Many group key management schemes that reduce the total communication cost and/or the computational cost imposed on client devices have been proposed. However optimizations of the key-management structure have not been studied. This paper proposes ways to optimize the key-management structure in a hybrid group key management scheme. The proposed method is able to minimize both the total communication cost and the computational cost imposed on client devices. First we propose a probabilistic client join/leave model in order to evaluate the communication and computational costs of group key management schemes. This model idealizes client actions generally and considers the existence of the peaks of the joining/leaving frequency. Thus we can analyze not only the average case scenario but also the worst case scenario using this model. Then we formalize the total computation cost and the computational cost imposed on client devices in group key management schemes under the model. We present both an average case analysis and a worst case analysis. Finally we show the parameters that minimize the total communication cost and the computational cost imposed on clients under the model. Our results should be useful in designing a secure group communication system for large and dynamic groups.

Many group key management schemes that reduce the total communication cost and/or the computational cost imposed on client devices have been proposed. However, optimizations of the key-management structure have not been studied. This paper proposes ways to optimize the key-management structure in a hybrid group key management scheme. The proposed method is able to minimize both the total communication cost and the computational cost imposed on client devices. First, we propose a probabilistic client join/leave model in order to evaluate the communication and computational costs of group key management schemes. This model idealizes client actions generally and considers the existence of the peaks of the joining/leaving frequency. Thus, we can analyze not only the average case scenario but also the worst case scenario using this model. Then, we formalize the total computation cost and the computational cost imposed on client devices in group key management schemes under the model. We present both an average case analysis and a worst case analysis. Finally, we show the parameters that minimize the total communication cost and the computational cost imposed on clients under the model. Our results should be useful in designing a secure group communication system for large and dynamic groups.