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Several groupware applications such as distributed databases, video conferences, distributed computation etc require secure transmission while communicating over open connected networks, and for which numerous group key agreement protocols for static/dynamic groups have been proposed for establishing a secret session key among the group members. This paper proposes ternary tree based new technique to establish a contributory secure group key for dynamic groups, where a ternary tree has at most three children per node. The proposed technique instead of using two-party Diffie-Hellman technique as used in most of the binary tree based group-key generation techniques, uses an existing three party key exchange technique called GDH.2 to establish a shared secret key between the participants. The method provides some advantages over the existing binary tree based technique as it reduces the number of iterations to log3N, where N is the number of participants, covers larger subgroup using broadcast messages than subgroup formed in binary tree based approaches etc. As a result, the total number of broadcast messages and the exponential operations are reduced and it becomes a communication and computation efficient group key agreement protocol. Since proposed technique is projected for dynamic groups, therefore after initialization operation, the method describes and calculates the complexity of major group key management operations like single join, mass join and mass leave. The results obtained are then compared with other efficient group key agreement protocols like CCEGK, EGK, TGDH, STR and it has been seen that proposed method in most of the cases performs well.