Dynamic security of group key distribution and its solutions

By analyzing the existing schemes of group key distribution, this paper proposes a mathematical model for scalable secure group key distribution schemes. The dynamic security of group key distribution is formally defined based on this model. The model is more practical by noting that existing formal models are only capable of characterizing the static security. Furthermore, a composition operation for group key distribution schemes is introduced, and a sufficient condition that preserves the security under the composition operation is given. Then an approach for constructing secure scalable group key distribution schemes is also given. As a practical example for applying this approach, a new group key distribution scheme for large and dynamic multicast groups is proposed. The scheme proposed in this paper is based on hierarchical management and can efficiently handle the joining and leaving of group members. Its security is provable under the assumption of one-way function and independent of the computational complexity of cryptography. In the scheme subgroup managers may be introduced to distribute the management for group members and reduce the overhead of the group center manager. Alternatively, the scheme can be applied to centralized and distributed environments.