## 1 Introduction
Subsequently, a variety of protocols have emerged, including those based on Bell states [10], entangled states [11], and single-particle systems [12; 13; 14]. Despite these developments, QKA protocols that leverage [PERSON]'s search algorithm (GSA) [15] are still rare. Only two such QKA protocols have been proposed. [PERSON] and [PERSON] [16] introduced the first GSA-based QKA protocol and emphasized that the traveling mode enhances efficiency over the distributed mode. [PERSON] et al. [17] later presented a GSA-based QKA protocol that enables authorized users to jointly establish a secret key without the need for quantum memory or entangled states. However, our evaluation suggests that the Huang-QKA protocol presents challenges in achieving complete fairness and security assurance, as the current framework may not guarantee uniform treatment or symmetric information access across all participants. A well-designed QKA protocol should satisfy the following three properties:  
* Security: Prevent external adversaries from gaining any useful information about the final key without being detected, and ensure that internal malicious participants cannot compromise the key generation process or undetectably influence the final key. * Correctness: Ensure that all legitimate users obtain the same final agreement key. * Fairness: Guarantee that all users have equal influence over the final key and that no user obtains the key unless all do, with equivalent assurance levels. With the growing reliance on IoMT and other mission-critical distributed systems, the demand for secure and fair QKA protocols has become increasingly urgent. While GSA offers promising computational advantages for quantum cryptographic applications, existing GSA-based QKA protocols remain limited in scope and robustness. In particular, our analysis reveals that the [PERSON] et al. 's QKA protocol fails to fully uphold the principles of fairness and security, as it does not ensure that all participants exert equal influence over the final key, nor does it guarantee symmetric protection against quantum attacks. These shortcomings motivate the development of a more balanced and resilient QKA scheme, particularly one that eliminates the dependence on authenticated classical channels--an impractical requirement in many real-world applications such as IoMT environments. The primary aim of this paper is to develop an improved GSA-based quantum key agreement protocol that guarantees fairness, security, and correctness among all participating users without relying on an authenticated classical communication channel. By modifying and extending the structure of existing GSA-QKA frameworks, we strive to construct a scheme in which each user's input contributes equally to the generation of the final key, and no subset of users can influence or predetermine the outcome. Our goal is to ensure that the key agreement process remains unbiased, robust against internal and external threats, and suitable for practical deployment in security-sensitive medical network environments. The proposed QKA protocol offers several key advantages over existing schemes. First, it enhances fairness by ensuring that all participants have equal control over the key generation process, thereby reducing the risk of insider dominance or manipulation. Second, the protocol strengthens security by resisting both classical and quantum attacks, even in the absence of classical authentication. Third, by avoiding the need for quantum memory and minimizing communication overhead, the protocol achieves high efficiency that is particularly well suited for medical devices with limited computational and power resources, making it especially applicable to IoMT environments where such constraints are prevalent. These advantages collectively position the proposed scheme as a practical solution for future secure quantum communication networks in healthcare settings where device limitations and operational constraints demand both security and efficiency. The rest of this paper is organized as follows.