The lower bound and exact value of the information rate of some developed graph access structures
Keywords:Graph access structure, Perfect secret sharing scheme, Information rate
AbstractVarious studies have focused on secret sharing schemes and in all of them, each shareholder is interested in a shorter share. The information rate of a secret sharing scheme shows the ratio between the size of the secret to the maximum number of shares given to each shareholder. In this regard, the researchers investigated the optimal information rate of the graph access structure. This paper aims to discover the exact values for the optimal information rates of the two graph access structures, which remained as open problems in Van Dijk’s paper. Furthermore, we introduced the developed multipartite graph and the developed cycle graph and calculated the exact value of their optimal information rate. Moreover, we presented a lower bound on the information rate for other developed graph access structures.
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