## 6 Performance Evaluation of the Proposed Protocol  
### Computation Costs Comparison  
As highlighted in the examination of security concerns associated with the Internet of Things (IoT), nodes operating in this network often have limited computational resources. Consequently, these components of the Internet of Things network require security arrangements and policies that can efficiently implement the security features, with low computational cost. This is crucial to ensure that the security measures do not hinder the performance or functionality of the IoT devices. It is a delicate balance between maintaining robust security and ensuring optimal device performance. In the subsequent analysis, we determined the time complexity of our protocol based on the operators involved in the authentication and key-exchange processes of the proposed method. A system is considered for implementation and determines the execution time of each operator utilized in the protocol. The system specifications encompass a 2.20 GHz Intel Pentium E2200 processor and 2 GB of RAM. As reported in [55; 56], Table 3 showcases the time required for executing various cryptographic operations pertaining to each cryptographic element. In an effort to highlight the enhanced efficiency of our proposed protocol compared to similar protocols within the IoT network, we conducted a comparative analysis of computational costs. The results of this comparison are provided in Table 4.  
Table 4 provides a comparative analysis of the computation time expenditure involved in the process of our presented method versus security protocols proposed by security researchers for securing Internet of Things communications. It can be inferred from the results displayed in the table that our proposed method offers a notably reduced execution time for the protocol process and attainment of the session key when compared to alternative methods. Considering the limited resources and low power constraints of IoT network nodes, it is essential to adopt security mechanisms that optimize energy usage during protocol operations and routing, especially when employing the RPL protocol. Consequently, our proposed protocol, characterized by its diminished computing time  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
[37] & \(\times\) & ✓ & \(\times\) & ✓ & \(\times\) & ✓ & ✓ & ✓ & ✓ & ✓ \\
[39] & ✓ & \(\times\) & ✓ & \(\times\) & \(\times\) & \(\times\) & ✓ & ✓ & ✓ & ✓ \\
[43] & ✓ & ✓ & ✓ & ✓ & ✓ & \(\times\) & ✓ & ✓ & ✓ & ✓ \\
[44] & \(\times\) & ✓ & ✓ & ✓ & ✓ & \(\times\) & ✓ & ✓ & ✓ & ✓ \\
[45] & ✓ & ✓ & ✓ & \(\times\) & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ \\
[46] & \(\times\) & ✓ & ✓ & ✓ & ✓ & ✓ & \(\times\) & ✓ & ✓ & ✓ \\
[47] & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & \(\times\) & ✓ & ✓ \\
[48] & ✓ & \(\times\) & \(\times\) & ✓ & ✓ & ✓ & \(\times\) & \(\times\) & ✓ & ✓ \\
[49] & ✓ & ✓ & ✓ & ✓ & ✓ & \(\times\) & \(\times\) & ✓ & ✓ & ✓ \\
[50] & ✓ & ✓ & ✓ & ✓ & ✓ & \(\times\) & ✓ & ✓ & ✓ & ✓ \\
[51] & ✓ & ✓ & ✓ & \(\times\) & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ \\
[52] & ✓ & \(\times\) & ✓ & ✓ & \(\times\) & ✓ & ✓ & ✓ & ✓ & ✓ \\
[53] & ✓ & ✓ & ✓ & ✓ & \(\times\) & ✓ & ✓ & ✓ & ✓ & ✓ \\
[54] & \(\times\) & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ \\ Our & & & & & & & & & & \\ protocol & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ \\ \hline \hline \end{tabular}
\end{table}
Table 2: Security Features Comparison.  
for the protocol process involving authentication operations and key agreement, can be effectively applied and integrated into different segments of an Internet of Things network.