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Over the past few years, the synergic usage of unmanned aerial vehicles (later drones) and Internet of Things (IoT) has successfully transformed into the Internet of Drones (IoD) paradigm, where the data of interest is gathered and delivered to the Zone Service Provider (ZSP) by drones for substantial additional analysis. Considering the sensitivity of collected information and the impact of information disclosure, information privacy and security issues should be resolved properly so that the maximum potential of IoD can be realized in the increasingly complex cyber threat environment. Ideally, an authentication and key agreement protocol can be adopted to establish secure communications between drones and the ZSP in an insecure environment. Nevertheless, a large group of drones authenticating with the ZSP simultaneously will lead to a severe authentication signaling congestion, which inevitably degrades the quality of service (QoS) of IoD systems. To properly address the above-mentioned issues, a lightweight group authentication protocol, called liteGAP, is proposed in this paper. liteGAP can achieve the authenticated key establishment between a group of drones and the ZSP concurrently in the IoD environment using lightweight operations such as hash function, bitwise XOR, and physical unclonable function (PUF). We verify liteGAP using AVISPA (a tool for the automatic verification of security protocols) and conduct formal and informal security analysis, proving that liteGAP meets all pre-defined security requirements and withstand various potential cyber attacks. Moreover, we develop an experimental framework and conduct extensive experiments on liteGAP and two benchmark schemes (e.g., GASE and rampIoD). Experimental findings show that liteGAP outperforms its counterparts in terms of computational cost as well as communication overhead.