## 4 Experiments and Analysis of Results
### Security
#### 4.4.4 Differential Attack  
To evaluate the resistance of the proposed algorithm against differential attacks, we employ the metrics of the number of pixel change rate (NPCR) and the uniform average change intensity (UACI) [39]. NPCR quantifies the rate of pixel modifications observed at corresponding locations between the original and encrypted images; a value closer to 100% signifies greater discrepancies between the images, reflecting a higher level of security for the algorithm. On the other hand, UACI calculates the average difference in pixel values across the two images. As per the findings by [PERSON] et al. [39], the optimal NPCR and UACI values for a secure encryption algorithm are 99.609% and 33.464%, respectively.  
In our study, we have implemented the (4, 5)-threshold algorithm detailed in the paper to embed random data into the six images depicted in Figure 5, with a fixed condition of \(B=32\). Following this, we conducted experimental assessments to ascertain the NPCR and UACI of the algorithm, the results of which are summarized in Table 13. Our algorithm showcases NPCR and UACI values closely tracking 99.609% and 33.464%, respectively, thus affirming its effectiveness in thwarting differential attacks. Noteworthy is the fact that the algorithm's ciphertext feedback mechanism induces notable modifications in the encrypted image even in the presence of minor fluctuations in the plaintext image. Moreover, the algorithm discussed in this paper integrates encoding techniques, scrambling encryption, and XOR encryption, culminating in a robust and indeterminate system with enhanced security measures.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Carrier Image** & **Original Image** & **Encrypted** & **Marked** & **Marked** & **Marked** & **Average of the** & **Marked** \\  & & **Image** & **Encrypted** & **Encrypted** & **Encrypted** & **Encrypted** \\  & & & **Image I** & **Image II** & **Image III** & **Images** \\ \hline [PERSON] & 7.4456 & 7.9911 & 7.9912 & 7.9913 & 7.9915 & 7.9913 \\ [PERSON] & 7.3577 & 7.9917 & 7.9912 & 7.9916 & 7.9911 & 7.9913 \\ [PERSON] & 7.3013 & 7.9916 & 7.9913 & 7.9915 & 7.9917 & 7.9915 \\ [PERSON] & 7.4778 & 7.9917 & 7.9915 & 7.9915 & 7.9912 & 7.9914 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Information entropy of test images.  
We have demonstrated through simulation the effectiveness of our algorithm in a controlled environment, but real-world validation in diverse and dynamic environments might reveal additional practical challenges and limitations. However, the validation of the algorithm is subject to numerous restrictive assumptions. The images used in our experiments are from existing image databases commonly used in algorithms to highlight the superiority of our algorithm, but real-world images vary in size. Furthermore, the performance evaluation metrics ER, PSNR, SRCC, and others used by existing algorithms are based on synthetic test data, which may not accurately reflect real-world scenarios. More diverse criteria are needed to test the effectiveness of the algorithm in practical applications. Lastly, limitations within the simulation environment may impact the scalability and applicability of the results. Therefore, the detection method of the existing RDH-EI algorithm in a controlled environment is still limited and requires further research.