The tremendous growth in the realm of Internet of Things (IoT) has materialized the architecture of Internet of Drones (IoD). Being an extension of the IoT technology, the IoD may control and monitor the drones in a particular flight area. The emerging 5G mobile communication infrastructure can greatly help in transmitting the High-Definition (HD) data making the drones to communicate even faster. Nonetheless, these drones remain vulnerable to known security threats due to exchange of communication messages on public channel. In addition, the drones may also be exposed to physical capture and examination by the malicious adversaries. Thus, more concerted efforts are required to address the security challenges for drone communication in IoD-based ecosystem. We propose a novel PUF-based authentication protocol SPAKE-DC to protect not only the drone communication on public channel but also if the drone is physically intercepted with captured resources. The SPAKE-DC protocol supports anonymity, mutual authenticity, perfect forward secrecy, and is also immune from drone physical capture attack. The proposed scheme is duly evaluated and formally analyzed under Real-or-Random Oracle model. The performance results show that SPAKE-DC carry convincing findings in terms of security, computation and communication. Moreover, it supports 42% more number of security features as compared to previous techniques.