# An Innovative Information Hiding Scheme Based on Block-Wise Pixel Reordering
## 3 Proposed Scheme
### Data Hiding
On the other hand, the entropy values for different encrypted images are consistently close to 8, significantly higher than the entropy values of the original images. Consequently, the distribution of pixel values in encrypted images exhibits heightened randomness, thereby enhancing security. As shown in Table 4, neighboring pixel values in the original image have strong positive correlation both horizontally and vertically, while the pixels of encrypted and marked images have only very low correlation both horizontally and vertically. Also, the correlation between the marked image and the encrypted image does not change much compared to the encrypted image both horizontally and vertically. This indicates that the Stream Cipher encryption completely encrypts the image, and the proposed scheme that utilizes the reordering of the codebook table to embed the secret data inherits this feature and does not make the correlation between the pixels higher due to the embedded data. The security of the proposed scheme is further analyzed in Table 5 using two metrics, NPCR and UACI. The definition and computation of both NPCR and UACI have been mentioned in Section 4.1. In terms of security analysis, the higher the NPCR value, the more effective the encryption algorithm is, because the higher the number of different pixels, \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Image Name**} & \multicolumn{2}{c}{**Original Image**} & \multicolumn{2}{c}{**Encrypted Image**} & \multicolumn{2}{c}{**Marked Image**} \\ \cline{2-6}  & **Hor** & **Ver** & **Hor** & **Ver** & **Hor** & **Ver** \\ \hline Airplane & 0.9606 & 0.9584 & \(-\)0.0019 & \(-\)0.0033 & \(-\)0.0019 & \(-\)0.0080 \\ Baboon & 0.8667 & 0.7498 & 0.0010 & \(-\)0.0034 & 0.0010 & \(-\)0.0131 \\ Barbara & 0.8956 & 0.9588 & \(-\)0.0009 & \(-\)0.0028 & \(-\)0.0009 & \(-\)0.0138 \\ Boat & 0.9383 & 0.9715 & 0.0000 & \(-\)0.0052 & 0.0000 & \(-\)0.0087 \\ Couple & 0.9433 & 0.9534 & \(-\)0.0035 & \(-\)0.0027 & \(-\)0.0034 & \(-\)0.0091 \\ Lena & 0.9719 & 0.9850 & 0.0002 & \(-\)0.0012 & 0.0001 & \(-\)0.0112 \\ Peppers & 0.9730 & 0.9762 & \(-\)0.0012 & \(-\)0.0028 & \(-\)0.0012 & \(-\)0.0103 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Horizontal and vertical correlation analysis. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Image Name**} & \multicolumn{2}{c}{**Encrypted Image**} & \multicolumn{2}{c}{**Marked Image**} \\ \cline{2-4}  & **NPCR** & **UACI** & **NPCR** & **UACI** \\ \hline Airplane & 99.8096 & 32.3892 & 99.61624 & 32.43519 \\ Baboon & 99.8096 & 27.9032 & 99.60213 & 27.58626 \\ Barbara & 99.8096 & 29.8222 & 99.60213 & 29.86593 \\ Boat & 99.8096 & 28.5168 & 99.61014 & 28.54057 \\ Couple & 99.8096 & 28.2082 & 99.63608 & 27.8268 \\ Lena & 99.8096 & 28.6750 & 99.61281 & 28.81635 \\ Peppers & 99.8096 & 29.6210 & 99.60632 & 29.64995 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: NPCR and UACI analysis of test images. the harder the encrypted image is to crack. For two uncorrelated images, the theoretical value of UACI is 33.33%. As shown in Table 5, for both encrypted and marked images, the NPCR value and UACI value of the proposed scheme are close to the theoretical optimal value, which indicates that our scheme can provide a high level of security against potential attacks. Table 6 shows the time in seconds spent by different stages of the proposed scheme on different test images. The pixel-block size of the proposed scheme is 8, the codebook size is 256, and 197,888 bits of secret data are embedded. From the table, we can see that the proposed scheme spends 6.30 s in the embedding stage at most, and 2.85 s in the extraction and recovering stage at most. Overall, the cost of time spent is acceptable. ### Comparison with State-of-the-Art Schemes

In this section, we primarily compare our proposed scheme with some state-of-the-art schemes for data hiding in encrypted images in terms of PSNR, SSIM, and embedding capacity.