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A logical key hierarchy (LKH) based key management approach is the most common way to manage a group key with less rekeying overhead. However, the LKH approach causes inefficiency of rekeying the group key in mobile cellular networks since it does not consider the characteristics of the networks, such as the cell-based network topology and the user's mobility. This paper proposes an efficient and practical group key management scheme dedicated to the mobile cellular networks. This new approach can achieve better performance with less management overhead than other currently available schemes, by the cell-based decentralization of key management functions. Through comparisons with other possible approaches, it is shown that the proposed scheme can obtain much better performance in terms of the communication overhead.