###### Abstract
Solutions such as measurement-device-independent QKD (MDI-QKD) and multipath key distribution offer improvements by removing traditional vulnerabilities and distributing keys across multiple paths, respectively [15, 16, 17]. However, these techniques introduce new challenges, such as increased system complexity and the need for precise knowledge of the locations of measurement nodes, which can be problematic near untrusted relays [18,19]. Given these considerations, developing robust and adaptive security mechanisms is crucial. An effective strategy is moving target defense (MTD), which dynamically alters key distribution paths to complicate potential attacks. This paper proposes a systematic approach for secure and efficient key distribution in networks with untrusted relays, adopting a zero-trust model in which all nodes are potential threats. The model incorporates a behavior inspection module that dynamically evaluates and adjusts node behavior based on trust variations, further strengthening network security. Therefore, to improve network security and efficiency, we propose a novel spatiotemporal diversification scheme that alternates key distribution paths. An adaptive model optimizes key reconstruction, incorporating a penalty mechanism to detect and exclude suspicious relays. This approach provides a resilient framework for secure quantum communication that addresses the challenges of untrusted relay environments. The main contributions of our work are summarized as follows:  
* To address the security challenges in QKD networks with untrusted relays, we propose a spatiotemporal diversification-based key distribution method. This method dynamically distributes multiple keys across various paths, ensuring high security in end-to-end key distribution while meeting diverse security requirements. The proposed approach effectively overcomes the limitations of the existing methods. * To meet the diverse security needs of applications, an adaptive path recovery process is introduced. The system employs a penalty-based strategy to detect and exclude suspicious relay nodes from path selection. It dynamically tests compromised routes, imposes penalties, and monitors node behavior to ensure compromised nodes are excluded from participation. * Extensive simulations were conducted under various scenarios to evaluate the performance of the proposed method. The results demonstrate that our method significantly outperforms traditional multipath methods in terms of both security and efficiency. The remainder of this paper is organized as follows: Section 2 provides the background research on QKD, covering key concepts such as point-to-point QKD, long-distance QKD, and multipath QKD. Section 3 presents the proposed zero-trust QKD system model, including network architecture, classification of trusted and untrusted relays, adversary model, and problem statement. Section 4 details the proposed spatiotemporal diversification-based multipath-multi-key distribution framework and its algorithmic components, including path selection criteria, routing procedures, execution phases, and an inspection/testing phase. Section 5 introduces the mathematical transmission model for multipath QKD networks based on zero-trust relays, incorporating probabilistic security analysis and a behavior inspection module. Section 6 presents the evaluation of the system through simulations, comparing the proposed approach with traditional multipath QKD methods without MTD. Finally, Section 7 concludes the paper and discusses potential future research directions. All notations used are defined in Table 1.