# Key-Recycling Strategies in Quantum-Key-Distribution Networks
## 6 Performance Evaluation and Analysis
### Comparative Analysis between Different QKR Algorithms  
In this section, the performance gap between the three key-recovery algorithms of all recycling, partial recycling, and mixed recycling is compared. Figure 12a illustrates that when the key-generation rate increases, no matter which recycling method is adopted, the security coverage of the service will increase. This is because the increase in key-generation rate means that more quantum keys can be used to provide security services. The partial-recycling algorithm performs best in this case because direct  
Figure 11: Relative security index of different QKR mechanisms compared to the no-recycling algorithm of traditional QKD networks.  
Figure 10: **(a)** The impact of service intensity on key utilization rate (KUR) and security coverage rate of service (SCR) of QKD networks with different QKR mechanisms and traditional QKD networks, when V\({}_{\text{key\_gen}}\) is 120 and service failure rate (SFR) is 30%.; **(b)** The impact of SFR on KUR and SCR of QKD networks with different QKR mechanisms and traditional QKD networks, when V\({}_{\text{key\_gen}}\) is 120.  
recycling does not affect the originally high security level of the business. Also, because the recycling key affects the original normal encryption service, the all-recycling algorithm performs the worst.  
Figure 12b illustrates that the change in key-generation rate has no significant effect on key-utilization rate. This indicates that the key-generation rate is not the main factor affecting key utilization. However, it is obvious that the key-utilization rate of the three algorithms is higher than 90%. Partial recycling and mixed recycling performances are similar and slightly higher than all recycling.  
As shown in Figure 13a, the horizontal axis represents the ratio of the number of low-security-level data services to the number of high-security-level services. The larger the horizontal axis, the larger the proportion of low security level services. Both mixed recycling and all recycling show similar performances for KUR and SCR indicators. It may be because the decision made by the mixed algorithm based on the historical data service information tends to all recycling, resulting in a decrease in the proportion of the partial-recycling algorithm being adopted during the entire key-recovery process. In addition, SCR embodies the proportion of services successfully encrypted in the network, the granularity of the service is larger than the key, so the jitter of the SCR is greater than KUR.  
Figure 12: (**a**) The effect of \(\mathrm{V_{key\_gen}}\) on SCR and (**b**) KUR of QKD networks with different QKR mechanisms, when SFR is 30%.  
Figure 13: (**a**) The impact of service mix ratios of different security levels on KUR and SCR of QKD networks with different QKR mechanisms, when \(\mathrm{V_{key\_gen}}\) is 120, SFR is 30%, and service intensity is 250. (**b**) The number of remaining keys in the key pool of each node after the simulation.  
Figure 13b present the balance of the key amount in the network after 100,000 data services. Both the x-axis and the y-axis represent the node number, and the xy plane determines the logical position of the QKP. The z-axis represents the ratio of the QKP key amount to the minimum key amount of all QKPs. In general, due to the design of the key-relay routing algorithm, the three recycling methods do not perform well in terms of balance. However, compared to the other two recycling algorithms, the mixed-recycling algorithm performs best in terms of balance, while the all-recycling algorithm performs the worst. For the all-recycling algorithm, the poor equalization provides an optimized direction for the optimization of the algorithm. Since the most important factor affecting the performance of the all-recycling algorithm is the consumption of the original key, the unbalanced key amount can just provide the original for the all-recycling algorithm through the relay, thereby improving the performance of the algorithm.