## 5 Experimental Study
### Real-Time Execution of the Proposed \(MPSA\) Scheme  
The system configuration employed for the experiments includes a x64-based Intel(R) Core(TM) i5-9300H CPU @ 2.40 GHz with 8 GB RAM. In a real-time scenario, the efficiency of an algorithm predominantly rests on time complexity. Here, we disclose the execution time taken by the proposed \(MPSA\) RDH scheme that supports its real-time applicability. The graph given in Figures 10 and 11 reveals the experimental time taken during secret data hiding in the encrypted image through the proposed \(MPSA\) scheme on the USC-SIPI and BOWS-2 image datasets, respectively. All images are standardized to \(512\times 512\) size pixels before computing the execution time. Figures 12 and 13 show the time taken by each image while extracting the hidden information and recovering the original cover image. Note that we used the USC-SIPI image dataset, which contains 210 images, and the BOWS-2 dataset, which contains 10,000 images in total, for the experiments. It should be noted that each line in the graph indicates the scenario of processing the image at a particular block size. Based on the experimental study, it is inferred that the computation time taken during the \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{1}{c}{**Scheme**} & **Airplane** & **Baboon** & **Boat** & **Peppers** & \
\begin{tabular}{c} **Entropy** \\ **Retained** \\ \end{tabular} &
\begin{tabular}{c} **Histogram** \\ **Retained** \\ \end{tabular} \\ \hline LSB replacement based RDH [21] & 0.0039 & 0.0009 & 0.0039 & 0.0015 & ✗ & ✗ \\ \hline Side match approach based RDH [22] & 0.0039 & 0.0009 & 0.0039 & 0.0039 & ✗ & ✗ \\ \hline LSB compression based RDH [41] & 0.0300 & 0.0100 & 0.0300 & 0.0300 & ✗ & ✗ \\ \hline Public key cryptosystem based RDH [42] & 0.0020 & 0.0020 & 0.0020 & 0.0020 & ✗ & ✗ \\ \hline Absolute mean difference based RDH [27] & 0.0020 & 0.0008 & 0.0049 & 0.0039 & ✗ & ✗ \\ \hline Difference expansion & 0.0040 & 0.0040 & 0.0040 & 0.0040 & ✗ & ✗ \\ + Public key cryptosystem [43] & 0.0080 & 0.0080 & 0.0080 & 0.0080 & ✗ & ✗ \\ \hline Histogram compression based RDH [44] & 0.0080 & 0.0080 & 0.0080 & 0.0080 & ✗ & ✗ \\ \hline Histogram shifting + & 0.0080 & 0.0080 & 0.0080 & 0.0080 & ✗ & ✗ \\ \hline Mean value based RDH [46] & 0.0039 & 0.0039 & 0.0039 & 0.0039 & ✗ & ✗ \\ \hline Joint RDH + Symmetric cryptosystem [47] & 0.0048 & 0.0011 & 0.0072 & 0.0072 & ✗ & ✗ \\ \hline Pseudo-random pixel mapping & 0.0313 & 0.0313 & 0.0313 & 0.0313 & ✗ & ✗ \\ + Weighted mesh graph RDH [48] & 0.0313 & 0.0078 & 0.0313 & 0.0313 & ✗ & ✗ \\ \hline Proposed \(MPSA\) RDH & 0.0313 & 0.0078 & 0.0313 & 0.0313 & ✗ & ✗ \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Distinguishing embedding rate of different RDH schemes for the well-known images. embedding and recovery phase is high while processing the image as 4 \(\times\) 4 size pixels, and it decreases with larger block size processing of the image. The average execution time incurred by images under various classes of the USC-SIPI dataset while processing as 8 \(\times\) 8-sized pixels is tabulated in Table 5. As we can observe, the worst-case average embedding time is 0.0106 s, and the worst-case average time during the data recovery and image restoration phase is 0.1090 s, while the average embedding time considering 10,000 images from the BOWS-2 dataset with 8 \(\times\) 8 block processing is 0.0086 s, and the average restoration time is 0.0986 s. This proves the real-time applicability of the proposed \(MPSA\) scheme. Moreover, all the RDH schemes mentioned in Table 4, including the proposed scheme, have a theoretical time complexity of O(\(K\)), where \(K=M.N\). Here, \(M\) is the number of rows in the processed image, and \(N\) is the number of columns in the processed image. Figure 11: Execution time taken by different images of the BOWS-2 dataset during the data-embedding phase. Figure 10: Execution time taken by USC-SIPI dataset images during the data-embedding phase.