Design and analysis of algorithms in managing dynamic group key trees

Abstract

We consider secure group communications using a group key to encrypt all messages sent to a designated group. When the group membership is updated dynamically, which means any group member may join and leave at any time, the group key needs to be updated to ensure security. A tree structure can be used to organize the group keys as well as certain auxiliary keys to lower the communication overhead incurred by key distribution and group membership updates. In this thesis, two different update models are taken into consideration. In the first update model, we consider the problem of finding the best tree that minimizes the amortized deletion cost. We give a dynamic programming algorithm that computes an optimal key tree in O(n3) time. In the second update model, the group keys are updated in a batch instead of being rekeyed individually. In this thesis, we propose an O(n) heuristic algorithm for the batch model when the replacement probability p ! 0. The algorithm produces a 1 + approximation to the optimal tree, where can be arbitrarily small.