# Autonomous Mutual Authentication Protocol in the Edge Networks
## 7 Experiments
### Results Analysis
The cryptography for every encryption/decryption for complete protocol is performed in 22 milliseconds, referred from the cipher suite 1, consisting of the LEA, SPONGENT, and HMAC algorithms [35]. Several cryptographic operations can be applied, such as lightweight, low latency, and optimal power communication network, for the HLCAS sensor [36], enhanced energy-efficient cryptography method E\({}^{3}\)LCM [37], and resource-constrained device networks, i.e., LED, TWINE, and LEA for 32-bit microcontrollers [38]. Table 3 provides the authentication time between the mobile workstation and IoT device with different LCG parameter settings [32]. GCC LCG parameters are observed to require the highest time for authentication, followed by Borland and Turbo. The time requirements may change on each protocol execution depending on the parameters and time. In the case of IoT device 1 to IoT device 2 authentication, given in Table 4, it is observed that computation time of session key 1 is quite high when compared to the session key 2 and session key 3 time. Similarly, in this case, the total time for GCC is higher when compared to Borland and Turbo. It can be noted that IoT devices require significant time to initialize the protocol when compared to other keys calculation. Table 5  
Figure 6: Total time analysis for the LCG: (**a**) GCC, (**b**) Borland, and (**c**) Turbo. Figure 7: Protocol total time analysis and comparison within the (**a**) mobile workstation, (**b**) IoT device 1, and (**c**) IoT device 2.  
presents the computational cost with parameters for hash function \(CC_{h}\) and cryptographic operations \(CC_{c}\) for encryption and decryption usage. The total cost provides an analysis for the functions used within the respective protocols. In Table 6, the feature comparison between multiple protocols is stated. It presents the achievements of the autonomous protocol over recent works. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**LCG/Key** & **Session Key 1** & **Session Key 2** & **Session Key 3** & **Total Time** \\ \hline GCC & 0.548990965 & 0.000441074 & 0.001973867 & 0.551431894 \\ \hline Borland & 0.089758873 & 0.001000166 & 0.00190115 & 0.092696905 \\ \hline Turbo & 0.41444993 & 0.000444174 & 0.001885176 & 0.41680479 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: LCG-based IoT device 1 to IoT device 2 authentication time (s). Figure 8: Total time for PRNG-based nodes comparison with cryptography. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **User Device** & **Gateway** & **Sensor Node** & **Total** \\ \hline Cloud-IoT [39] & \(11*CC_{h}\) & \(7*CC_{h}\) & \(5*CC_{h}\) & \(23*CC_{h}\) \\ \hline Ad hoc wireless sensors [40] & \(7*CC_{h}\) & \(5*CC_{h}\) & \(7*CC_{h}\) & \(19*CC_{h}\) \\ \hline Edge-IoT [41] & \(9*CC_{h}\) & \(15*CC_{h}\) & \(8*CC_{h}\) & \(32*CC_{h}\) \\ \hline IoT devices [42] & \(4*CC_{h}\) & \(3*CC_{h}\) & \(2*CC_{h}\) & \(9*CC_{h}\) \\ \hline Autonomous protocol & \(2*CC_{h}+3*CC_{C}\) & \(N.A.\) & \(2*CC_{h}+3*CC_{C}\) & \(4*CC_{h}+6*CC_{C}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Protocol computation cost comparison. In Table 7, the comparison with multiple schemes includes parameters \(T_{H}\) as one-way hash function, \(T_{ECM}\) as ECC scalar multiplication, \(T_{fe}\) as fuzzy extraction operator, and \(T_{SE/D}\) as symmetric encryption and decryption [49; 50; 51]. In Table 8, the total time for protocol completion including communication time is presented. The two IoT schemes referenced, which have efficient mutual authentication [46] and two-phase authentication protocol in WSN [49], suffer due to the inclusion of a server/third party for the certificate-based authentication. In comparison, the autonomous protocol performs much better by excluding the dependency on server/third-party systems for the authentication. Furthermore, in comparison to the referenced systems, the calculation time for the autonomous protocol is also less.