# Autonomous Mutual Authentication Protocol in the Edge Networks
## 7 Experiments
### Results Analysis  
In Figure 4, the 100 keys generated for session key 1 \(K_{S,R}\), session key 2 \(K_{R,S}\), and session key 3 \(PK_{S}{}^{\prime}\) are shown. The time required for the calculation on the mobile workstation is seen to be growing at a similar rate amongst the session keys. Figure 4 shows the session-key-generation time analysis, where the time for session key 2 is the highest due to communicating the challenge matrix \(M_{8\times 8}\); session key 1 has a similar time to session key 2 for calculating challenge 1, and session key 3 has the lowest time requirements by sharing the final sessional key in the authentication protocol. The PRNG used within this work refers to the linear congruential generator (LCG) parameters from the standard declared for cryptographic random number preferences [33; 34; 32]. The session keys generation time in Figure 5 with different LCG parameters can be seen in graph analysis. In the LCG 1 with GCC parameters, the key generation usually grows at an increasing rate because of the computation time requirements, and in (a), (b), and (c), it can be seen that a spike occurs around the 8000 node's key generation. Similarly, in the case of LCG 2 Borland- and LCG 3 Turbo-based parameters, the graph behavioral analysis spiked after crossing some node limits. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**System** & Mobile Workstation (Laptop) & IoT Device 1 & IoT Device 2 \\ \hline
**Model** & MacBook Pro & Raspberry Pi 3B & Raspberry Pi 3B+ \\ \hline
**Processor** & Intel Core i7 @ 2.6 GHz & Broadcom Quad Core @ & Broadcom, Cortex-A53 (ARMv8) 64-bit SoC @ 1.4 GHz \\ \hline
**Main Memory** & 16 GB & 1 GB SDRAM & 1 GB LPDDR2 SDRAM \\ \hline
**Programming** & Python 2.7 (Libraries: random, hashlib, datetime, sys, pandas, base64, and getnode.) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: System configuration. This evaluation can be performed using less computation time if the workstation used is of higher configuration. In Figure 6, the total time required by different LCG parameters is shown by the graph analysis, which is quite similar to each other for 1000 to 10,000 node protocol implementation on the mobile workstation. Even though the parameters are distributed randomly and without any similarity between them, which is known as unpredictable, the time taken by the autonomous protocol implementation in 10,000 nodes is still quite similar. Figure 4: Initial session key time analysis. Figure 5: LCG-based session key generation: LCG 1 GCC (**a**) session key 1, (**b**) session key 2, (**c**) session key 3; LCG 2 Borland (**d**) session key 1, (**e**) session key 2, (**f**) session key 3; and LCG 3 Turbo (**g**) session key 1, (**h**) session key 2 and (**i**) session key 3. In Figure 7, the protocol time analysis for mobile workstation, IoT device 1, and IoT device 2 is shown. The time required on the mobile workstation is less when compared to IoT devices due to the high processing capacity, as shown in Table 2. While increasing the nodes from 100 to 1000, the total time can be seen increasing due to computation requirements for the protocol implementation. In comparison, the protocol implementation on the Raspberry Pi IoT device can be seen increasing smoothly due to less computation capacity. Therefore, the total time is smoother in the low-end device but has higher time implementation requirements on the resource-constrained devices. Figure 8 shows the comparison of different PRNG parameter settings for the autonomous-protocol-based authentication for the nodes from 1000 to 10,000. As the pseudo-random numbers used here are highly variable in their numerical range, it can be observed in the graph that the time requirements for every one-thousand-node authentication changes in every computation event. Here, the channel encryption is used in such a way that the nodes are generated in parallel so that cryptographic time operation is considered to be in parallel time for every event.