An improved information rate of perfect secret sharing scheme based on dominating set of vertices

Due to the fast development in data communication systems and computer networks in recent years, the necessity to protect the secret data is of great demands. Several methods have been arisen to protect the secret data; one of them is the secret sharing scheme. It is a method of distributing a secret K among a finite set of participants, in such a way that only predefined subset of participant is enabled to reconstruct a secret from their shares. A secret sharing scheme realizing uniform access structure described by a graph has received a considerable attention, where each vertex represents a participant and each edge represents a minimum authorized subset. In this paper, an independent dominating set of vertices in a graph $G$ is introduced and applied as a novel idea to construct a secret sharing scheme such that the vertices of the graph represents the participants and the dominating set of vertices in $G$ represents the minimal authorized set. This new scheme is based on principle of non-adjacent vertices, whereas, most of the previous works are based on the principle of adjacent vertices. We prove that the scheme is perfect, and the lower bound of the information rate for this new construction is improved as compared to some well-known previous constructions.

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