# Authentication and Billing for Dynamic Wireless EV Charging in an Internet of Electric Vehicles
## 7 Performance Evaluation
### Computational Cost  
Using the message exchange sequences described in Figures 4 and 5, the total computational cost of each entity in the proposed DWC authentication and billing system is analyzed, excluding the key pre-distribution phase, and is compared to the computational cost of the scheme proposed in [46], as shown in Table 3, with the following notation:  
* \(N\) is the number of charging segments,
* \(x\) is the number of EVs,
* \(T_{s}\) and \(T_{p}\) are the time durations for signature and verification, respectively, \begin{table}
\begin{tabular}{l l l} \hline \hline
**Message** & **Message Content** & **Message Size (bytes)** \\ \hline \(m_{3}\) & \(\{I_{e},t_{e},reqE,SIG_{gk_{c}}\}\) & \(128+8+8+56=200\) bytes \\ \(m_{4}\) & \(\{I_{e},p,k_{p},t_{c},SIG_{gk_{c}}\}\) & \(128+32+38+8+56=256\) bytes \\ \(m_{5}\) & \(\{HashChReq,p,t_{e},SIG_{gk_{c}}\}\) & \(8+32+8+56=104\) bytes \\ \(m_{6}\) & \(\{I_{b},h_{1},h_{2},...,h_{N},t_{c},SIG_{gk_{c}}\}\) & \(32N+8+56=32N+64\) bytes \\ \(m_{7}\) & \(\{h_{N},p,C,t_{e},param,SIG_{gk_{c}}\}\) & \(32+32+8+8+32+56=168\) bytes \\ \(m_{8}\) & \(\{cost,PO,t_{PO},SIG_{gk_{PO}}\}\) & \(8+8+8+56=80\) bytes \\ \(m_{9}\) & \(\{h_{N},t_{PO}\}\) & \(32+8=40\) bytes \\ \(m_{10}\) & \(\{p,h_{N-1},C,t_{e}\}\) & \(32+32+8+8=80\) bytes \\ \(m_{11}\) & \(\{p,s,h_{N-1}\}\) & \(32+8+32=72\) bytes \\ \(m_{12}\) & \(\{p,s,t_{p}^{s},t_{s,p}^{s},P_{s,p}\}\) & \(32+8+8+8+8=64\) bytes \\ \(m_{13}\) & \(\{p,t_{p}^{s},t_{p}^{s},E_{p},SIG_{gk_{PO}}\}\) & \(32+8+8+8+56=112\) bytes \\ \(m_{14}\) & \(\{I_{e},I_{e},SIG_{gk_{c}}\}\) & \(128+8+8+56=200\) bytes \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculation of message sizes for message \(m_{3}\) to \(m_{14}\) exchanged during EV registration, authentication, charging activation and billing. * \(T_{E}\) and \(T_{dE}\) are the time durations to encrypt and decrypt messages using RSA, respectively,
* \(T_{e}\) and \(T_{de}\) are the time durations to encrypt and decrypt the message using AES, respectively,
* \(T_{h}\) is the time for one hashing operation, \(\mathcal{H}(. )\), and
* \(T_{r}\) is the time for random number generation, required for generating \(h_{0}\) at the CSC. In addition, \(T_{MAC}\) and \(T_{pm}\) are the times for one message authentication code (MAC) and for one point multiplication operation, respectively, which are utilized in the model proposed in [46]. The model in [46] is particularly selected for comparison with the proposed scheme in this work because it utilizes similar cryptographic protocols and hashing operations to achieve lightweight authentication. Nevertheless, the message structures and the underlying authentication and billing algorithms are different between the two schemes and the corresponding computational efficiencies are compared accordingly. As observed in Table [46], the scheme proposed in [46] requires additional operations of MAC, hashing, random number generation and point multiplication by the EV, the CSC and the PO. This increases the computational cost incurred by these entities, in comparison with the proposed scheme in this work, despite the additional encryption and decryption operations incurred in this work compared to [46]. The scheme proposed in [46] requires \(N\) hashing operations to be performed by the EV and the PO, which increases their computational requirements. In contrast, \(N\) hash keys are generated by the CSC only in the scheme proposed in this work. Furthermore, the additional operations in [46] aim to minimize the role of the CS to a pure comparison of the hash keys generated and shared by the PO and the EV, respectively, without performing any hashing operations. This, however, introduces additional delay, in the computational time required to run the hashing algorithm on the EV side, and in the transmission of messages with hash keys from both the EV and the PO, to be compared and verified by the CS prior to charging activation.