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In mobile ad hoc networks, authentication of users and management of group keys require more specialized solutions than traditional security protocols. Mobility of the users and unavailability of trusted central servers are major known issues for mobile networks. In this paper, an efficient and practical solution has been proposed for the group key management problem. Members authenticate each other with a fast and efficient hybrid key establishment scheme which combines elliptic curve cryptography, modular squaring operations and a secret key encryption algorithm. The proposed group key management model is based on hierarchical binary trees. Users exchange the group secret keys and form an ad hoc group in a distributed and self-organizing manner with no central control. This paper also discusses the total backward and forward security in the case of modification in membership. Finally, the proposed group key management system is scalable and respectful of the constraints of ad hoc networks. It also has comparable efficiency to the other HBT based key management protocols which employ real time key distribution authority.