Optimal Key Tree Structure for Deleting Two or More Leaves

Authors:
Weiwei Wu;Minming Li;Enhong Chen
Affiliations:
Department of Computer Science, University of Science and Technology of China,;Department of Computer Science, City University of Hong Kong,;Department of Computer Science, University of Science and Technology of China,
Venue:
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Year:
2008

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Abstract

We study the optimal tree structure for the key managementproblem. In the key tree, when two or more leaves are deleted orreplaced, the updating cost is defined to be the number ofencryptions needed to securely update the remaining keys. Ourobjective is to find the optimal tree structure where the worstcase updating cost is minimum. We first prove the degree upperbound (k + 1)2 - 1 when k leaves aredeleted from the tree. Then we focus on the 2-deletion problem andprove that the optimal tree is a balanced tree with certain rootdegree 5 ≤ d ≤ 7 where the number of leaves in thesubtrees differs by at most one and each subtree is a 2-3 tree.