## 6 Performance Evaluation of the Proposed Protocol
### Communication Costs Comparison  
Within this segment of the evaluation paper, we have elucidated the communication cost linked to our proposed method and conducted comparisons with those of other pertinent protocols. To determine the communication cost, the following conditions are taken into consideration: the SHA-1 one-way hashing algorithm, the identity parameter comprises 160 bits, 160 bits are allocated for random numbers, the hash algorithm yields an output of 160 bits, and the time interval is represented by 32 bits. For an elliptic curve point characterized by P = (P\({}_{X}\); Py), where Px and Py signify the coordinates of two points, x and y, respectively, the conjectures equate to \((160+160)\) = 320 bits [43]. In the progression of the provided protocol, two communicating parties interchange two messages via the channel until they attain the session key, designated as (MSG\({}_{1}\)= E\({}_{\text{Ni(y)}}\) {S\({}_{1}\), S\({}_{3}\), PU\({}_{\text{Node}}\)},K MSG\({}_{2}\) = E\({}_{\text{Ni(y)}}\) {SA, S\({}_{4}\)}). The communication cost associated with these messages is detailed as:  
\[\text{MSG}_{1}=(480+160+320+320)\;(2)\;\text{MSG}_{2}=(160+160)\]  
As evident from the comparative data showcased in Table 5, our proposed protocol demonstrates a notably lower communication cost in contrast to other protocols showcased within the Internet of Things network platform. In two cases [46; 60], the number of bits in the transmitted messages is lower; however, the method presented in [46] is vulnerable to impersonation and man-in-the-middle attacks. The method presented in [60] \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Computations** & **Computational Cost (ms)** \\ \hline
[45] & \(10T_{\text{H}}+4T_{\text{M}}+3T_{\text{SE}}\) & 8.9408 \\
[46] & \(6T_{\text{M}}+21T_{\text{H}}\) & 13.4043 \\
[47] & \(5T_{\text{P}}+13T_{\text{E}}+9T_{\text{M}}+2T_{\text{A}}+7T_{\text{H}}\) & 99.2127 \\
[48] & \(4T_{\text{M}}+7T_{\text{H}}\) & 8.9201 \\
[49] & \(5T_{\text{M}}+13T_{\text{H}}\) & 11.1599 \\
[50] & \(6T_{\text{M}}+2T_{\text{A}}+12T_{\text{H}}\) & 13.4292 \\
[51] & \(17T_{\text{M}}+8T_{\text{H}}\) & 37.8604 \\
[52] & \(11T_{\text{M}}+4T_{\text{H}}\) & 24.5182 \\
[53] & \(12T_{\text{M}}+12T_{\text{A}}+1T_{\text{E}}+10T_{\text{H}}\) & 30.9306 \\
[54] & \(15T_{\text{M}}+18T_{\text{H}}\) & 33.4314 \\
[57] & \(34T_{\text{H}}+14T_{\text{M}}+4T_{\text{A}}+1T_{\text{F}}\) & 33.5834 \\
[58] & \(6T_{\text{M}}+4T_{\text{SE}}+5T_{\text{H}}\) & 13.3859 \\
[59] & \(6T_{\text{M}}+21T_{\text{H}}\) & 13.4043 \\
[60] & \(4T_{\text{AE}}+1T_{\text{F}}+8T_{\text{H}}\) & 17.6444 \\
[61] & \(10T_{\text{SE}}+5T_{\text{M}}+8T_{\text{E}}+6T_{\text{H}}\) & 41.9898 \\
**Proposed Protocol** & \(3T_{\text{M}}+10T_{\text{H}}+2T_{\text{SE}}\) & 6.70102 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computation cost comparison of the related protocols. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Notation** & **Description** & **Time Cost (ms)** \\ \hline T\({}_{\text{H}}\) & Time for a general hash operation & \(\approx\)0.0023 \\ T\({}_{\text{SE}}\) & Time for a symmetric encryption/decryption & \(\approx\)0.0046 \\ T\({}_{\text{AE}}\) & Time for an asymmetric encryption/decryption & \(\approx\)3.85 \\ T\({}_{\text{E}}\) & Time for an exponentiation & \(\approx\)3.85 \\ T\({}_{\text{M}}\) & Time for an EC point multiplication & \(\approx\)2.226 \\ T\({}_{\text{A}}\) & Time for an EC point addition & \(\approx\)0.0288 \\ T\({}_{\text{P}}\) & Time for a bilinear pairing & \(\approx\)5.811 \\ T\({}_{\text{HM}}\) & Time for an HMAC operation & \(\approx\)0.0046 \\ T\({}_{\text{F}}\) & Time for Fuzzy Extraction & \(\approx\)0.2.226 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Execution time of cryptographic elements. requires 17.64 milliseconds of computation time, while our proposed method requires 6.70 milliseconds for the protocol process, making it more optimal.