Abstract
One of the basic problems in secret sharing is to determine the exact values of the information ratio of the access structures. This task is important from the practical point of view, since the security of any system degrades as the amount of secret information increases. A Dutch windmill graph consists of the edge-disjoint cycles such that all of them meet in one vertex. In this paper, we determine the exact information ratio of secret sharing schemes on the Dutch windmill graphs. Furthermore, we determine the exact ratio of some related graph families.
Highlights
Let P = {p1, p2, . . . , pn} be the set of participants among which the dealer wants to share some secret s in such a way that only the qualified subsets of P can reconstruct the secret s
A secret sharing scheme is called perfect if the non-qualified subsets of P can not obtain any information about the secret s. 2P denotes the set of all subsets of the set P, and Γ is a collection of subsets of P
In the secret sharing schemes, the access structure Γ over P is a collection of all qualified subsets of P that is monotone and ∅ ∈/ Γ
Summary
In the secret sharing schemes, the access structure Γ over P is a collection of all qualified subsets of P that is monotone and ∅ ∈/ Γ. For arbitrary monotone access structures, Benaloh and Leichter proposed another construction to realize secret sharing schemes [1]. Stinson introduced the decomposition construction method to obtain an upper bound for the information ratio of graphical access structure [21]. The information ratio of secret sharing schemes on graphical access structures with six vertices has been studied by Van Dijk in [24]. Key words and phrases: Secret sharing, information ratio, access structure, Dutch windmill graphs.
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