# Key-Recycling Strategies in Quantum-Key-Distribution Networks
## 1 Introduction  
With the development of technologies such as 5G, big data, and cloud computing, large amounts of data need to be generated, sent, and stored every day [1]. These data include sensitive personal finances, health information, and business and state secrets. Once the data is leaked, it will cause an unpredictable loss. In conventional encryption systems, data security relies on the cryptographic algorithms, public-key and symmetric, based on computational complexity. However, the emergence of quantum computers will allow breaking currently used public-key cryptosystems and thereby put an end to the secure distribution of business secrets, banking information, health data, and so on, over the Internet. Even though the current quantum-computing technology is immature, the data related to census, military technology, and other sensible information must be kept secret from the eavesdropper. The eavesdropper can wait for the arrival of the quantum computing by \"saving at first and then decrypting\". QKD makes full use of the advantages of quantum mechanical signals' no-cloning theorem and uncertainty principle, which makes it impossible for an eavesdropper to keep a transcript of quantum signals sent in a QKD process. Therefore, it is a promising method to distribute a cryptographic key, which can be used in conjunction with one-time pad (OTP) for absolutely secure communication theoretically, between a legal sender and a receiver without making assumptions on the computational power of a potential eavesdropper [2; 3; 4; 5]. A separate point-to-point QKD link does not support some applications very well, and therefore, QKD network structures must be considered in order to enable access by a greater number of users and also to extend the reach and geographical coverage [6]. However, point-to-point quantum-key-generation rate is limited by distance. Some schemes are designed to extend the distance of secure QKD [7; 8]. Among them, the trusted-relay scheme is the easiest and most convenient, and has been used as a standard for existing QKD networks [9; 10]. Some studies are carried out based on the trusted-relay QKD network. By constructing a quantum key pool (QKP) to allocate and manage quantum keys, the optimizations of survivability [11], cost [12; 13], and resource utilization [14] in QKD networks have been realized. However, research on QKP management always focuses on how to use the keys that are relayed successfully, and rarely cares about the keys that are in the failed relay process. In terms of key recycling, some researches focus on the reuse of authentication keys in quantum channels [15] and theoretically prove the security of the keys recycled [16]. The QKR mechanism based on QKD is a classical protocol, and the existing classical-channel security [17] and intrusion-detection technology [18] cannot guarantee that the signals be immune to eavesdropping. However, quantum channels can theoretically detect all eavesdropping behaviors, which is very different from the classical channels. Therefore, the keys recycling in the classical channel cannot directly reuse all the recycled keys. In this paper, we focus on how to manage, recycle, and securely reuse keys that are failed to be relayed under abnormal circumstances. The main contributions in this work are three-fold: (1) The idea of recycling the relay key is proposed, and a QKP communication mechanism based on QKD-over-optical-network architecture is proposed to synchronize algorithm information; (2) The types of keys that can be recycled are defined, the QKR mechanism and three specific implementation algorithms are proposed and the service-security-classification method is adopted to use different keys for different security needs of the service; and (3) The simulation shows that the QKD system with QKR is superior to the QKD system without QKR mechanism in terms of key-utilization rate and service-security coverage. The rest of this paper is organized as follows.