Approximation Algorithms for Key Management in Secure Multicast

Authors:
Agnes Chan;Rajmohan Rajaraman;Zhifeng Sun;Feng Zhu
Affiliations:
Northeastern University, Boston, USA 02115;Northeastern University, Boston, USA 02115;Northeastern University, Boston, USA 02115;Cisco Systems, San Jose, USA
Venue:
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Year:
2009

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Abstract

Many data dissemination and publish-subscribe systems that guarantee the privacy and authenticity of the participants rely on symmetric key cryptography. An important problem in such a system is to maintain the shared group key as the group membership changes. 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 first present a polynomial-time approximation scheme for minimizing the average number of multicast messages needed for an update. 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.