Optimal Trees for Minimizing Average Individual Updating Cost

Key tree is a popular model to maintain the security of group information sharing by using a tree structure to maintain the keys held by different users. Previously, researchers proved that to minimize the worst case updating cost in case of single user deletion, one needs to use a special 2-3 tree. In this paper, we study the average case for user update. We prove that in the optimal tree, the branching degree of every node can be bounded by 3 and furthermore the structure of the optimal tree can be pretty balanced. We also show the way to construct the optimal tree when there are loyal users in the group.

[1]  Yang Richard Yang,et al.  Reliable group rekeying: a performance analysis , 2001, SIGCOMM 2001.

[2]  Minming Li,et al.  Optimal tree structure with loyal users and batch updates , 2011, J. Comb. Optim..

[3]  Guevara Noubir,et al.  Optimal tree structure for key management of simultaneous join/leave in secure multicast , 2003, IEEE Military Communications Conference, 2003. MILCOM 2003..

[4]  Minming Li,et al.  Approximately optimal trees for group key management with batch updates , 2009, Theor. Comput. Sci..

[5]  Enhong Chen,et al.  Optimal tree structures for group key tree management considering insertion and deletion cost , 2009, Theor. Comput. Sci..

[6]  Enhong Chen,et al.  Optimal key tree structure for two-user replacement and deletion problems , 2013, J. Comb. Optim..

[7]  Zhi-Zhong Chen,et al.  Optimizing deletion cost for secure multicast key management , 2008, Theor. Comput. Sci..

[8]  Xiaozhou Li,et al.  Batch rekeying for secure group communications , 2001, WWW '01.

[9]  George Varghese,et al.  A lower bound for multicast key distribution , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[10]  Minming Li,et al.  Optimal Tree Structures for Group Key Management with Batch Updates , 2007, SIAM J. Discret. Math..

[11]  Mohamed G. Gouda,et al.  Secure group communications using key graphs , 1998, SIGCOMM '98.