# Authentication and Billing for Dynamic Wireless EV Charging in an Internet of Electric Vehicles
## 7 Performance Evaluation
### Authentication Delay  
In order to evaluate the system delay of the proposed authentication and billing scheme, the computational time for the different cryptographic protocols needs to be estimated. Accordingly, the different cryptographic protocols used in the proposed model are implemented using OpenSSL library on a system with Intel Core i7-3537U processor, 16-GB RAM, 256-GB SSD hard drive and a 64-bit Windows 10 operating system. To validate the results, the obtained computational time for the different protocols is compared with the time reported in Reference [56], which uses a machine with similar hardware specifications, \begin{table}
\begin{tabular}{l l l} \hline \hline
**Entity** & **This Work** & **Ref. [46]** \\ \hline EV & \(NT_{\varepsilon}+4T_{s}+3T_{\texttt{p}}+4T_{E}+3T_{dE}\) & \(T_{\varepsilon}+T_{de}+2T_{s}+3T_{\texttt{p}}+2T_{E}+3T_{dE}\) \\  & & \(+2T_{MAC}+2 NT_{h}+2T_{r}+2T_{PM}\) \\ CSC (PSS in [46]) & \(2 xT_{s}+4 xT_{\texttt{p}}+2 xT_{E}+4 xT_{dE}\) & \(2 xT_{s}+xT_{\texttt{p}}+2 xT_{E}+xT_{dE}+2 xT_{\varepsilon}\) \\  & \(+NT_{h}+T_{r}\) & \(+xT_{de}+2T_{MAC}+T_{h}+2T_{r}+3T_{PM}\) \\ PO (RSU in [46]) & \(2 xT_{s}+xT_{\texttt{p}}+2 xT_{E}+xT_{dE}+\) & \(xT_{s}+xT_{\texttt{p}}+xT_{E}+xT_{dE}+xT_{de}\) \\  & \(xT_{\varepsilon}+xNT_{de}\) & \(+(2+N)T_{h}+T_{MAC}+T_{r}+2T_{PM}\) \\ CS & \(3 xT_{de}+2 xT_{e}+xT_{h}\) & Negligible \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computational cost calculation for each network entity. namely an Intel Core i7-4702 MQ processor, 16-GB RAM, 256-GB SSD hard drive and 64-bit Ubuntu 16.04 operating system. This comparison is presented in Table 4.  
As observed in Table 4, the computational time for executing the different cryptographic protocols on the machine used for this work is comparable and reasonably lower than the values reported in [56]. This validates the reliability of the utilized processor and its effectiveness for running the different cryptographic protocols. Nevertheless, the aforementioned hardware specifications are typically utilized at the CSC and the PO but are quite costly to be implemented on EV OBUs and at the charging segments. Hence, to account for the limited computational capabilities of the EV and the charging segments, the computational time for the cryptographic protocols in Table 4 is increased by 60% when used to compute the time required to run these protocols on the OBUs of the EV and at the CS. The short computational times reported in Table 4, in microseconds and nanoseconds, confirm that the adopted protocols are sufficiently lightweight and can be efficiently implemented for the proposed authentication scheme in an IoEV. For the protocols executed by the charging segments in particular, namely the hash function algorithm and symmetric key encryption/decryption, a significantly low computational time is required, which is around two orders of magnitude less than that needed for the digital signatures and asymmetric cryptography protocols. This is also significantly lower than the expected transmission delay in the DSRC link between the EV and the CS, which proves the advantage of off-loading the hashing verification operation from the EV and PO sides to the CS side, to enable faster authentication between the EV and the CS and faster charging activation as the EV approaches the charging lane. In order to accurately assess the speed of the authentication process, the total time required to execute the proposed authentication scheme needs to be evaluated, including the time taken to sign and encrypt messages, the transmission delay of the wireless communication channel, and the time taken to decrypt the messages and verify the signatures. Accordingly, the communication links between the different network entities in the proposed model are simulated on ns-3 network simulator, using the 5G-K SimNet tool developed by [57].