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A group key agreement (GKA) protocol is a mechanism to establish a cryptographic key for a group of participants, based on each onepsilas contribution, over a public network. In ad-hoc networks, the movement of the nodes may quickly change the topology resulting in the increased overhead during messaging for topology maintenance. The region-based schemes of ad-hoc networks, aim of handling topology maintenance, managing node movement and reducing overhead. In this paper, a simple, secure and efficient region-based GKA protocol using CRTDH&TGDH well suited to dynamic ad-hoc networks is presented and also introduces a region-based contributory group key agreement that achieves the performance lower bound by utilizing a novel CRTDH and TGDH protocol called CRTDH&TGDH protocol. Both theoretical and experimental results show that the proposed scheme achieves communication, computation and memory cost is lower than the existing group key agreement schemes.