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The rising popularity of ICT and the Internet has enabled Unmanned Aerial Vehicle (UAV) to offer advantageous assistance to Vehicular Ad-hoc Network (VANET), realizing a relay node's role among the disconnected segments in the road. In this scenario, the communication is done between Vehicles to UAVs (V2U), subsequently transforming into a UAV-assisted VANET. UAV-assisted VANET allows users to access real-time data, especially the monitoring data in smart cities using current mobile networks. Nevertheless, due to the open nature of communication infrastructure, the high mobility of vehicles along with the security and privacy constraints are the significant concerns of UAV-assisted VANET. In these scenarios, Deep Learning Algorithms (DLA) could play an effective role in the security, privacy, and routing issues of UAV-assisted VANET. Keeping this in mind, we have devised a DLA-based key-exchange protocol for UAV-assisted VANET. The proposed protocol extends the scalability and uses secure bitwise XOR operations, one-way hash functions, including user's biometric verification when users and drones are mutually authenticated. The proposed protocol can resist many well-known security attacks and provides formal and informal security under the Random Oracle Model (ROM). The security comparison shows that the proposed protocol outperforms the security performance in terms of running time cost and communication cost and has effective security features compared to other related protocols.