The information rate is an important metric of the performance of a secret-sharing scheme. In this paper we consider 272 non-isomorphic connected graph access structures with nine vertices and eight or nine edges, and...The information rate is an important metric of the performance of a secret-sharing scheme. In this paper we consider 272 non-isomorphic connected graph access structures with nine vertices and eight or nine edges, and either determine or bound the optimal information rate in each case. We obtain exact values for the optimal information rate for 231 cases and present a method that is able to derive information-theoretical upper bounds on the optimal information rate. Moreover, we apply some of the constructions to determine lower bounds on the information rate. Regarding information rate, we conclude with a full listing of the known optimal information rate （or bounds on the optimal information rate） for all 272 graphs access structures of nine participants.展开更多
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 61373150） and the Key Technologies R ＆ D Program of Shaanxi Province （2013k0611）.
文摘The information rate is an important metric of the performance of a secret-sharing scheme. In this paper we consider 272 non-isomorphic connected graph access structures with nine vertices and eight or nine edges, and either determine or bound the optimal information rate in each case. We obtain exact values for the optimal information rate for 231 cases and present a method that is able to derive information-theoretical upper bounds on the optimal information rate. Moreover, we apply some of the constructions to determine lower bounds on the information rate. Regarding information rate, we conclude with a full listing of the known optimal information rate （or bounds on the optimal information rate） for all 272 graphs access structures of nine participants.
