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
Approximately optimal trees for group key management with batch updates
Theoretical Computer Science
Optimal tree structures for group key tree management considering insertion and deletion cost
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 with loyal users and batch updates
Journal of Combinatorial Optimization
Optimal key tree structure for two-user replacement and deletion problems
Journal of Combinatorial Optimization
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We investigate the key management problem for broadcasting applications. Previous work showed that batch rekeying can be more cost-effective than individual rekeying. Under the assumption that every user has probability $p$ of being replaced by a new user during a batch rekeying period, we study the structure of the optimal key trees. Constant bounds on both the branching degree and the subtree size at any internal node are established for the optimal tree. These limits are then utilized to give an $O(n)$ dynamic programming algorithm for constructing the optimal tree for $n$ users and any fixed value of $p$. In particular, we show that when $p 1 - 3^{-1/3} \thickapprox 0.307$, the optimal tree is an $n$-star, and when $p\leq 1 - 3^{-1/3}$, each nonroot internal node has a branching degree of at most 4. We also study the case when $p$ tends to $0$ and show that the optimal tree resembles a balanced ternary tree to varying degrees depending on certain number-theoretical properties of $n$.