# Implementation of MS Circle Map in Digital Image Encryption
## 3 Results and Discussion
### Image Quality Analysis  
Digital image quality analysis is performed using the Peak Signal to Noise Ratio (PSNR) test to determine the quality of encrypted and decrypted images. The PSNR testing refers to the Mean Square Error (MSE) value. The MSE and PSNR values can be calculated through Equations (7) and (8) [33], where N is the number of pixels in the image, and \(x_{i}\) and \(y_{i}\) are the values of the \(i\)th pixel of the original and encrypted/decrypted images, respectively. The quality of the decrypted image will be exactly the same as the original image when the MSE value is equal to zero (MSE = 0) and the PSNR value is equal to infinity (PSNR = \(\infty\)). On the other hand, for encrypted images, the higher the MSE value and the closer the PSNR value is to zero, the better the quality and security level of an encrypted image. In other words, the information contained in the encrypted image becomes increasingly difficult to read, the level of security is higher, and making it more difficult for unauthorized parties to access the original image data.  
\[MSE=\frac{1}{N}{\sum_{i=1}^{N}}[x_{i}-y_{i}]^{2} \tag{7}\]  
\[PSNR=10 log_{10}\frac{255^{2}}{MSE} \tag{8}\]  
Table 4 shows the measurement results of MSE and PSNR values of 30 encrypted images. It can be seen that the MSE values of all images are very large in the range of 7792 \(>\) MSE \(<\) 15,456, and the PSNR values are very small in the range of 623 dB \(>\) PSNR \(<\) 9.22 dB. These values indicate that the quality of information security in encrypted images is very good.  
Furthermore, the measurement results of MSE and PSNR values of 30 decrypted images are described in Table 5. It can be seen that the MSE values of all decrypted images are zero and the PSNR values are \(\infty\) dB. These values indicate that the quality of the decrypted images is very good, where all information can be restored as the original without any errors.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test** & \multirow{2}{*}{**MSE**} & **PSNR** & **Test** & \multirow{2}{*}{**MAE**} & **PSNR** & **Test** & \multirow{2}{*}{**MAE**} & **PSNR** \\
**Data** & & **(dB)** & & & & **(dB)** & **Data** & **(dB)** \\ \hline
1 & 12,197.9 & 7.26794 & 11 & 10,601.3 & 7.85564 & 21 & 8562.34 & 8.80487 \\ \hline
2 & 12,476.2 & 7.16997 & 12 & 10,654.0 & 7.85564 & 22 & 7886.87 & 9.16175 \\ \hline
3 & 12,473.6 & 7.17087 & 13 & 15,174.4 & 6.31968 & 23 & 7888.86 & 9.16076 \\ \hline
4 & 8774.36 & 8.71352 & 14 & 15,381.1 & 6.26092 & 24 & 7898.16 & 9.15553 \\ \hline
5 & 9003.19 & 8.58683 & 15 & 15,456.8 & 6.23959 & 25 & 10,079.1 & 8.09654 \\ \hline
6 & 9059.46 & 8.55977 & 16 & 7792.84 & 9.21384 & 26 & 10,221.8 & 8.03552 \\ \hline
7 & 10,369.4 & 7.97323 & 17 & 7897.38 & 9.15596 & 27 & 10,287.3 & 8.00775 \\ \hline
8 & 10,376.2 & 7.96532 & 18 & 7930.13 & 9.13799 & 28 & 14,951.4 & 6.38396 \\ \hline
9 & 10,388.3 & 7.96532 & 19 & 8285.94 & 8.96471 & 29 & 15,136.3 & 6.33058 \\ \hline
10 & 10,484.5 & 7.92531 & 20 & 8508.42 & 8.83231 & 30 & 15,197.0 & 6.31319 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Value of MSE and PSNR of encrypted image.