Construction of a Uniform Access Structure Using Minimum Independent Dominating Vertices
Abstract
The most important technologies in modern society are the information security; it is founded to provide a protection to the transmitted data. Secret sharing scheme is one of the methods designated to protect the secret data. It is a method that allows a secret to be shared among a set of participants in such a way that only qualified subsets of them can recover the secret by pooling their share together, but no less sets can do that. Many mathematical structures are used to create a secret sharing scheme; the one that based on graph access structure is the most widely used structure. In this paper, a new horizon for the construction of the perfect secret sharing schemes of rank 2 and 3 is opened by proposing of a new algorithm to construct a uniform access structure in a connected, simple, undirected, r-regular graph G.This has been done by introducing for the first time the minimum independent dominating set of vertices in a graph. The efficiency of this method is deduced to prove that the proposed method has an improvement over other previous methods.
Keywords
Uniform Access Structure, Minimum Independent Dominating Set, MID, Secret Sharing Scheme, SSS, Information Rate, RankMetrics