# Reversible Data Hiding in Encrypted Images Based on the Mixed Multi-Bit Layer Embedding Strategy
## 4 Experimental Results and Discussion
### Embedded Capacity Analysis  
Several factors affect the embedding capacity. One is the size of the block: \(m\) and \(n\). The larger size will reduce \(L_{S_{1}}\) and \(L_{5_{2}}\). However, it will also increase the \(\max(D)\) to limit the number of AHBs and the embedding capacity. Therefore, the two-round segmentation of block size needs to be studied. The second factor is \(T\), which directly determines the number of AHBs. The larger \(T\) is, the greater the number of AHBs that satisfy the condition. This section uses the \(BT_{1}\) block in AHBs as an example to simulate the above parameters and analyzes the relationship between them and the embedding capacity. Parameters \(m\) and \(n\) are set to 2 \(\times\) 2, 2 \(\times\) 4, and 4 \(\times\) 4. \(T\) is set to 4, 8, 16, 32, and 64. Here, the FMLE strategy is used for analysis, and the results are shown in the figure below. In Figure 5a, the horizontal axis represents different thresholds, and the vertical axis represents the average pure capacity of the experimental images. The curves in (a) represent four block size schemes: \(m2n2\), \(m2n4\), and  
Figure 4(b) shows the embedding ability of the \(BT_{2}\) block in the sub-block segmentation method (\(T=16\), \(m=2\), \(n=4\)). The horizontal axis represents the segmentation method, and the vertical axis represents two data types. The left Y axis represents the number of \(BT_{2}\) blocks in the \(P\) and \(Q\) sub-blocks, and the right Y axis represents the pure embedding number of \(BT_{2}\) blocks under different sub-block segmentation methods. \(Pm2 Qn2\) refers to two sub-blocks and their length. Where \(m2+n2=8\) and \(m2\), \(n2\in[1,7]\). Sub-blocks \(Q1\) and \(P1\) with length 1 have no embedded capacity. The figure shows that the number of AHBs increases with the decrease in \(P\) length from 7 to 2, and \(Q\) has the same trend because the smaller the block length, the easier it is to meet the hidden conditions. It can be observed that the \(P4Q4\) mode corresponds to the highest embedding capacity. Therefore, \(m2=4\) and \(n2=4\) are the second-round segmentation method, which also means \(l_{2}=4\). According to the embedding strategy selection conditions in Table 1, \(l_{2}=4<n_{f}+1=5\). Therefore, AMLE is applied to \(BT_{1}\) blocks (\(l_{1}=8\)) and FMLE is applied to \(BT_{2}\) blocks (\(l_{2}=4\)) to maximize the embedded capacity. Figure 6 shows the number and proportion of each block type with \(T=16\) as an example. It can be found that in the image with a smooth texture, the proportion of AHBs is high, such as Peppers (78%), Lena (76%), and Airplane (75%). In the complex image Baboon, the proportion of AHBs is 32%, and the proportion of UHBs is 68%, which is the highest among several images. Generally, the higher the proportion of AHBs, the stronger the embedding ability of the cover image. The scheme is verified on the experimental images according to the above parameters, and the cover image of each stage is shown as follows:  
Figure 7 shows two examples of the results of each stage in the processing process. The process of all cover images is similar. Column 1 shows the original cover images (a) and (f). Then, the original cover images are encrypted using stream cipher to obtain figures (b) and (j). Next, according to the \(Kd\), the secret data are embedded to obtain the encrypted images containing secret data (c) and (h). After transmission, the receiver decrypts the received images to obtain figures (d) and (i). Figure 7e,j are the final recovered images. Visually, the encrypted images and the transmission image are messy, improving the security of the secret data and the content of the cover image at the same time. The experimental data also show that the PSNR of the encrypted image and the transmission image are between 8-10 dB, which has a very low correlation with the original image. Meanwhile, the decrypted and recovered images are highly similar to the original cover images.