# An On-Demand Fault-Tolerant Routing Strategy for Secure Key Distribution Network
## 1 Introduction  
The distribution of a secure symmetric key is essential to ensure the confidentiality of data transmission in secure communication. General symmetric key distribution methods such as the Diffie-Hellman algorithm have high convenience [1]. However, the emergence of quantum computing [2] reduces the complexity of discrete logarithm problems and increases the risk of key cracking. Quantum Key Distribution (QKD) ensures the security of distributed keys through the fundamental principles of quantum mechanics [3]. However, this method requires a dedicated optical channel and has the drawback that the key generation rate decays exponentially with distance [4]. Physical Unclonable Functions (PUF) based on Semiconductor Superlattice (SSL) is a Secure Key Distribution (SKD) system designed by synchronizing random numbers generated by the space-separated chaotic systems of both parties through the public channel [5, 6]. The random information outputted by the SSL device is a complex nonlinear function of the driving signal, and the two twinning SSL devices under the same wafer are strongly correlated but difficult to be cloned in different wafers at some time in the future even if the same process isadopted [7]. These properties not only ensure the security of distributed keys [8], but also avoid the deployment of dedicated channels, and can be used on high-mobility terminals such as satellites [9]. To enable more users to communicate securely through a one-time pad cipher, each user needs to install a twinning SSL device with each other. However, in large-scale networks, a single node will have communication and computing performance bottlenecks due to the need to deal with tasks such as fuzzy extraction [6]. At the same time, the high manufacturing cost of SSL devices will also limit the installation and deployment of a large number of devices [9]. Therefore, this kind of PUF technology still has shortcomings, such as poor scalability to apply to complex network application scenarios. By organizing a point-to-point SKD system to establish Secure Key Distribution Networks (SKDN), the application scope of the SKD system can be expanded. Enabling the provision of a secure symmetric key distribution service between any nodes using existing limited resources, which is the basic functional requirement of SKDN. In QKD, one implementation uses quantum repeaters to employ quantum entanglement of photons to communicate over different optical channels, and there is no need for trust in the network nodes to ensure unconditional security during QKD operations facilitated by such quantum repeaters [10]. Due to the limitations of the underlying physical mechanism, these methods are only suitable for QKD. The SKDN based on trusted relay has the characteristics of flexibility and strong scalability. The secure key distribution among the connected nodes can be completed by hop-by-hop forwarding in a public channel [11]. Moreover, it can support nodes to deploy other PUF devices for heterogeneous networking [12]. Compared with classical routing [13], the design goals of the routing strategy in SKDN have changed. During the key forwarding process, the routing strategy is responsible for finding a path with sufficient local key resources to encrypt the forwarded key to prevent the key from being eavesdropped on the way. Besides, the trusted relay on the selected path needs to avoid key leakage. The increase in the scale of SKDN, however, leads to a higher probability of network layer faults [14]. The term fault is used to refer to disruptions that can significantly impact key distribution performance. The causes may be benign, such as node movement, fail-stop caused by bugs, shortage of local key resources, congestion caused by bursting traffic, etc. It may also be malicious. For example, when a trusted relay normally participates in the routing process, it will exhibit Byzantine behavior such as tampering, forging, and selectively discarding packets.