# An Innovative Information Hiding Scheme Based on Block-Wise Pixel Reordering
## 3 Proposed Scheme
### Data Hiding
Since the efficient pairing of codebook table size and pixel-block size was utilized, the LSB of each pixel in a pixel-block was used to record the original pixel-block index in a group, and the PSNR values of all tested scenarios were around 51 dB. The PSNR values indicated that our recovered image had a good visual quality. As shown in Table 2, the proposed scheme involves replacing the LSB of pixels with the initial block index in a group after encrypting the image. Consequently, after extracting information and decrypting the image, the LSB of each pixel cannot be fully restored, with a 50% probability of being flipped. As a result, NPCR values are around 50% across various test images. UACI values are notably low, with the highest UACI not exceeding 0.2%, indicating that the average pixel changes induced by the proposed scheme are small, even if the images cannot be fully recovered. Mean Absolute Error (MAE) is also an indicator for assessing image quality, where a smaller MAE value corresponds to better image quality. From Table 2, we can see that the MAE values are small for all images. In summary, the proposed scheme causes very little damage to the cover images when embedding the secret data and the recovered images are very similar to the cover images. ### Execution Results and Security Analysis

Figure 10 presents the performance results of various test images at different stages. After image encryption, pixel values become disordered, rendering meaningful information indiscernible, and the pixel distribution in the histogram of the encrypted image is consequently uniform. Since our proposed data embedding scheme involves merely scrambling the positions of encrypted pixels after recording the original block indices using LSB replacements, the distribution of pixel values in the encrypted image does not undergo substantial changes. The histogram distributions of the recovered images that we are able to obtain after extracting the information are also very similar to the original histogram distributions. In addition to information entropy, another way to analyze the differences between adjacent pixels is to use the correlation coefficient to assess the correlation between adjacent pixels. A natural image has a high correlation between neighboring pixels normally, but for a secure encrypted image, the lower the correlation between its neighboring pixels, the more secure it is. It is defined as follows:

\[\text{Corr}=\frac{\sum_{i=1}^{N}\left(x_{i}-\frac{1}{N}\sum_{i=1}^{N}x_{i} \right)\left(y_{i}-\frac{1}{N}\sum_{i=1}^{N}y_{i}\right)}{\sqrt{\sum_{i=1}^{N} \left(x_{i}-\frac{1}{N}\sum_{i=1}^{N}x_{i}\right)^{2}\times\sum_{i=1}^{N}\left(y _{i}-\frac{1}{N}\sum_{i=1}^{N}y_{i}\right)^{2}}}. \tag{17}\]

We divide the image into pixel pairs, take the former of all pixel pairs as \(x_{i}\) and the latter of all pixel pairs as \(y_{i}\), with \(N\) denoting the number of pixel pairs, and then calculate the correlation coefficient between them. Tables 3-5 were tested with a pixel-block size of 8 and a codebook table size of 256. The information entropy and the pixel correlation results for horizontal and vertical pairs are shown in Tables 3 and 4, respectively. Figure 10: Execution results of our proposed scheme: (**a1**) is original “Airplane” image with \(512\times 512\) pixels. (**a2,a3**) are encrypted image and embedded encrypted image (block size = \(1\times 8\), codeword table size = 256). (**a4**) is the decrypted image. (**b1–b4**) are the corresponding histograms of (**a1–a4**). In (**c1–c4,d1–d4**), the results of “Baboon” (block size = \(1\times 8\), codeword table size = 256), are given. Table 3 provides measurements for the original, encrypted, and embedded encrypted images of different test images. Clearly, the entropy values for the encrypted and embedded encrypted images of each image are quite similar, as our proposed scheme only employs one-bit LSB replacement on encrypted pixels and subsequently scrambles the pixel positions.