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The group key management is for a group manager to maintain a consistent group key for a dynamic group of members through a broadcast channel. In this paper we propose a group key management scheme based on a meta proxy re-encryption (PRE) scheme. In particular, we propose an RSA-based PRE scheme with special properties. It is the first RSA-based PRE scheme for group key management and has the desired properties of uni-directionality and multi-hop. In our group key management scheme, each group member holds just one secret auxiliary key and logN public auxiliary keys. The size of rekey messages for each group key update remains O(logN). Additionally, our scheme has some distinct features. Firstly, the size of the key update history is a constant O(N) no matter how many times of group key updates occur. Secondly, the computation time of computing the newest group key from the key update history is always O(logN) no matter how many group key updates are missed. This feature provides a practical solution for group key update when members go offline from time to time. Finally, the proposed scheme is immune to the collusion attack of other members.