Minimizing center key storage in hybrid one-way function based group key management with communication constraints

We study the problem of designing a storage efficient secure multicast key management scheme based on one-way function trees (OFT) for a prespecified key update communication overhead. Canetti, Malkin and Nissim presented a hybrid model that divides a group of N members into clusters of M members and assigns each cluster to one leaf node of a key tree. Using the model, we formulate a constrained optimization problem to minimize the center storage in terms of the cluster size M . Due to the monotonicity of the center storage with respect to M , we convert the constrained optimization into a fixed point equation and derive the optimal M∗ explicitly. We show that the asymptotic value of the optimal M∗, given as μ+ a−1 loge a loge μ with μ= O(logN) and a being the degree of a key tree, leads to the minimal storage as O( N logN ), when the update communication constraint is given as O(logN). We present an explicit design algorithm that achieves minimal center storage for a given update communication constraint.  2004 Elsevier B.V. All rights reserved.