The Optimal Information Rates of the Graph Access Structures on Seven Participants

Abstract

The information rate is an important metric of the performance of a secret-sharing scheme. In this paper, we deal with determining the exact values for the optimal information rates of the six graph access structures and improving the information rate of a graph access structure on seven participants, which remained as open problems in Song's and Wang's paper([1,2]). We prove that the optimal information rate for each of the six graph access structures is equal to 4/7