Multicast and broadcast are efficient ways to deliver messages to a group of recipients in a network. Due to the growing security concerns in various applications, messages are often encrypted with a secret group key. The key tree model which has been widely adopted maintains a set of keys in a tree structure so that in case of group member change, the group key can be updated in a secure and efficient way. In this paper, we focus on the updating cost incurred by member deletions. To implement a sequence of member deletions in any key tree, a certain number of encrypted messages need to be broadcast to accomplish the updates. Our goal is to identify the best key tree which can minimize the worst case deletion cost (i.e., the amortized cost over n member deletions). We prove that there is an optimal tree where all internal nodes have degree at most 5. Furthermore, any internal node with degree not equal to 3 must be such that all of its children are leaves. Based on these characterizati...
Zhi-Zhong Chen, Ze Feng, Minming Li, F. Frances Ya