Efficient and Secure Keys Management for

This paper presents an e#cient algorithm for the secure group key management of mobile users. The most promising protocols to deal with group key management are those based on logical key hierarchy (LKH). The LKH model reduces to logarithmic size the resources needed: computation time, message exchanged, and memory space. In the framework of the LKH model, we present a new protocol LKH++ that outperforms the other proposed solutions in the literature. Such performance improvements are obtained exploiting both the properties of one-way hash functions and the information that the users already share in the LKH model. In particular, when a user eviction occurs in LKH++, each remaining user autonomously constructs a new key along the path from the evicted user to the root as a function of a specific logical child key. Therefore, the center can carry on the re-keying phase by distributing only a subset of the new keys and by reducing the number of communications to the users. When a join occurs, a minimal information is broadcast, while most of the communications are unicast toward just the joining user. The proposed LKH++ protocol establishes a group communication of n users requiring to unicast ((n 1) log n)/2 keys, while standard algorithms require to deliver n log n keys. Such a solution allows the users to form promptly a new group if the wireless ad hoc network should be reconfigured. Moreover, the proposed extension to deal with mass leave and mass join allows a considerable savings in the messages sent by the center, as well as in the computations required by both the center and the users. Finally, the LKH++ protocol enhances the reliability of the key management due to the reduced number of communications needed in the re-keying phase