# Authentication and Billing for Dynamic Wireless EV Charging in an Internet of Electric Vehicles
## 7 Performance Evaluation
### Authentication Delay
For the conducted simulations, equally-sized charging segments, each of length \(L=1\) m, are deployed on a road of 500 m length with segment-to-segment spacing, \(d=0.25\) m, and a 5G g-Node-B (gNB) is assumed to be located in the middle of the road. A total of 400 charging segments, one EV, one CSC and one PO are simulated and a constant EV speed of 60 km/h is considered throughout the EV motion along the charging lane. When the EV enters the charging lane, it starts to communicate with the different network entities using different communication technologies shown in Figure 3. Using the message length calculations in Table 2, the transmission delay, \(T_{d}\), for sending a message between the EV and the CSC (or the PO) using the 5G network modeled on ns-3 is found to be 11.75 ms. Furthermore, the wired link between the CSC and the PO, and between the PO and each charging segment has an average communication delay of 4.28 ms. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Operation** & **This Work** & **Ref. [56]** \\ \hline SHA-256 (16 bytes) & 225 ns & 255 ns \\ AES-256 CBC Encryption (16 Bytes) & 109 ns & 192 ns \\ AES-256 CBC decryption (16 Bytes) & 122 ns & - \\
256-bit ECDSA (nistp256) signature & 30 μs & 46 μs \\
256-bit ECDSA (nistp256) verification & 100 μs & 116 μs \\ RSA 2048 Encryption & 651 μs & 728 μs \\ RSA 2048 Decryption & 20 μs & 32 μs \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computational time for the cryptographic protocols. Hence, the total computational and transmission time requirements of the proposed scheme up to message \(m_{g}\), i.e., before the EV starts communicating with the charging segments, is shown in Figure 6. To acknowledge the difference in the computational capabilities between the different entities, an additional subscript \(c\) is used to indicate the computational time for the CSC and the PO, while the subscript \(e\) indicates the time for the EV and the CS, which is 60% higher than the values reported in Table 4.  
As shown in Figure 6, the time required to authenticate the EV to the PO and the CSC before reaching the first charging segment is 81.22 ms. Hence, for an EV traveling with a constant speed of 60 km/h, the authentication protocol proposed in this work needs to be executed at least 1.35 m before the EV reaches the first charging segment. Furthermore, the delay for the DSRC link between the EVs and the charging segments is measured by ns-3 simulations to be 0.24 ms. The time required by the EV to encrypt the message shared to the CS is \(T_{e_{x}}=0.17\) us and the time required by the CS to decrypt the EV message, verify the hash key sent by the EV and encrypt the message forwarded to the next segment is \(T_{d_{e_{x}}}+T_{h_{x}}+T_{e_{x}}=0.73\) us, which are negligible compared to the DSRC transmission delay. Accordingly, for a CS of length 1 m, the EV-segment crossing time at 60 km/hr is \(\simeq\)60 ms, of which \(\simeq\)0.241 ms shall be used for message encryption/decryption and transmission, while the remaining time is allocated for charging.