<p>Unmanned Aerial Vehicles (UAVs) have become the preferred tool for terrain exploration due to their aerial perspective and maneuverability. Communication security between parties is ensured through the Authentication and Key Agreement (AKA) protocol. Traditional terrain exploration data processing relies on large-scale data centers, which suffer from inconvenient setup and insufficient real-time capabilities. Existing AKA protocols are susceptible to physical attacks and machine learning attacks, and they also suffer from high overhead and single-point-of-failure issues. To address these challenges, we propose a three factors authentication and key agreement protocol for UAVs-assisted terrain exploration. Specifically, we design an elliptic curve cryptography-based AKA framework to avoid single-point-of-failure issues at ground control stations, ensuring the security of the entire AKA process. Using portable terminals as fog nodes to serve as data transit stations, addressing the issues of inconvenient data center setup and insufficient real-time performance. During the login phase, three-factor authentication combining passwords, biometric features, and smart cards ensures the legitimacy of user identities. The physical properties of physically unclonable function (PUF) are utilized to resist physical attacks. Use reconfigurable PUF to update responses and resist machine learning attacks. We use the ROR model, informal security analysis, and ProVerif tool to rigorously verify our scheme. The results indicate the protocol can resist various attacks. Finally, compared to existing protocols, U2D and U2U achieve computational efficiency improvements of 56.9% and 33.4%, respectively, while reducing communication overhead by 38.1% and 28.0%, and lowering energy consumption by 24.5% and 39.2%, simultaneously, they against physical attacks and machine learning attacks, significantly enhancing security.</p>