# Reversible Data Hiding in Encrypted Images Based on the Mixed Multi-Bit Layer Embedding Strategy
## 3 Proposed Scheme
### Data Embedding  
In this section, \(Kd\) is used to control the embedding process of secret data. Namely, the secret data are embedded in the encrypted image \(B\) through the embedding strategy. This section describes two strategies: the FMLE strategy and the AMLE strategy. * The FMLE strategy  
In this way, all AHBs use a fixed threshold. Each AHB uses the same \(T\), so all hidden pixels in the AHBs use the same number of error bits with the length of \(\log_{2}(T)\). The remaining number of embeddable bit layers is fixed. Figure 3 illustrates the FMLE strategy. Figure 3a,b show how the AHBs for types of \(BT_{1}\) and \(BT_{2}\) are processed under the strategy. Below, blocks of type \(BT_{1}\) will be elaborated as the example. In Section 3.1, \(x_{1}\) in the block is LSB marked to obtain the marked block (see the left part in the sub-figure). Figure 3a gives the strategy of the first AHB. To consider decryption recovery at the receiver, it is necessary to embed \(m\) and \(n\). The strategy adopted by other AHBs is shown in Figure 3b. Then, the encrypted block (see the middle part of the sub-figure) is obtained by encryption in Section 3.2. The encrypted image block loses relevance, and the LSB mark is covered. Therefore, during data embedding, the two location maps, Map1 and Map2, and the hiding key are used to guide secret data embedding. If the value in the location map is 1, the block belongs to the AHB, otherwise, it belongs to the UHB. Meanwhile, the value is embedded in the MSB position in \(x_{2}\) of the block with 1 bit in each block. In this paper, \(x_{1}\) is the reference pixel and plays an essential role in the cover recovery phase, so it cannot be used for data embedding. The data embedding structure is given in the third sub-figure of Figure 3a,b. The auxiliary information \(T\), \(E_{1}\), and \(S\) of the block are embedded in the low position of the pixels. The remaining space is used for secret data hiding. Thus, the order of embedding data is MSB, \(m\), \(n\), \(T\), \(E_{1}\), \(S_{1}\), and secret data in the first AHB. For other AHBs, unlike Figure 3a, there is no need to embed the parameters again. Figure 3c shows the processing method of UHBs. Although secret data are not hidden in the UHBs, the marking information MSB must also be embedded for the receiver to correctly distinguish the AHBs and the UHBs. * The AMLE strategy  
In this way, all AHBs adopt dynamic thresholds. Each AHB directly uses the max(\(D\)) of the block itself as the threshold and the number of error bits is dynamic with a length of log\({}_{2}\)(max(\(D\))). Because the max(\(D\)) corresponding to each block is inconsistent, the remaining number of embeddable bit layers in a hidden pixel is dynamic. Figure 4 illustrates the AMLE strategy. The process is consistent with the FMLE strategy, but there is a difference in data embedding. Under the FMLE strategy, the fixed \(T\) must be embedded into the first AHB but there is no need in other AHBs. However, during the embedding process under the AMLE strategy, each dynamic \(T\) generated by the original block can be embedded. \(T\) may be max(\(D\))-1, max(\(D\))-2,... and so on. As shown in Figure 3(a),b, they are embedded with fixed bits in AHBs in turn. If the max(\(D\)) \(<\) \(T\), the number of error bits will decrease. Therefore, this strategy dynamically compresses the  
Figure 3: Schematic diagram of the FMLE embedding strategy: (a) the AHB (the 1 st \(BT_{1}\) block), (b) the AHB (other \(BT_{1}\) blocks and \(BT_{2}\) blocks), and (c) the UHB (\(BT_{3}\)). auxiliary information \(E_{1}\) into \({E_{1}}^{\prime}\) which further increases the available hidden space for secret data embedding. The data embedding structure is given in the third sub-figure of Figure 4a,b. The auxiliary information \(\max(D)\), \(E_{1}\) and \(S_{1}\) of the block are embedded in the low position of the pixels. The order of embedding data is MSB, \(m\), \(n\), \(\max(D)\), \({E_{1}}^{\prime}\), \(S_{1}\), and secret data in the first AHB.