## 4 Experimental Results and Analysis  
### Encryption Results  
Two 600 \(\times\) 600 DEMs with different complexities tabulated in Table 1 were considered experimental images. Their data formats were plain text, and their elevation values were integer. Figure 6 shows these two DEMs, showing different complexities and various ranges of pixel values. For convenience conducting the experiments, both \(m\) and \(n\) were set to 10 to encrypt two DEMs. The development environment was Microsoft Visual studio 2013 with.Net Framework 4.5, and the language used for programming was C#. The keys for generating chaotic sequences and corresponding \(|DS_{R}|\) of the confused DEM A in the confusion phase \begin{table}
\begin{tabular}{c c c c c c} \hline
**DEM** & **Latitude Extent** & **Longitude Extent** & \(S_{R}\) & \(S_{A}\) & **Size (KB)** \\ \hline A & \(34^{\circ}27^{\prime}04^{\prime\prime}\) N-\(35^{\circ}02^{\prime}53^{\prime\prime}\) N & \(100^{\circ}36^{\prime}21^{\prime\prime}\) E-\(101^{\circ}49^{\prime}23^{\prime\prime}\) E & 2,502,048.3 & 401,204,550.0 & 1758 \\ B & \(31^{\circ}23^{\prime}17^{\prime\prime}\) N-\(32^{\circ}06^{\prime}40^{\prime\prime}\) N & \(104^{\circ}07^{\prime}31^{\prime\prime}\) E-\(105^{\circ}06^{\prime}55^{\prime\prime}\) E & 2,416,595.3 & 308,809,911.3 & 1459 \\ \hline \end{tabular}
\end{table} 
Table 1: Two DEMs for the experiments [28]; \(S_{R}\) and \(S_{A}\) denote relative and absolute configurational entropy, respectively. Figure 6: Two experimental DEMs with different complexities. of the first round are tabulated in Table 2. Figure 7 shows the scrambled images, while they have the same histogram. The fourth one was selected for the diffusion phase because its \(|DS_{R}|\) was the maximum compared with the remaining confused images. By using the proposed encryption algorithm, we obtained 10 encrypted DEM A, which are shown in Figure 8, and the key pairs are shown in Table 3, where \(C_{R}\) represents the lossless compression ratio (i.e., the ratio between the bytes used for storing the original data and that for storing the compressed data) by using LZMA [34; 35], which is a dictionary-based compression algorithm and takes into consideration the spatial structure of data. From Figure 8, we find that the pixel value range has been modified and the tenth one has the maximum \(|DS_{A}|\) and \(S_{A}\) as shown in Table 3. Therefore, it is selected as the best one when mode (i) is activated. Regarding mode (ii), Figure 8e is considered the best one. From Figure 9, we find that the \(S_{A}\) values of the encrypted images increased, whereas the \(C_{R}\) values decreased with the increase in the total encryption rounds (i.e., \(m\)). This can be explained by the viewpoint derived from [19] that, from a theoretical perspective, the lower the redundancy (which is measured by configurational entropy here) of an image, the lower the compression ratio of the image achieved. \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **(\(\mathbf{r_{0}}\), \(\mathbf{x_{0}}\))** & **(\(\mathbf{r_{0}}\), \(\mathbf{y_{0}}\))** & \(1 DS_{R}1\) \\ \hline
1 & (3.6949202, 0.94) & (3.6477592, 0.16) & 1,425,882.9 \\
2 & (3.7278720, 0.12) & (3.7657562, 0.64) & 1,455,723.6 \\
3 & (3.6158898, 0.54) & (3.7451577, 0.34) & 1,440,030.0 \\
4 & (3.6694297, 0.82) & (3.6036054, 0.56) & 1,490,201.9 \\
5 & (3.7033331, 0.43) & (3.8601213, 0.80) & 1,478,572.8 \\
6 & (3.5919501, 0.58) & (3.7767205, 0.53) & 1,472,217.3 \\
7 & (3.7562061, 0.76) & (3.9686558, 0.74) & 1,449,584.6 \\
8 & (3.7254665, 0.13) & (3.942484, 0.03) & 1,455,760.0 \\
9 & (3.7873567, 0.05) & (3.6882554, 0.48) & 1,443,565.6 \\
10 & (3.8638823, 0.83) & (3.6808917, 0.04) & 1,453,363.9 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparisons of relative configurational entropy of confused DEM A under different keys in the first round. (\(r_{0}\), \(x_{0}\)) and (\(r_{0}\), \(y_{0}\)) denote the keys to scramble the row and column of DEM A, respectively. \(|DS_{R}|\) means the absolute \(S_{R}\) difference compared to the original one.