The secret sharing realizing the prohibited structure, which specifies the corruptible subsets of participants, can be determined directly by exploitation of the system setting and the attributes of all participants. Recently, Sun et al. had proposed a construction of secret sharing for graph-based prohibited structures where a vertex denotes a participant and an edge a pair of participants who cannot recover the secret. But their scheme is inefficient and costly. In this paper, we present a new and efficient secret sharing realizing graph-based prohibited structures and prove that the scheme satisfies both properties of the secret sharing scheme, i.e. the reconstruction property and the perfect property. The main features of our scheme are that it only needs some modular additions and subtractions in both shares assignment phase and secret recovery phase, which is an advantage in terms of computational complexity, and it can achieve higher information rate than existing ones.
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