Controller-Pilot Data Link Communications (CPDLC) are rapidly replacing voice-based Air Traffic Control (ATC) communications worldwide. Being digital, CPDLC is highly resilient and bandwidth efficient, which makes it the best choice for traffic-congested airports. Although CPDLC initially seems to be a perfect solution for modern-day ATC operations, it suffers from serious security issues. For instance, eavesdropping, spoofing, man-in-the-middle, message replay, impersonation attacks, etc. Cyber attacks on the aviation communication network could be hazardous, leading to fatal aircraft incidents and causing damage to individuals, service providers, and the aviation industry. Therefore, we propose a new security model called AKAASH, enabling several paramount security services, such as efficient and robust mutual authentication, key establishment, and a secure handover approach for the CPDLC-enabled aviation communication network. We implement the approach on hardware to examine the practicality of the proposed approach and verify its computational and communication efficiency and efficacy. We investigate the robustness of AKAASH through formal (proverif) and informal security analysis. The analysis reveals that the AKAASH adheres to the CPDLC standards and can easily integrate into the CPDLC framework.