Approximation Algorithms for Key Management in Secure
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摘要
A number of data dissemination systems, such as interactive gaming, stock data distribution, video conferencing, and publish-subscribe systems need to guarantee the privacy and authenticity of the partic- ipants. Many such systems rely on symmetric key cryptography, whereby all legitimate group members share a common key for group communication. An important problem in such a system is to maintain the shared group key as the group membership changes. The focus of this paper is on a well-studied key management approach that uses a hierarchy of auxiliary keys to update the shared group key and main- tain the desired security properties. In this key hierarchy scheme, a group controller distributes auxiliary keys to subgroups of members; when the group membership changes, an appropriate subset of the keys are updated and multicast to the relevant subgroups. We consider the problem of determining a key hierarchy that minimizes the average communication cost of an update, given update frequencies of the group members and an edge-weighted undirected graph that captures routing costs. We rst consider the objective of minimizing the average number of multicast messages needed for an update (thus ignoring the underlying routing graph), for which we present polynomial-time approximation scheme (PTAS). We next show that when routing costs are considered, the problem is NP-hard even when the underlying routing network is a tree network or even when every group member has the same update frequency. Our main result is a polynomial time constant-factor approximation algorithm for the general case where the routing network is an arbitrary weighted graph and group members have nonuniform update frequencies. We obtain improved constant approximation factors for the special cases where the routing network is a tree and when the update frequencies are uniform.
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