Perfect secret sharing scheme based on vertex domination set

Al-Saidi, Nadia M. G.; Rajab, N. A.; Said, Mohamad Rushdan Md.; Kadhim, K. A.

doi:10.1080/00207160.2014.941360

Cited by 4 publications

(5 citation statements)

References 18 publications

(19 reference statements)

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“…(3) is a [8,2,6] code over F 7 with the weight enumerator 1 + 24x 6 + 24x 8 . We can then obtain nonzero codewords of C(r, 6) in this example through programming, as follows : When N 1 = 3 or N 1 = 4, the weight enumerator of some irreducible cyclic codes C(r, N ) were studied [24,26].…”

Section: A N U S C R I P Tmentioning

confidence: 99%

“…An ideal secret sharing scheme is well-known to be the best efficiency that one can achieve with lowest storage complexity and the communication complexity [5,6]. We say that Γ ⊂ 2 P is an ideal access structure if there exists an ideal secret sharing scheme for Γ.…”

Section: Introductionmentioning

confidence: 99%

“…1,3,4,6,6,4,3), (5, 6, 5, 0, 2, 1, 2, 0), (1, 5, 5, 1, 6, 2, 2, 6), (5, 5, 1, 6, 2, 2, 6, 1), (4, 2, 4, 0, 3, 5, 3, 0),(2,5,4,4,5,2,3,3), (1, 0, 6, 3, 6, 0, 1, 4), (1, 3, 4, 6, 6, 4, 3, 1),…”

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confidence: 99%

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Ideal access structures based on a class of minimal linear codes

Song

2015

International Journal of Computer Mathematics

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Coding theory is one of ways to construct ideal access structures. However, in general, determining the ideal access structures of the secret sharing schemes based on linear codes is very hard. According to the concept of minimal liner codes we proposed, this paper concentrate on irreducible cyclic codes and construct the ideal access structures of the schemes based on the duals of minimal irreducible cyclic codes. In order to study the conditions whether several types of irreducible cyclic codes are minimal, we investigate the weight enumerators of certain irreducible cyclic codes by means of cyclotomic classes and Gaussian periods. On the basis of our aforementioned studies, we obtain ideal access structures and show the corresponding examples through programming.

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Section: A N U S C R I P Tmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ideal access structures based on a class of minimal linear codes

Song

2015

International Journal of Computer Mathematics

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“…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. In this approach, an independent dominating set of vertices in a graph G was introduced and applied as a novel idea to construct a perfect secret sharing scheme such that the vertices of the graph represent the participants and the dominating set of vertices in G represents the minimal qualified set.…”

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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“…In Perfect secret sharing scheme based on vertex domination set [4], the authors present a method for protecting secret data. They introduce the novel idea of constructing a secretsharing scheme using a graph G whose vertices represent the participants and the dominating set of vertices in G represents the minimal authorized set.…”

mentioning

confidence: 99%