## 4 Implementation and Performance Analysis of CAES-Based Image Encryption
### Connected Component Analysis  
Generally speaking, for a plain image, a high correlation between adjacent pixels is an obvious feature. Therefore, it would be better if the encryption algorithm could result in smaller correlation values between adjacent pixels. Here, 3000 pixels were randomly selected from the information of the plant and encrypted images of image 1 in Figure 10. The correlation coefficients for the horizontal, vertical, and diagonal directions were calculated using the following equations [2]:  
\[CCA=\frac{\sum\limits_{i=1}^{N}(x_{i}-\frac{1}{N}\sum\limits_{i=1}^{N}x_{i})( y_{i}-\frac{1}{N}\sum\limits_{i=1}^{N}y_{i})}{\sqrt{\sum\limits_{i=1}^{N}(x_{i}- \frac{1}{N}\sum\limits_{i=1}^{N}x_{i})^{2}\times\sum\limits_{i=1}^{N}(y_{i}- \frac{1}{N}\sum\limits_{i=1}^{N}y_{i})^{2}}} \tag{12}\]  
where \(x_{i}\) and \(y_{i}\) denote the pixel values of the two adjacent pixels, and \(N\) is the number of pair \((x_{i},y_{i})\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Image**} & \multicolumn{3}{c}{**Histogram MAD Uniform Distribution Test**} \\ \cline{2-4}  & **AES-ECB** & **AES-CBC** & **CAES-CBC** \\ \hline \hline \multirow{2}{*}{Average MAD} & \multirow{2}{*}{38.325} & \multirow{2}{*}{12.52} & \multirow{2}{*}{12.4} & \multirow{2}{*}{11.87} \\  & & & \\ \end{tabular}
\end{table}
Table 2: \(Cont.\)  
Figure 12: Information entropies for comparison.  
image encryption, and several tests and analyses, such as visual effect, statistical analysis, histogram, information entropy analysis, and connected component analysis, were all performed to determine the capability and security of the CAES algorithm. Recently, as a result of the impact of COVID-19 and to reduce the risk of infection caused by conversation contact, people have become accustomed to using wireless networks for communication. In addition, with the ultra-high computing speed of quantum computers, the existing encryption algorithms might be able to be cracked. Therefore, knowing how to ensure the security of data exchange is a very important issue. In the future, the robustness and synchronization speed of the proposed random key generators should be further discussed and promoted, such that the chaos-based cryptosystem could be applied in order to ensure the communication security of video/audio streaming in the network environment.  
Conceptualization, C.-H.L., G.-H.H., C.-Y.C., and J.-J.Y.; methodology, C.-H.L., G.-H.H., and J.-J.Y.; software, G.-H.H. and C.-Y.C.; validation, [PERSON]-H.H. and C.-Y.C.; formal analysis, C.-H.L. and J.-J.Y.; investigation, C.-H.L. and [PERSON]-H.H.; writing--original draft preparation, C.-H.L. and J.-J.Y.; writing--review and editing, J.-J.Y.; visualization, [PERSON]-H.H. and C.-Y.C.; supervision, C.-H.L.; project administration, J.-J.Y. All authors have read and agreed to the published version of the manuscript.  
This work was financially supported by the Ministry of Science and Technology, Taiwan, under MOST-107-2221-E-167-032-MY2 and MOST-109-2221-E-992-070.  
Not applicable.  
No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
The authors declare no conflict of interest.