## 5 Experimental Study
### Analysis of Efficiency of Image Encryption  
The encryption algorithm's efficiency can be analyzed from (a) the entropy of the encrypted image and (b) the histogram of the encrypted image. Entropy estimates the level of randomness of an image pixel. It characterizes the texture of the image. The entropy is defined as follows:  
\[E(I(Y))=\sum_{l=0}^{Y-1}P(L)\log_{2}\frac{1}{P(L)}\, \tag{23}\]  
where \(I\) is the image, \(Y\) indicates the peak gray level (256 for a grayscale image), and \(P(L)\) indicates the probability of a pixel with intensity value \(L\). If the encrypted image is highly random, then the entropy measure should be near 8 for a grayscale image. The value of entropy measured over the original cover image, the image acquired through encrypting the cover image, and the image acquired from hiding a given sequence of secret data are given in Table 3. It is worth mentioning that the pixels of the encrypted image and the image acquired from the data-embedding process are both the same (only the position of the pixels is changed), and hence the entropy measurement of both images is also the same. This confirms that the security level of the marked image is as strong as the encrypted image, further substantiating the title of the paper. It is apparent from Table 3 that the encrypted image entropy remains the same after the data-hiding process. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Image Used**} & \multirow{2}{*}{**Block Length**} & \multirow{2}{*}{\begin{tabular}{c} **Entropy** \\ **(Original Image)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Entropy** \\ **(After the Encryption Process)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Entropy** \\ **(After the Data-Embedding Process)** \\ \end{tabular} } \\ \hline \multirow{4}{*}{Airplane} & \(4\times 4\) & 6.7025 & 7.9993 & 7.9993 \\ \cline{2-5}  & \(8\times 8\) & 6.7025 & 7.9993 & 7.9993 \\ \cline{2-5}  & \(16\times 16\) & 6.7025 & 7.9993 & 7.9993 \\ \cline{2-5}  & \(32\times 32\) & 6.7025 & 7.9993 & 7.9993 \\ \cline{2-5}  & \(64\times 64\) & 6.7025 & 7.9993 & 7.9993 \\ \hline \multirow{4}{*}{Baboon} & \(4\times 4\) & 7.3583 & 7.9994 & 7.9994 \\ \cline{2-5}  & \(8\times 8\) & 7.3583 & 7.9994 & 7.9994 \\ \cline{2-5}  & \(16\times 16\) & 7.3583 & 7.9994 & 7.9994 \\ \cline{2-5}  & \(32\times 32\) & 7.3583 & 7.9994 & 7.9994 \\ \cline{2-5}  & \(64\times 64\) & 7.3583 & 7.9994 & 7.9994 \\ \hline \multirow{4}{*}{Boat} & \(4\times 4\) & 7.1914 & 7.9993 & 7.9993 \\ \cline{2-5}  & \(8\times 8\) & 7.1914 & 7.9993 & 7.9993 \\ \cline{2-5}  & \(16\times 16\) & 7.1914 & 7.9993 & 7.9993 \\ \cline{2-5}  & \(32\times 32\) & 7.1914 & 7.9993 & 7.9993 \\ \cline{2-5}  & \(64\times 64\) & 7.1914 & 7.9993 & 7.9993 \\ \hline \multirow{4}{*}{Peppers} & \(4\times 4\) & 7.5937 & 7.9992 & 7.9992 \\ \cline{2-5}  & \(8\times 8\) & 7.5937 & 7.9992 & 7.9992 \\ \cline{1-1} \cline{2-5}  & \(16\times 16\) & 7.5937 & 7.9992 & 7.9992 \\ \cline{1-1} \cline{2-5}  & \(32\times 32\) & 7.5937 & 7.9992 & 7.9992 \\ \cline{1-1} \cline{2-5}  & \(64\times 64\) & 7.5937 & 7.9992 & 7.9992 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Analysis of entropy measure. The histogram of an image indicates how the image pixels are distributed. Any kind of changes that occur during data hiding will alter the original image's pixel distribution. A uniform distribution of pixel values is anticipated from an encrypted image. In such a case, the encrypted image histogram will look flat. Hence, changing encrypted image pixel values during the data-hiding process can lead to a different histogram. However, as we discussed earlier, the proposed \(MPSA\) scheme makes no attempt to change the encrypted image histogram.