Growth of civil air traffic worldwide poses a great challenge for the supporting Communication, Navigation and Surveillance (CNS) infrastructure. Analogue systems have to be replaced by digital means to optimize spectrum efficiency and automation is becoming much more important to be able to handle the amount of participants in the air traffic system. As safety and security are strongly intertwined in aviation, cybersecurity is one key enabler for digitalization in civil aviation. As such we investigate mutual authentication and key agreement methods for the digital aeronautical ground-based communications system L-band Digital Aeronautical Communication System (LDACS). Thereby, we compare the suitability of three different Diffie Hellmann (DH) key exchange flavors used in a modified version of the Station-To-Station (STS) protocol, for digital aeronautical communication in terms of latency and security data overhead. We conclude, the STS protocol based on a central Public Key Infrastructure (PKI) trust solution with Supersingular Isogeny Diffie–Hellman (SIDH) for post-quantum security to be best suited for long term security. However, due to the smaller key sizes, Elliptic Curve Diffie-Hellman (ECDH) is the more resource efficient candidate and may play a role in low resource authentication scenarios for LDACS.