As the utilization of Underwater Acoustic Sensor Networks (UASNs) in industrial and military operations increases, there is a requirement to guarantee the confidentiality and integrity of the data being transmitted. However, protecting communication in UASNs is very challenging as they are often deployed in unattended environments without physical protection. The slow propagation speed of underwater acoustic waves and low channel bandwidth are additional challenges affecting the design and implementation of security mechanisms. This paper outlines the main disadvantages of using conventional key-exchange protocols in resource-constrained environments such as UASNs, and proposes the utilization of implicit certificates and Hashed One-pass Menezes-QuVanstone (HOMQV) key-exchange protocol as an alternative. We implemented the proposed solution on several computing platforms and present the performance evaluation results in terms of computational time and communication overhead. Our analysis shows that using HOMQV in combination with Elliptic Curve Qu-Vanstone (ECQV) protocol for implicit certificate generation can significantly reduce communication and power consumption requirements compared to Diffie-Hellman (DH) protocol based on X.509 certificates.