The integration of unmanned aerial vehicles (UAVs) into remote and beyond-visual-line-of-sight missions has increased the demand for secure, efficient, and low-latency communication systems, particularly in scenarios where satellite connectivity is the only viable option. However, high-latency satellite links and constrained onboard resources pose significant challenges to traditional cryptographic protocols. In this paper, we present a lightweight, symmetric key-based authentication and secure communication protocol designed specifically for satellite-driven UAV applications. Our protocol replaces resource-intensive public key operations with a pre-shared key approach and incorporates AESHA3, a variant of AES that leverages SHA-3 for key scheduling, along with SHA2-512 for hashing. We implement this design within the TLS and QUIC frameworks, adapting their internal packet structures to accommodate constrained environments. Experimental evaluations on Raspberry Pi testbeds reveal that our proposed QUIC implementation significantly outperforms TLS in encryption speed, handshake latency, and overall protocol execution time. The results demonstrate the suitability of the proposed system for real-time mission-critical UAV operations over satellite links, highlighting the benefits of integrating optimized symmetric cryptography into modern transport protocols.