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Authenticated group key exchange (AGKE) enable a set of participants in a public network to share a key which can be further used to achieve confidentiality and authe.ntication. Most of the schemes required a linear number of communications round with respect to the number of group members, such schemes are not practical. Others are inefficient being required some additional condition such as central authority or logic structure. After analyzed the security of Bresson's protocol, a improved scheme is proposed, which is simple and efficient. The scheme is proven secure under Decisional Diffie-Hellman assumption.