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Logic key hierarchy is a leading scheme for key distribution in secure multicast. An improved logic key hierarchy scheme, based on one-way hash function, is proposed. Besides its simplicity, the improved scheme can reduce key server's average cost by about 1/3. Moreover, a batch update algorithm for this improved scheme is also presented, and its performance is evaluated through experiments. Compared with batch update algorithm in logic key hierarchy scheme, it shows the algorithm presented in this paper can reduce key server cost by at least 1/3.