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To achieve secure group communications, it is critical to develop a secure group key management strategy to guarantee security of the group keys. In this paper, based on the forward security and secret sharing techniques, we propose a new dynamic group key management scheme to minimize the rekeying cost. The forward security technique reduces the rekeying operations in joining event, while the secret sharing technique ensures the scalability in leaving event. In addition, the proposed scheme can provide anonymous authentication as well as forward and backward confidentiality. Theoretical analysis also confirms the efficiency of the proposed scheme.