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In recent times, the popularity of group oriented applications such as electronic conferences and collaboration works has increased manifold. Thus, secure group communication has become one important research issue for network security. For secure group communication, the first and important step is to design a group key establishment protocol. A group key is a common secret key which can be used to achieve confidentiality and authentication services for different group applications. The focus of the current work is on the design of secure group key agreement protocols suitable for such mobile environment where a node with high computational ability is connected to a number of (mobile) nodes with low computational efficiency. The contribution of this work is to provide a truly contributory group key agreement protocol with dynamic user join and leave facility. The security of the protocol is based on decisional Diffie-Hellman (DDH) assumption.