Optimal level-homogeneous tree structure for logical key hierarchy

Many attempts have been made to reduce the number of re keying messages in group key management by optimizing the tree structure for logical key hierarchy (LKH) (X.S. Li et al., 2001), (W.T. Zhu, 2005). Contrary to the conventional assumption of complete alpha-ary trees, we investigate in this paper into more general tree structures called complete level-homogeneous trees. Specifically, we derive an analytical model of the average number of re keying messages in the complete level-homogeneous trees. Furthermore, since we found from the analysis results that no definite optimal tree structure is identified in terms of the conventional cost metric, we propose an algorithm that finds one of the candidate tree structures. As an another approach, in order to determine a definite optimal tree structure, we also propose a new cost metric that considers member dynamics as well as the average number of re keying messages.