Internet of Things (IoT) networks have advanced and have made the lives of humans much easier, during the past few decades. Raspberry Pi (RP) is a type of IoT device with memory constraints. Both military and civilian applications have used drones or Unmanned Aerial Vehicles (UAVs) over the past several decades. Internet of Drones (IoD) networks are subsets of IoT networks. Drones are resource-constrained devices. Moreover, IoD networks are vulnerable to different security attacks. Hence, 2 RP 3B+ boards are used for the network model to be treated like a drone and a Ground Control Station (GCS) respectively. Moreover, an Authenticated Key-Agreement (AKA) algorithm is designed based on Elliptic Curve Cryptography (ECC). The proposed algorithm has been designed using Python programming language, and the performance metrics analysis is done using Jupyter-Notebook. An idea of integration of timestamps and trigonometric concepts has been introduced to improve the security of the designed ECC-based AKA algorithm. The designed AKA algorithm provides different properties in terms of security, and can also resist some known attacks, as shown by the algorithm's security analysis. The proposed AKA algorithm's analysis in terms of performance shows that it outperforms 3 recent related security mechanisms in terms of performance metrics like Total Computation Cost, Total Storage Cost, and Total Communication Cost.