## 9 Conclusions  
This study demonstrated that [PERSON] et al.'s scheme cannot defend against various potential attacks such as masquerade, SG device stolen, and session key disclosure attacks. We also showed that [PERSON] et al.'s scheme does not ensure mutual authentication. To overcome these security shortcomings of [PERSON] et al.'s scheme, we present a privacy-preserving lightweight authentication protocol for demand response management in the SG environments. Our protocol prevents against various attacks, including masquerade, replay, SG device stolen, and session key disclosure attacks and achieves secure mutual authentication and anonymity. We proved that our protocol ensures secure mutual authentication between \(SD_{i}\) and \(UC_{j}\) using BAN logic, and then we showed that the proposed protocol withstands various potential attacks using informal security analysis and ROR model. We also demonstrated that our scheme was secure against replay and MITM attacks using AVISPA simulation tool. Furthermore, we compared communication overheads, computation overheads, and storage overheads with existing schemes. Therefore, our protocol is applicable for practical SG environments because it is more secure and efficient than other existing schemes.  
**Author Contributions:** Conceptualization, S.Y. and K.P.; Formal analysis, S.Y., K.P. and J.L.; Methodology, J.L., S.L. and B.C.; Software, J.L., S.L. and B.C.; Supervision, Y.P. (YoungHo Park) and Y.P. (YoHan Park); Validation, Y.P. (YoungHo Park) and Y.P. (YoHan Park); Writing--original draft, S.Y.; Writing--review & editing, Y.P. (YoungHo Park) and K.P. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A3B07050409) and in part by the Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MIST) (No. 2018-0-00312, Developing technologies to predict, detect, respond, and automatically diagnose security threats to automotive Ethernet-based vehicle).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Schemes** & **Communication Cost** & **Number of Messages** \\ \hline [PERSON] [28] & 3648 bits & 4 messages \\ [PERSON] [20] & 1408 bits & 3 messages \\ [PERSON] et al. [21] & 1920 bits & 3 messages \\ [PERSON] et al. [6] & 1376 bits & 3 messages \\ Ours & 960 bits & 2 messages \\ \hline \hline \end{tabular}
\end{table}
Table 7: A comparative summary: communication overheads.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Schemes** & **Stored Message (Smart Device)** & **Stored Message (Utility Center/Service Provider)** \\ \hline [PERSON] [28] & - & - \\ [PERSON] [20] & \(K_{i}\approx 40\) bytes & \(K_{j}\approx 40\) bytes \\ [PERSON] et al. [21] & \(s_{i},R_{i}\approx 80\) bytes & \(k_{j},K_{i}\approx 80\) bytes \\ [PERSON] et al. [6] & \(RID_{i},TC_{i}\approx 40\) bytes & \(RID_{j},TC_{j}\approx 40\) bytes \\ Ours & \(A_{i},B_{i},C_{i}\approx 60\) bytes & \(RID_{i},RID_{j},X_{i}\approx 80\) bytes \\ \hline \hline \end{tabular}
\end{table}
Table 8: A comparative summary: storage overheads.