A Mobile Ad Hoc Network (MANET) is an autonomous network developed using wireless mobile nodes without the support of any kind of infrastructure. In a MANET, nodes can communicate with each other freely and dynamically. However, MANETs are prone to serious security threats that are difficult to resist using the existing security approaches. Therefore, various secure routing protocols have been developed to strengthen the security of MANETs. In this paper, a secure and energy-efficient routing protocol is proposed by using group key management. Asymmetric key cryptography is used, which involves two specialized nodes, labeled the Calculator Key (CK) and the Distribution Key (DK). These two nodes are responsible for the generation, verification, and distribution of secret keys. As a result, other nodes need not perform any kind of additional computation for building the secret keys. These nodes are selected using the energy consumption and trust values of nodes. In most of the existing routing protocols, each node is responsible for the generation and distribution of its own secret keys, which results in more energy dissemination. Moreover, if any node is compromised, security breaches should occur. When nodes other than the CK and DK are compromised, the entire network’s security is not jeopardized. Extensive experiments are performed by considering the existing and the proposed protocols. Performance analyses reveal that the proposed protocol outperforms the competitive protocols.