## 9 Performance Analysis and Results
### The Time Required for Conducting Computations  
Because the transmission of messages has a time constraint, it is necessary to investigate the amount of time required to complete the maximum number of calculation jobs within a certain period of time. In accordance with the procedures of the key management, the following is an overview of the calculation technique for computing time costs for each of the three ways of transmission, which can be found in Table 9.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Transmission Way** & **MS (\(\mathbf{u_{0}}\))** & **SX ( \(\mathbf{u_{i}}\),\(\mathbf{i\
eq\)0})** \\ \hline Unicast & \(\leq(C_{HMAC}+2C_{H}+3C_{XOR}).n\) & \(\leq(C_{HMAC}+2C_{H}+3C_{XOR})\) \\ \hline Broadcast & \((2C_{H}+C_{XOR})\) & \((2C_{H}+C_{XOR})\) \\ \hline Multicast & \(\leq(C_{R}+C_{Kgen}).N_{P}+(C_{HMAC}+2C_{H}+3C_{XOR}).N_{G}+(2C_{H}+C_{XOR}).m\) & \(\leq(C_{HMAC}+2C_{H}+3C_{XOR})+(2C_{H}+C_{XOR})\) \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline
Embedded systems are always used to conduct the implementation of the SX. To perform computations involving cryptography, embedded cipher chips are often used. Hash functions, symmetric cryptographic methods, and HMAC all have an approximate operating rate in the range of 10-50 Mb/s. An XOR operation has an extremely low throughput, making it impossible to take it into account.  
The time investment required for computing in each SX can be tallied. Table 10 presents an overview of the results. According to the results, the amount of time consumed on the calculation in each SX was extremely limited for SXs that did not have an effect on the transmission of various messages.  
The PCI cryptographic coprocessor could be used to help with the calculation in MS. Symmetric cryptographic techniques, hash functions, and HMAC operate at a pace of between 50 Mb/s and 1 Gb/s, while the rate of random number generation was 1 Gb/s. The speed of an XOR operation need not be taken into consideration. Table 11 contains the results of calculations that were performed to calculate the computation time cost for broadcast and unicast modes. The results indicate that the time cost was incredibly low and practically had no effect on the numerous messages being transmitted because it was so minutely high.  
The value of NP and NG should be considered while determining the time cost for the multicast mode. The results of this calculation can be seen in Table 12. The amount of time consumed increases according to the value of the NG. However, the time cost does not have any effect on the transmission of messages, even if NG is set to a value of ten thousand. The value of Np changed from 5 to 15, and the time consumed did not have any effect.  
Figure 12 shows the relation between the total number of users in DR projects and the time cost of the computation. It is shown that when the number of users increased, the time cost of computation increased. It is also shown that when the number of projects changed from 5, 10, and 15, however, the time cost of computation did not change. Thus, the time cost of computations depended on the number of users, not the number of DR projects.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Unicast** & **Broadcast** & **Multicast** \\ \hline Time cost of computation in each SX (\(\mu\)s) & 7.68–38.4 & 5.12–25.6 & 12.8–38.4 \\ \hline \end{tabular}
\end{table}
Table 10: Time consumed in each SX for three transmission way.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **Unicast** & **Broadcast** & **Multicast** \\ \hline Time cost of computation in MS (\(\mu\)s) & 0.384–7.68 & 0.256–5.12 & \\ \hline \end{tabular}
\end{table}
Table 11: Time consumed in MS for unicast and broadcast.