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A distributed group key agreement protocol based on authenticated-BD and logical tree, namely T-BD, was proposed. Although the communication and computation costs are increased at the beginning of the proposed protocol, the protocol can guarantee honesties of participants and prevent attacks from internal malicious members. Since the protocol has authentication ability, it can detect the internal malicious attackers. And, the communication and computation costs decrease when new members join and leave, dealing with members' joining and quitting efficiently. As the protocol is constructed on top of authenticated-BD, the internal malicious members can not attack initiatively. Compared with the existing protocols, the proposed protocol has low communication cost and efficient modular exponentiation and is more scalable for distributed P2P application. [ABSTRACT FROM AUTHOR]