## 2 Background and Related Works
### Multipath QKD  
Multipath QKD has emerged as a critical strategy for improving security in networks containing partially trusted relays. The fundamental principle involves dividing the global key into multiple segments, each transmitted over distinct paths. Techniques such as secret sharing and error correction ensure secure key reconstruction at the destination. As depicted in Figure 1, for example, if [PERSON] and [PERSON] share \(K_{1}\) on the first path (nodes \(A\), \(B\), and \(C\)) and \(K_{5}\) on the second path (nodes \(D\) and \(E\)), the final key shared by [PERSON] and [PERSON] is \(K=K_{1}\oplus K_{5}\). Even if one path is compromised, overall security can still be preserved, as [PERSON] would need to intercept all key segments to reconstruct the final key.  
[PERSON] et al. [23] presented a hybrid-trusted QKD network using semi-trusted nodes and multipath transmission, significantly improving efficiency and load balancing. However, their static trust assumptions limit adaptability against dynamically compromised nodes. Similarly, [PERSON] et al. [24] proposed a progressive recovery scheme employing deep reinforcement learning (DRL) for rapid restoration of the network after failure. Although this model is effective for recovery, it lacks proactive defensive measures for ongoing threats. Moreover, [PERSON] et al. [25] developed a DRL-based routing strategy that reduces blocking probabilities in optical QKD networks. Although efficient, their method assumes an inherently secure infrastructure and does not address dynamic compromises. [PERSON] et al. [22] optimized routing by minimizing the number of activated trusted nodes, significantly reducing vulnerabilities but remaining static in trust management. [PERSON] et al. [26] introduced a collaborative routing algorithm, improving key distribution rates but employing static strategies without real-time adaptability. In [27], the authors explored joint optimization for routing and photon source provisioning, enhancing resource efficiency. However, their framework does not dynamically adapt to real-time node compromise.  
[PERSON] et al. [17] investigated a probabilistic multipath routing model, improving security through stochastic selections but lacking dynamic penalty mechanisms for suspicious nodes. The authors in [28] studied multipath routing for entanglement distribution, significantly increasing distribution rates yet failing to explicitly manage security threats from untrusted relays. In [29], the authors proposed routing strategies that minimize node compromise vulnerabilities using multiple non-overlapping paths but lacked dynamic threat detection. [PERSON] et al. [30] and [PERSON] et al. [19] introduced partially trusted routingalgorithms in ring networks and segment-based multipath methods, respectively, achieving security enhancements but restricted by static segmentation and topology limitations.  
The reviewed studies highlight several unresolved challenges: (1) Limited dynamic mechanisms for identifying and managing compromised nodes in real time; (2) static or semi-static assumptions about node trust, hindering adaptability and resilience; (3) insufficient integration of proactive and reactive security strategies to actively mitigate attack scenarios. Addressing these gaps, this paper proposes a zero-trust, adaptive QKD routing framework employing an MTD-based approach. Our model dynamically diversifies routing paths, incorporates recursive penalty mechanisms to isolate compromised nodes, and utilizes adaptive key transmission strategies based on real-time security assessments. This comprehensive strategy significantly improves network security and resilience, directly overcoming limitations identified in the previous literature.