# Key-Recycling Strategies in Quantum-Key-Distribution Networks
## 6 Performance Evaluation and Analysis
### Comparative Analysis about Whether QKR Mechanism is Employed  
Key utilization rate (KUR) and security coverage rate of service (SCR) were established as two indicators to evaluate QKD network performance. Key utilization rate indicates the ratio of the key used by the business to the total key amount, which is expressed as:  
\[KUR=\left(N_{key\_used}+N_{key\_before}\right)/N_{key\_generated} \tag{9}\]  
Nkey_used indicates the number of keys successfully used by the service. Nkey_leftover indicates the key stock of QKP at the end of the simulation and Nkey_generated represents the amount of key generation for the entire run cycle of the simulation. Security coverage rate of service indicates the ratio between the number of services that the encryption requirement has satisfied and all services with encryption requirements, and is expressed as:  
\[SCR=N_{ser\_encrypted}/N_{ser} \tag{10}\]  
Nser indicates the total amount of service with security requirements. Nser_encrypted indicates the number of services that were successfully encrypted.  
Figure 9(a) shows the trend of KUR and SCR with different service intensity (inflow of service per unit). It is obvious that regardless of the value of the service intensity, the KUR and SCR of the network are far superior to the algorithm without the QKR strategy than when using the QKR strategy. With the increase of service intensity, whether or not the QKR strategy is adopted, KUR is declining. Furthermore, the partial-recycling algorithm always stays ahead. On the other hand, the change in service intensity has no significant impact on the SCR for the algorithm of no recycling. However, as the service intensity grows, the SCR indicator of the key recycling algorithm is also growing.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**R\({}_{\text{sec}}\)** & **Service Type** & **Key Type** & **Encryption Algorithm** \\ \hline
1 & QKD service & Original key & One time pad \\
2 & High security level service & Original key & 192 bit AES \\
3 & Low security level service & Recycled key & 192 bit AES \\
3 & Low security level service & Original key & 128 bit AES \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristic of Service.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Key Type** & **Original Key** & **All Recycling** & **Mixed Recycling** & **Partial Recycling** \\ \hline Relative security & 1 & 0.9 & [0.9, 0.6] & 0.6 \\ factor & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Relative Security Factor of the Key.  
Figure 10b indicates that the effect of SFR increase on KUR and SCR under all recycling, partial recycling, mixed recycling, and no-recycling algorithms. In the case of different SFRs, the three key-recycling algorithms are better than no recycling in both KUR and SCR.  
Referring to the setting of the service security factor in Table 3, Figure 11 shows the relative security index of the service under different service numbers. The red line indicates that when no recycling is used, the relative security index of the service is always 1. This means that the key recycled by the QKR algorithm may not be as secure as the key directly generated by the traditional QKD. But it can provide encryption services for some businesses with low security requirements. Furthermore, the average relative security capability of the business has no obvious relationship with the number of services.