# Side-Channel Power Analysis Based on SA-SVM
## 4 Results and Analysis
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Kernel**} & \multicolumn{8}{c}{**Accuracy (\%) of Different POIs**} \\ \cline{2-7}  & **4** & **14** & **20** & **29** & **53** & **84** & **117** \\ \hline Linear & 77.75 & 84.00 & 87.75 & 87.25 & 91.00 & 91.00 & 91.75 \\ RBF & 78.50 & 86.75 & 88.50 & 90.05 & 93.75 & 92.00 & 92.75 \\ Morlet wavelet & 78.00 & 86.75 & 88.50 & 91.00 & **94.50** & 91.75 & 92.25 \\ Mexican hat wavelet & 78.00 & 85.25 & 88.25 & 89.25 & 92.75 & 91.25 & 91.25 \\ Morlet–RBF wavelet & 79.50 & 87.25 & 89.00 & 91.00 & 93.25 & 91.25 & 92.25 \\ \hline \hline \end{tabular}  
* The highest classification accuracy rate on SA-SVM. The total time spent includes the time for kernel processing data, training model parameters, and test set in model training. Comparing the Morlet–RBF kernel and the RBF kernel in SA-SVM, the former spends more time processing data than the latter, but the total time is less, indicating that the Morlet–RBF kernel is quicker in optimizing parameters than the RBF kernel.  
\end{table} 
Table 3: Testing results (accuracy) of SA-SVM. number of POIs was fixed, for example, at 53 POIs, the least time-consuming was the linear kernel, which took 17.44 s, and the most time-consuming was RBF, which took 81.77 s for SA-SVM. For SVM, the fastest was the linear kernel with 78.69 s, while the slowest was the Morlet-RBF kernel, which took 2836.91 s. The running time of SA-SVM was 39.96-98.02% less than that of the SVM model. Additionally, the time spent by the different kernels in SA-SVM was not significantly different, whereas the time spent by the different kernels in SVM increased with the complexity of the core. This means that, while the number of POIs affects SA-SVM, the parameter search time is significantly reduced when compared to SVM. The total time spent included the time it takes for the kernel to process data, the time it takes to train the parameters of the model, and the time it takes to test the trained model. A comparison of the Morlet-RBF kernel and the RBF kernel in SA-SVM revealed that the Morlet-RBF wavelet spent more time processing data than the RBF kernel, but the total time was less. This indicates that the Morlet-RBF kernel is faster in parameter optimization than the RBF kernel. Figure 5a-f illustrate the guessing entropy results for POIs of 4, 53, and 117 when using 1000 traces in total. When there were four POIs, the kernel function required seven traces to recover the keys under SA-SVM and only six under SVM, in addition to the linear kernel. When there were 53 POIs, the wavelet kernel in the SA-SVM model only required 3 traces to recover the key, whereas the Morlet-RBF wavelet and Mexican hat wavelet kernels in the SVM model required 4 traces. The number of traces to recover the keys increased when there were 117 POIs. Under the SA-SVM model, the kernel function required at least five keys to recover, whereas it needed more than six keys to recover under the SVM model. These results show that SA-SVM slightly improved the unmasked AES algorithm's key recovery ability. In addition, the performance of the wavelet kernel was better than that of the RBF kernel, and the performance of the linear kernel was the worst. Figure 4: Computational time analysis (in second) of SVM and SA-SVM.