# A Reversible Data-Hiding Method with Prediction-Error Expansion in Compressible Encrypted Images
## 2 Related Work
### RDH-EI Methods  
In addition to RDH methods proposed for plain images, RDH in encrypted images has been actively studied in recent years [24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. RDH-EI methods are effective in embedding data in the encrypted domain without knowing the secret key used for encryption and disclosing the original-image content. They are mostly used for both copyright protection for image owners, and for the authentication and management purposes of third parties such as service providers. Therefore, a high hiding capacity is required in the field of RDH-EI methods.  
[PERSON] et al. [24] introduced MSB prediction and replacement instead of using LSB replacement to greatly extend the capacity. This method does not require any complex processes. [PERSON] et al. [25] enhanced the security of [24], and [PERSON] et al. [26] further improved the capacity of [24]. [PERSON] et al. [27] introduced the method of [PERSON] et al. [24] to an RDH-EI scheme based on bit-plane partition. Since redundancy is still preserved in images after the self-embedding process, this method [27] attained a hiding capacity of 2.2 bpp on average by utilizing the method in [24]. Nonetheless, there still exist multiple cases where reversibility is not fully ensured. [PERSON] et al. [28] extended the method of [PERSON] et al. [24] to guarantee full reversibility by defining precise conditions.  
[PERSON] et al. [29] proposed a new RDH-EI method called RDH-MSB with a higher capacity that guaranteed full reversibility and high capacity. Figure 1 illustrates the framework of the RDH-MSB method. This method uses bit planes of a target image from MSB to LSB until the iterative process becomes invalid. The first step is prediction-error (PE) detection to identify pixels that are not correctly predicted from their neighbor ones. Pixel values are updated in accordance with PE values, so that the original image can be perfectly reconstructed through the restoration process. The whole current bit plane is encrypted, and PE values are then embedded from a top-left pixel in the bit plane. Some marker bits are embedded ahead of the PE values. Consequently, regions not containing marker bits and PE values become an embeddable area for an arbitrary payload. The same steps are repeated for the latter bit planes. When a PE value cannot be embedded, the process is stopped, and only current and all latter bit planes are encrypted. The hiding capacity of the RDH-MSB method is 2.4 bpp on average. These high-capacity RDH-EI methods, however, cannot compress their marked encrypted images because a bitwise exclusive-or operation is used for encryption. Additionally, previous RDH-EI methods cannot decrypt marked encrypted images without data extraction.  
[PERSON] et al. [30] proposed RDH-EI method RDH-EtC with effective compressibility for marked encrypted images. An outline of the RDH-EtC method is shown in Figure 2. This method uses two of four processes in block-scrambling-based encryption for EtC systems [34; 35]: position scrambling and block rotation or flip. Since an image histogram is not transformed before or after the encryption processes, we can embed a payload in plain and/or encrypted domains by using RDH-HS [3]. Additionally, this method can flexibly extract payloads from either domain. Thus, a marked encrypted image can be decrypted without extracting a payload. Further, this method can compress marked encrypted images with loss using image coding standards, such as JPEG-LS [37] and JPEG 2000 [38]. This method, however, has an extremely low hiding capacity, i.e., about 0.1 bpp.  
The proposed method simultaneously achieves high compression efficiency and high hiding capacity. We compare our method with the related work in Table 1. The method has the advantages of both the RDH-MSB and RDH-EtC methods.  
Figure 1: Block diagram of RDH-MSB method [29].  
Figure 2: Block diagram of RDH-EtC method [30]. \(PP\) and \(ZP\) are bins with the highest and lowest frequency, respectively, in original-image histogram.