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
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
Optimal Tree Structures for Group Key Tree Management Considering Insertion and Deletion Cost
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Optimal Key Tree Structure for Deleting Two or More Leaves
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Approximation Algorithms for Key Management in Secure Multicast
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
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
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We study the optimal tree structure for the key management problem. In the key tree, when two or more leaves are deleted or replaced, the updating cost is defined to be the number of encryptions needed to securely update the remaining keys. The objective is to find the optimal tree structure where the worst case updating cost is minimum. We extend the result of 1-replacement problem in Snoeyink et al. (Proceedings of the twentieth annual IEEE conference on computer communications, pp. 422---431, 2001) to the k-user case. We first show that the k-deletion problem can be solved by handling k-replacement problem. Focusing on the k-replacement problem, we show that the optimal tree can be computed in $O(n^{(k+1)^{2}})$ time given a constant k. Then we derive a tight degree bound for optimal tree when replacing two users. By investigating the maximum number of leaves that can be placed on the tree given a fixed worst case replacement cost, we prove that a balanced tree with certain root degree 5驴d驴7 where the number of leaves in the subtrees differs by at most one and each subtree is a 2-3 tree can always achieve the minimum worst case 2-replacement cost. Thus the optimal tree for two-user replacement problem can be efficiently constructed in O(n) time.