Approximately optimal trees for group key management with batch updates

  • Authors:
  • Minming Li;Ze Feng;Ronald L. Graham;Frances F. Yao

  • Affiliations:
  • Department of Computer Science, City University of Hong Kong;Department of Computer Science, City University of Hong Kong;Department of Computer Science and Engineering, University of California at San Diego;Department of Computer Science, City University of Hong Kong

  • Venue:
  • TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
  • Year:
  • 2007

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Abstract

We investigate the group key management problem for broadcasting applications. Previous work showed that, in handling key updates, batch rekeying can be more cost-effective than individual rekeying. One model for batch rekeying is to assume that every user has probability p of being replaced by a new user during a batch period with the total number of users unchanged. Under this model, it was recently shown that an optimal key tree can be constructed in linear time when p is a constant and in O(n4) time when p → 0. In this paper, we investigate more efficient algorithms for the case p → 0, i.e., when membership changes are sparse. We design an O(n) heuristic algorithm for the sparse case and show that it produces a nearly 2-approximation to the optimal key tree. Simulation results show that its performance is even better in practice. We further design a refined heuristic algorithm and show that it achieves an approximation ratio of 1 + Ɛ as p → 0.