# A Lightweight Chaotic Map-Based Key Agreement Scheme for the Advanced Metering Infrastructure
## 6 Performance Evaluation
### Computation Cost  
In order to measure the computational overheads of the proposed scheme in the key agreement process, according to [25; 26], we conducted experiments on different encryption primitives using the big data computing library to measure their execution time. Our experimental environment was set as follows: (1) hardware environment: Inter Core I5-12500H processor (Intel, Santa Clara, America) with clock frequency of 2.50 GHz, 16 GB RAM Memory; (2) software configuration: Windows 10 operating system, Visual C++ 2017 Software, MIRACL (Multiprecision Integer and Rational Arithmetic C/C++ Library) big data library computing. We took the average value of one hundred operations as the execution time of the related operations to reduce the error. According to the migration experiment in [29], the time cost required for smart meters equipped with microprocessor R5F212B8 SDFP (Renesas, Tokyo, Japan) to perform corresponding operations can be obtained by migration  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Security Features 1** & **Ref. [2]** & **Ref. [13]** & **Ref. [17]** & **Ref. [18]** & **Ref. [20]** & **Ours** \\ \hline S1 & \(\check{\mathsf{V}}\) & \(\check{\mathsf{V}}\) & \(\check{\mathsf{V}}\) & \(\check{\mathsf{V}}\) & \(\check{\mathsf{V}}\) & \(\check{\mathsf{V}}\) \\ S2 & \(\mathsf{x}\) & \(  
experiments. The time cost corresponding to different operations is shown in Table 2, and Table 3 lists the computational costs required for the proposed scheme compared to other representative schemes. The computation costs for XOR and string concatenation operations can be ignored compared to the operations in Table 2, so they were omitted. Figure 4 shows the computation cost of the smart meter in different schemes, indicating that the computation cost of our scheme on the smart meter side is the lowest, which is mainly due to the time-consuming bilinear pairing and elliptic curve point multiplication operation replaced by the Chebyshev chaotic map. The overhead of the smart meter side was reduced by 77.35%, 69.37%, 68.89%, 53.42%, and 52.96%, respectively. Figure 5 shows the time required for this scheme and the comparison scheme to complete the key agreement when the number of smart meters is 100, 200, 300, 400 and 500, respectively. The time required of our scheme is much smaller than that of the comparison scheme, and the overhead is only about 1.1 s when the number of smart meters reaches 500, which accounts for only 22% of the message transmission time threshold (5 s) in AMI. Our scheme is better than the existing lightweight schemes. With the increase in the number of smart meters and the limited computing resources of the AMI network infrastructure, our scheme has the slowest growth rate in time overhead. It means that in the same hardware and software environment, this scheme allows more smart meters to access. Compared with other schemes, our scheme has better scalability. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Operation** & **Description** & **DC Execution** & **SM Execution** \\  & & **Time (ms)** & **Time (ms)** \\ \hline \(T_{m}\) & Time of elliptic curve point multiplication & \(\approx\) 2.234 & \(\approx\) 53.616 \\ \(T_{a}\) & Time of elliptic curve point addition & \(\approx\) 0.245 & \(\approx\) 5.88 \\ \(T_{C}\) & Time of Chebyshev chaotic map & \(\approx\) 0.642 & \(\approx\) 15.408 \\ \(T_{H}\) & Time of a hash function & \(\approx\) 0.023 & \(\approx\) 0.552 \\ \(T_{s}\) & Time of symmetric encryption/decryption & \(\approx\) 0.068 & \(\approx\) 1.632 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Execution time. Figure 4: SM’s computational cost comparison of [2, 13, 17, 18, 20].