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As applications of secure multicast in networks continue to grow, the demand for an efficient scheme to manage group keys for secure group communication becomes more urgent. In this paper, we propose a new key tree structure for group key management. With this optimal tree structure, system resources such as network bandwidth can be saved. We devise an algorithm to generate this optimal tree and show that it can be implemented efficiently. We also design an adaptive system for group key management which consists of four components: a request receiver, a key tree update controller, a delay calculator and a request predictor. This system can maintain the optimality of the key tree dynamically. It is verified by theoretical analysis and simulation result that the performance of our scheme is better than other schemes based on traditional tree structures.