A novel high-order tree for secure multicast key management

Multicast is used to deliver packets to a group of users. To prevent users outside the group from eavesdropping, a group key is maintained to encrypt the group communication, and the group key is changed (rekeying) when a new member joins the group or an existing member leaves the group. Rekeying costs could be as high as n for a group with n members. The hierarchical key-tree approach is widely used to achieve logarithmic rekeying costs. However, the key tree has to be kept balanced in order to keep logarithmic rekeying costs. Goshi and Ladner [8] propose the height-balanced 2-3 tree (a B-tree of order m = 3) and found that it has the best performance among the balancing strategies tested. However, balancing a B-tree [8] after member joining involves splitting oversized tree nodes and results in (m + 2)h worst-case rekeying cost, where h is the tree height. We propose an NSBHO (Non-Split Balancing High-Order) tree in which balancing tree after member joining does not involve node splitting, thus having 2h worst-case rekeying cost. An NSBHO tree is always balanced and its nodes may not satisfy the node properties of a standard B-tree. Our proposed NSBHO tree has the same worst-case rekeying cost incurred by a member removing as a B-tree [8] does. Our experiments show that the NSBHO tree has better average-case rekeying performance and far superior worst-case rekeying performance than a B-tree.