Extended research on optimal tree for group key management

Abstract

Key tree is a popular model to maintain the security of group information sharing by using a tree structure to maintain the keys held by different users. Previously, researchers have proved that to minimize the worst case updating cost in case of single user deletion, one needs to use a special 2-3 tree. In this project, we study the average case, loyal user case and weighted user case for single user update. We proved that in the optimal tree, the branching degree of every node can be bounded by 3 and furthermore the structure of the optimal tree can be pretty balanced. Then we introduce the loyal user concept into the project and explore the optimal structure under this assumption. Again a balanced degree 3 tree is optimal for any number of normal users and one single loyal user. Replacing the one single user in the previous optimal tree with a loyal user star can be the optimal tree with more than one loyal user. At last, we bring weighted user on the table. Also, a degree bound 3 applies in this case. Based on that, we provide an approximate algorithm to generate a tree with good performance.