## 1 Introduction  
As flying devices controlled by built-in computer and communication equipment, unmanned aerial vehicles (UAVs) are characterized by low environmental requirements and high survivability [1]. In recent years, they have been used in many fields and are increasingly showing a trend towards networking and collaboration [2]. Wireless communication is the main method for UAVs to network and collaborate and has now become an important capability component of UAV systems. Consequently, the quality of wireless communication has a significant effect on the operation of UAVs. However, because wireless channels are transmitted in open areas, they can easily be intercepted, deceived, and manipulated by attackers [3], resulting in the illegal theft of private data, failure or accidental execution of important operations, and incalculable losses to users [4, 5]. Therefore, ensuring the security of the wireless communication between UAVs and ground stations is a problem that must be solved urgently. To improve the security of wireless communication, researchers must first address the legitimacy of the identity of the communication entity and the confidentiality and integrity of the communication data [6]. The key question is how to ensure the security of the communication key under the premise of acceptable communication delays [7]. At present, the academic community typically uses authenticated key-agreement protocols to solve this problem, such as those proposed by [PERSON] et al. [8], [PERSON] et al. [9], and [PERSON] et al. [10]. These protocols all design corresponding identity-authentication processes and key-exchange mechanisms, which to a certain extent achieve identity legitimacy verification and data-integrity verification. The above security protocols are mainly based on public key cryptography theory [11]. The session participants can securely negotiate the session key required for data encryption and achieve identity authentication in open channels [12; 13]. The session key is generated using the private parameters of each session participant in combination with an asymmetric encryption calculation, and the key changes with each session. This method ensures a high degree of key security. Therefore, the development of protocols for authenticated key negotiation in UAV communication scenarios has become a research focus (e.g., the protocols described in [14; 15], and [PERSON] [16] and [PERSON] [17], which implement identity verification and key-exchange strategies based on the asymmetry and interchangeability of public key cryptography). Common authentication-key negotiation protocols are based on the ECC (Elliptic-Curve Cryptography) [18] algorithm and DH (Diffie-Hellman) key-exchange [19] concept, and implement key exchange and identity authentication through a combination of scalar multiplication [20] and point addition [21]. Typical protocols include those described in [22; 23; 24; 25]. However, because the computing and storage devices on UAVs are usually electronic components with low computing power and limited memory space, existing protocols for negotiating authentication keys based on the ECC algorithm generally require a large number of time-consuming scalar multiplication operations. This results in an unacceptable amount of time to establish a session between the UAV and ground station, and thus, the requirements for low-latency communication cannot be met. For example, the lightweight two-party two-factor authentication protocol proposed by [PERSON] et al. [26] is based on ECC computation. It combines the identity of the protocol instance with a temporary identity and uses ECC scalar multiplication and symmetric encryption operations to perform identity authentication and key computation in advance. It can be applied to two-to-two communication scenarios, but the protocol requires eight time-consuming operations. [PERSON] [27] and [PERSON] et al. [28] proposed a learner implementation; however, their works require six time-consuming operations.