## 6 Performance Evaluation  
In this section, we conduct experiments to assess the performances of our proposed algorithm for the QKD network based on multipath-multi-key spatiotemporal diversification in a zero-trust environment. We denote our proposed MTD-based framework as the \"proposed method\". To establish a baseline for comparison, we refer to benchmark schemes that do not involve untrusted relay nodes or incorporate adaptive algorithms to avoid compromised relay [51]. In particular, this benchmark relies on multipath selection in a zero-trust environment. This benchmark scheme is denoted as the \"traditional method\". Figure 6 illustrates the time required to execute multipath QKD using both the proposed and traditional methods. As the number of nodes increases, the delay also increases in both frameworks. It is important to note that the proposed method employs more delay due to additional steps needed to determine the best path and transmit multiple QKD pairs simultaneously. Observing Figure 6, we can see that both methods initially achieve similar results, but the gap between them increases as the number of nodes increases. In Figure 7, the plot illustrates the success rate of the attack versus the pervasiveness of the attacker, which refers to the extent or degree of the presence or influence of the attacker within the system. Attacker pervasiveness represents how extensively an attacker can penetrate or impact the system's security. In this context, it reflects the percentage or proportion of the network compromised or controlled by the attacker. As the attacker's pervasiveness increases, there is a greater likelihood for the attacker to exploit system vulnerabilities and intercept QKD transmissions. However, increasing the number of transmission paths reduces the attack success rate by enhancing system complexity and making it more challenging for the attacker to compromise the system. The proposed  
Figure 6: The required time to execute the multipath QKD using the proposed and traditional methods. method consistently achieves a lower attack success rate compared to traditional methods, even with a lower number of active transmission paths. Specifically, at a 20% attacker pervasiveness level, the proposed spatiotemporal diversification algorithm with two active paths demonstrates a 97.22% lower success rate compared to the traditional method. In Figure 8, the total security percentage versus the attacker's pervasiveness is depicted as a function of different multipath selections (\(n=2,4,6\)) for both the proposed and traditional methods. The total security percentage of the system increases as the number of active paths increases and decreases as the attacker's pervasiveness increases. Notably, the proposed method enhances overall security by nearly 35% when the attacker's pervasiveness is 20%. Remarkably, even in the worst-case scenario with 80% attacker pervasiveness, the proposed spatiotemporal diversification algorithm achieves a substantial 90% overall security percentage. In conclusion, as we can see from Figures 7 and 8, leveraging additional transmission paths enhances the system's dimensionality, thereby mitigating the impact of pervasive attackers. In Figure 9, the attack success rate versus multipath selections as a function of the QKD pairs (number of QKD = 1, 3, 5) for both the proposed and traditional methods is illustrated. Remarkably, the attack success rate decreases as the number of QKD pairs increases. It's noteworthy that the proposed method achieves a significant improvement over the traditional method, with a reduction of 91.42% in the attack success rate for single key transmission and 75% for multiple QKD pairs. In Figure 10, the total security percentage versus multipath selections is depicted as a function of the QKD pairs (number of QKD = 1, 3, 5) for both the proposed and traditional methods. Notably, as the number of QKD pairs increases, the proposed model demonstrates a security enhancement of 79.6% compared to the traditional approach.