This paper presents an efficient contributory group key agreement protocol for secure communication between the lightweight small devices in cognitive radio mobile ad hoc networks. A Ternary tree based Group ECDH.2 (TGECDH.2) protocol that uses a batch rekeying algorithm during membership change is proposed in this paper. This ternary tree is a balanced key tree in which appropriate insertion point is selected for the joining members during rekeying operation. TGECDH.2 combines the computational efficiency of ECDH protocol and the communication efficiency of GDH.2 protocol. From the performance analysis, it is inferred that the TGECDH.2 outperforms an existing ternary tree based protocol. Hence, it is best suited for the resource constrained mobile devices such as notebooks, laptops, sensors, etc. in cognitive radio mobile ad hoc networks.