Hui-Chuan Lu
A Study on the Average Information Ratio of Perfect SecretSharing Schemes for Access Structures Based On Bipartite Graphs
1343 - 1348
2012
6
9
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/13176
https://publications.waset.org/vol/69
World Academy of Science, Engineering and Technology
A perfect secretsharing scheme is a method to distribute a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of participants in any unqualified subset is statistically independent of the secret. The collection of all qualified subsets is called the access structure of the perfect secretsharing scheme. In a graphbased access structure, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. The average information ratio of a perfect secretsharing scheme realizing the access structure based on G is defined as AR (Pv2V (G) H(v))(V (G)H(s)), where s is the secret and v is the share of v, both are random variables from and H is the Shannon entropy. The infimum of the average information ratio of all possible perfect secretsharing schemes realizing a given access structure is called the optimal average information ratio of that access structure. Most known results about the optimal average information ratio give upper bounds or lower bounds on it. In this present structures based on bipartite graphs and determine the exact values of the optimal average information ratio of some infinite classes of them.
Open Science Index 69, 2012