# Key-Recycling Strategies in Quantum-Key-Distribution Networks
## 3 Problem Statement  
The relaying process of quantum keys can be implemented by transmitting information through a public data channel. As shown in Figure 4, [PERSON] and [PERSON] need to share the keys by using the trusted relay, where the Alice-Repeater pair and the Repeater-Bob pair have shared the keys \(\mathrm{K_{Ai}}\) and \(\mathrm{K_{B}}\) (i, j\(\mathrm{eN}\)), respectively. Due to the differences in the relay-routing algorithm, the keys \(\mathrm{K_{Ai}}\) and \(\mathrm{K_{Bj}}\) may have separately experienced different numbers (the number may be 0) of trusted-relay nodes before sharing to the Repeater. According to the trusted-relay and the one-time-pad principle, in order to share one united end-to-end key, each node that is selected by the relay route will consume the same number of point-to-point keys. It is assumed that if the length of \(\mathrm{K_{A1}}\) is n and the Alice-Repeater pair needs to pass through two trusted relay nodes, sharing the \(\mathrm{K_{A1}}\) between the Alice-Repeater pair will require an additional 2n keys. \(\mathrm{K_{A1}}\) is generated by [PERSON] and the first relay node for point-to-point  
Figure 3: QKD over Optical Network Architecture. QKD. The key-relay process consumes a large number of keys, and the number of keys consumed is positively correlated with the number of relay nodes. If [PERSON] and [PERSON] want to share the key pair K\({}_{\text{A1}}\), firstly K\({}_{\text{A1}}\) XOR K\({}_{\text{B1}}\) is executed at the trusted relay (step()) and then the XOR-ed result is sent to [PERSON]. Packet loss and bit errors in actual operational IP networks may occur due to different factors like, rerouting, network congestion, cache processing, the device's actual performance, network environment, and other factors. Packet loss (step ) or bit error (step ) occurs while the key is being relayed, which may result in the key not being successfully shared. When the key K\({}_{\text{A1}}\) is not successfully distributed, a redistribution process is performed. The key redistribution process is similar to the former process. Because the failure of the key-relay process may be caused by the eavesdropper's activity or malicious attack. When the redistribution process occurs, in order to ensure the absolute security of the keys that need to be shared (to meet the condition that the key is used only once), the key pairs K\({}_{\text{A1}}\) and K\({}_{\text{B1}}\) that got successfully relayed before the current QKD, must be destroyed. The new key pairs K\({}_{\text{A2}}\) and K\({}_{\text{B2}}\) are used to re-relay (step ). The new key K\({}_{\text{A2}}\) is shared between [PERSON] and [PERSON]. However, the practice of discarding the key pair K\({}_{\text{A1}}\) and K\({}_{\text{B1}}\) directly results in a great waste of the keys, not only the keys K\({}_{\text{A1}}\) and K\({}_{\text{B1}}\) are wasted, but also the relay keys used in the relay process are wasted. Further, the network key demand is increased, and the security requirements of the service are difficult to guarantee. Therefore, the idea of key recycling is proposed that collects and processes the keys that failed in similar scenarios discussed above, and reuses those keys to encrypt the services with low security level. The probability and characteristics of packet loss and bit error are different in different network scenarios. The typical two scenarios are satellite networks and optical networks, representing networks with the characteristics of high packet loss rate (PLR) and low PLR, respectively [23; 24; 25; 26]. The PLR in the scenario of satellite relay is as high as 30% or higher [27; 28], and the QKR strategy has natural advantages in high bit error ratio (BER) scenarios. The lower PLR in optical packet switched networks is generally between 1/10,000 and 1%, [26] but it does not mean that the key-recycling strategy is not useful in this scenario. The necessity of key recovery mechanism in optical network (low BER and PLR) scenarios is analyzed from three perspectives.