## 4 Numerical Simulation
### Timing Analysis
As a result, the maximum value in each column is normalized to '1', the minimum value to '0', and all other values fall between '0' and '1'. This ensures that all metrics are on a common scale, eliminating distortions caused by differences in their original ranges. After normalization, the values are used in the VBPM Equation (8), to calculate the overall performance efficiency for each configuration. The last column in Table 4 represents the obtained values of VBPM for all the normalized performance metrics. Overall, the system achieves its highest performance when N = 4, where the VBPM value is 6.0775, after which performance begins to degrade. This trend highlights that while increasing the number of cascaded levels improves security and system complexity up to a certain point, adding too many levels may introduce inefficiencies or diminish overall performance, as reflected by the declining VBPM beyond N = 4. Thus, the optimal number of cascaded levels for this system is N = 4, where performance efficiency peaks. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Number of Levels (N)** & **SNR** & **PSNR** & **PRD** & **Correlation Coefficient (ICC)** & **Encryption Time (te)** & **Decryption Time (td)** & **Logic Utilization** & **Maximum Frequency** & **VBPM** \\ \hline
1 & 0 & 0.7246 & 0 & 1 & 0 & 0 & 0 & 0.8667 & 1.5748 \\
2 & 0.1664 & 0.9668 & 0.0219 & 0.3043 & 0.0408 & 0.0395 & 0.0522 & 0.3125 & 3.6983 \\
3 & 0.2794 & 1 & 0.0466 & 0.0870 & 0.1141 & 0.1299 & 0.1084 & 0.8 & 5.2676 \\
4 & 0.3628 & 0.9824 & 0.0727 & 0 & 0.1332 & 0.1356 & 0.1647 & 1 & 6.0775 \\
5 & 0.4352 & 0.8809 & 0.1028 & 0.0435 & 0.2120 & 0.2090 & 0.2209 & 0.4563 & 2.8723 \\
6 & 0.4975 & 0.57676 & 0.1360 & 0.0870 & 0.2391 & 0.2566 & 0.2610 & 0.5562 & 2.3800 \\
7 & 0.5553 & 0.6426 & 0.1729 & 0.1739 & 0.2663 & 0.2655 & 0.3173 & 0 & 1.3786 \\
8 & 0.6028 & 0.5352 & 0.2123 & 0.3043 & 0.4022 & 0.3220 & 0.3655 & - & 0.9884 \\
9 & 0.6028 & 0.5352 & 0.2583 & 0.4348 & 0.4022 & 0.3785 & 0.4257 & - & 0.8642 \\
10 & 0.6507 & 0.4141 & 0.3150 & 0.5652 & 0.4293 & 0.4350 & 0.4739 & - & 0.7314 \\
15 & 0.6964 & 0.2949 & 0.6390 & 0.6957 & 0.7283 & 0.7740 & 0.6827 & - & 0.5678 \\
20 & 1 & 0 & 1 & 0.6087 & 1 & 1 & 1 & - & 0.5542 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Normalized security analysis of N-level cascaded coupled chaotic systems with VBPM. Figure 5 provides a graphical representation of VBPM for different values of N, illustrating the relationship between the number of cascaded levels and system performance. It is evident that as the number of levels (N) increases, the VBPM rises, reaching a peak at N = 4. However, further increasing the number of levels beyond 4 results in a gradual decline in VBPM. Comparison with Existing WorkWhile our proposed system shows significant improvements in terms of correlation coefficient and SNR, as seen in Table 4, it is essential to thoroughly examine how these results compare with existing work that used different chaotic systems to encrypt voice signals. For instance, the 4-level cascaded chaotic-based secure communication system using the unified hyperchaotic system achieves a correlation coefficient of 0.0004, which is lower than that of some other methods, listed in Table 5, indicating better correlation between the original and encrypted signals. Similarly, the SNR of \(-\)71.68 dB indicates stronger encryption, as it is much lower than the other systems, such as the Zaslavsky map (\(-\)56.87 dB) and the chaotic circle map (\(-\)16.05 dB). This lower SNR highlights the increased noise added to the signal using our proposed encryption system, making it more difficult for an unauthorized party to reconstruct the original signal. It could be concluded that the presented N-Levels cascaded system for voice encryption when (N = 4) overrides the other existing schemes since our proposed scheme offers the best encryption results, so it is difficult to hack the voice signal in the channel during  
Figure 5: Value-Based Performance Metric (VBPM) for different values of N.