## 4 Security Analysis and Discussion
### Discussion  
Table 1 provides a comparative analysis of three QKA protocols based on GSA: the protocols proposed by [PERSON] and [PERSON] [16], [PERSON] et al. [17], and the scheme proposed in this study. All three utilize GSA as their foundational approach. In terms of key sharing channels, both the [PERSON] and [PERSON] protocol and our proposed scheme operate over quantum channels, whereas the protocol by [PERSON] et al. requires an \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **[PERSON] and [PERSON] [16]** & **[PERSON] et al. [17]** & **Ours** \\ \hline Methodology & GSA & GSA & GSA \\ \hline Key sharing channels & quantum channels & authenticated classical channel & quantum channels \\ \hline Requires authenticated classical channel & No & Yes & No \\ \hline Quantum memory problem & No & No & No \\ \hline Security & Yes & No & Yes \\ \hline Fairness & Yes & No & Yes \\ \hline Number of measurements & 8n & 4n & 8n \\ \hline Number of unitary operations & 3n + 3n & 2n & 4n + 4n \\ \hline Quantum communication & \(\frac{2n}{8n+0}=\frac{1}{4}\) & \(\frac{2n}{4n+2n}=\frac{1}{3}\) & \(\frac{2n}{8n+0}=\frac{1}{4}\) \\ \hline Qubit efficiency \(\eta_{2}\) & \(\frac{2n}{8n}=\frac{1}{4}\) & \(\frac{2n}{4n}=\frac{1}{2}\) & \(\frac{2n}{8n}=\frac{1}{4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of quantum key agreement protocols based on Grover’s search algorithm. authenticated classical channel. This dependency is particularly problematic in IoMT environments, where establishing authenticated classical infrastructure is not only impractical due to resource constraints, but also exposes the protocol to potential quantum computing attacks on classical authentication mechanisms. Additionally, the Huang et al. scheme suffers from a classical-quantum dependence issue, which is not present in the Cao and Ma protocol or in our design. Regarding quantum memory requirements, all three protocols avoid the need for quantum memory, a favorable attribute for medical devices. Security-wise, Table 1 identifies the Huang et al. protocol as partially insecure, while the other two schemes are deemed secure. This distinction is crucial given the sensitive nature of medical data in IoMT applications. Fairness, which ensures equal participation in the key generation process, is also lacking in the Huang et al. protocol but maintained in the other two. These assessments align with prior evaluations cited in the Introduction, which confirmed the Huang et al. scheme's potential deficiencies in both fairness and security. From an efficiency perspective, the theoretical quantum communication efficiency (\(\eta_{1}\)) of the Huang et al. protocol is \(1/3\), which is higher than both our proposed scheme and the Cao and Ma protocol, each with an \(\eta_{1}\) value of \(1/4\). Table 1 further details the qubit efficiency (\(\eta_{2}\)) and associated operational metrics: the Huang et al. protocol requires 4n measurements and 2n unitary operations; our proposed scheme involves 8n measurements and 8n unitary operations; and the Cao and Ma protocol requires 8n measurements and 6n unitary operations. Our protocol achieves 25% efficiency (2n key bits from 8n qubits consumed: 4n for initial state preparation plus 4n for decoy states). This efficiency is acceptable for IoMT applications because: (1) medical devices prioritize security over throughput due to life-critical data handling, (2) IoMT requires periodic rather than continuous key generation, (3) quantum states can be pre-computed during idle periods, and (4) our efficiency is competitive with other measurement-device-independent protocols. The security benefits justify the efficiency trade-off in medical contexts where patient safety is paramount. On the other hand, recent work by [PERSON] and [PERSON] [26] provides valuable insights into the practical implementation challenges of quantum asymmetric encryption using generalized Grover search algorithms (GGSAs), which directly relates to our protocol's scalability concerns.