficiency of the proposed scheme, we discuss all possible kinds of attacks and proof that the security in ensured. Finally, we include a detailed didactic example for a small company organization chart.

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“…Farrás and Padró formalized the concept of hierarchical access structure [7]. Secret sharing schemes based on graph access structures were also proposed [8]- [10]. These schemes obtain the optimal information rates for some access structures, but these schemes cannot be applied to many access structures.…”

Section: Introductionmentioning

confidence: 99%

Recursive General Secret Sharing Scheme Based on Authorized Subsets

Itoh¹,

Tochikubo²

2019

IJMLC

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The basic idea of secret sharing is that a dealer distributes a piece of information about a secret to each participant in such a way that authorized subsets of participants can reconstruct the secret but unauthorized subsets of participants cannot determine the secret. We propose a new secret sharing scheme realizing general access structures, which is based on authorized subsets. The proposed scheme is perfect and can reduce the number of shares distributed to one specified participant. In the implementation of secret sharing schemes for general access structures, an important issue is the number of shares distributed to each participant. We can apply the proposed scheme to the same access structure recursively. That is, the proposed scheme can reduce the number of shares distributed to another participant once again by applying the proposed scheme recursively. We apply the proposed scheme to all access structures on five participants in order to evaluate the efficiency of the proposed scheme.Index Terms-Secret sharing scheme, general access structure, ( , )-threshold scheme.∈ Γ, ⊂ ′ ⊂ ⟹ ′ ∈ Γ.Let Γ 0 be a family of the minimal sets in Γ, called the minimal access structure. Γ 0 is denoted by Γ 0 = { ∈ Γ ∶ ′ ⊄ for all ′ ∈ Γ − { }}.

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Decomposition Construction for Secret Sharing Schemes with Graph Access Structures in Polynomial Time

Cited by 9 publications

References 32 publications

Perfect secret sharing scheme based on vertex domination set

Perfect secret sharing scheme based on vertex domination set

An ideal hierarchical secret sharing scheme

Recursive General Secret Sharing Scheme Based on Authorized Subsets

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