# Implementation of MS Circle Map in Digital Image Encryption
## 3 Results and Discussion
### Performance Comparison  
This section describes the performance measurement of the image encryption and decryption method based on the proposed MS Circle Map (MSCM) function using four images commonly used by other researchers. Furthermore, a comparison of its performance with several other methods is also described. The four images are Pepper, Butterfly, Boat, and Architecture, as shown in the first row of Table 13, where each has a size of 256 \(\times\) 256 pixels. The second row shows the encryption results of each image using the key parameter values: x\({}_{0}\) = 0.9, \(\lambda\) = 2.1, \(\Omega\) = 0.5, K = 1000, and r = 3.8. The third row shows the decryption results when using the same key parameter values. However, if one of the key parameter values is different, a decryption error occurs. This is shown in the fourth row when using the values x\({}_{0}\) + 10\({}^{-15}\), \(\lambda\) + 10\({}^{-15}\) in the fifth row, \(\Omega\) + 10\({}^{-18}\) in the sixth row, K + 10\({}^{-13}\) in the seventh row, and r + 10\({}^{-17}\) in the last row. These values indicate the sensitivity of each key parameter of the MSCM function. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Original Images**} & \multicolumn{2}{c}{**(a) Pepper**} & \multicolumn{2}{c}{**(b) Butterfly**} & \multicolumn{2}{c}{**(c) Boat**} & \multicolumn{2}{c}{**(d) Architecture**} \\ \cline{  
A comparative analysis of the MSCM method was carried out against four other image encryption methods, as shown in Table 14. The entropy value in the fifth column is the average entropy of the four images (a)-(d) calculated using the MSCM method. This value is similar to the average entropy value in Table 11. When compared to the average entropy values in other methods, the MSCM is better than [36,37], and similar to [38]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**(a)** & **(b)** & **(c)** & **(d)** & **MSCM** & [36] & [37] & [38] & [38] \\ \hline Entropy 7.9993 & 7.9994 & 7.9992 & 7.9993 & 7.9993 & 7.9982 & 7.9991 & 7.9994 & 7.9994 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Comparative analysis of entropy values. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Original Images** & **(a)** Pepper & **(b) Butterfly** & **(c) Boat** & **(d) Architecture** \\ \hline Decrypted images with same keys & & & & & & \\ Key: \(x_{0}+10^{-15}\) & & & & & & \\ Error decryption & & & & & & \\ Key: \(\lambda+10^{-15}\) & & & & & & \\ Error decryption & & & & & & & \\ Key: \(\Omega+10^{-18}\) & & & & & & & \\ Error decryption & & & & & & & \\ Key: \(K+10^{-13}\) & & & & & & & \\ Error decryption & & & & & & & \\ Key: \(r+10^{-17}\) & & & & & & & \\ Error decryption & & & & & & & \\ Key: \(r+10^{-17}\) & & & & & & & & \\ Error decryption & & & & & & & & \\ Key: \(r+10^{-17}\) & & & & & & & & \\ Error decryption & & & & & & & & \\ Key: \(r+10^{-17}\) & & & & & & & & \\ Error decryption & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: _Cont._Table 15 presents the NCPCR and UACI assessment results for the MSCM method (sixth column) and four other methods (in the last four columns). It can be seen that the average NPCR and UACI values for the MSCM method are very close to the ideal NPCR values of 99.6094% and UACI of 33.4635%. These values are not much different from the NPCR and UACI values of the other four methods. Table 16 describes the analysis of neighboring pixel correlation coefficients of encrypted images using the MSCM method and the methods developed in [36; 37; 38]. In the sixth column, it can be seen that the average correlation coefficient values of the MSCM in all directions have very small values and are relatively similar to the other four methods. This indicates that the MSCM has an exceptional capability in randomizing and eliminating the correlation of neighboring pixels, so that all information in the image is completely unreadable.