Secure group communications using key graphs
IEEE/ACM Transactions on Networking (TON)
Batch rekeying for secure group communications
Proceedings of the 10th international conference on World Wide Web
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Optimal Tree Structures for Group Key Management with Batch Updates
SIAM Journal on Discrete Mathematics
Optimizing deletion cost for secure multicast key management
Theoretical Computer Science
Approximately optimal trees for group key management with batch updates
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Optimal tree structure for key management of simultaneous join/leave in secure multicast
MILCOM'03 Proceedings of the 2003 IEEE conference on Military communications - Volume II
Optimal tree structure with loyal users and batch updates
Journal of Combinatorial Optimization
| Hi-index | 5.23 |
We study the optimal structure for the group broadcast problem where the key tree model is extensively used. The objective is usually to find an optimal key tree to minimize the cost based on certain assumptions. Under the assumption that n members arrive in the initial setup period and only member deletions are allowed after that period, previous works show that when only considering the deletion cost, the optimal tree can be computed in O(n^2) time. In this paper, we first prove a semi-balance property for the optimal tree and use it to reduce the running time from O(n^2) to O(loglogn) multiplications of O(logn)-bit integers. Then we study the optimal tree structure when insertion cost is also considered. We show that the optimal tree is such a tree where any internal node has degree at most 7 and children of nodes with degree not equal to 2 or 3 are all leaves. Based on this result we give a dynamic programming algorithm with O(n^2) time to compute the optimal tree.