# Enhanced Joint and Separable Reversible Data Hiding in Encrypted Images with High Payload
## 1 Introduction
As an authorized receiver, it is essential that hidden information can be extracted and the original cover can be recovered error-free without any loss or distortion after image decryption and data extraction. Reversible data hiding in encrypted images (RDH-EI) gratifies these requirements. The existing RDH-EI methods can be classified into two categories: \"vacating room before encryption (VRBE)\" and \"vacating room after encryption (VRAE)\". In VRBE, the content owner creates room for embedding data in the cover image before encryption [13; 14]. As VRBE requires the content owner to do an extra preprocessing before content encryption, so this method might be impractical. In this sense, the VRAE method is more practical. In VRAE methods, the original content is encrypted by the content owner, and the data-hider embeds the additional information by modifying a small part of the encrypted data [15; 16; 17; 18; 19; 20; 21; 22; 23]. The VRAE methods can be further divided into two categories: joint method and separable method. In joint methods [15; 16; 17; 18; 19; 20], with an encrypted image containing additional data, a receiver may first decrypt it using the encryption key, and then extract the embedded data and recover the original image from the decrypted image using the data-hiding key. In 2011, [PERSON] [15] proposed a novel reversible data hiding technique in encrypted images. In 2012, [PERSON] et al. [16] improved [PERSON]'s technique by using a side match technique. [PERSON]'s and [PERSON]'s systems were further enhanced with other techniques [17; 18]. In these systems, the encrypted image is divided into blocks, and the spatial correlation in the block cannot fully reflect the smoothness of natural images, especially when the block size is small. In 2014, [PERSON] et al. [19] introduced a new scheme where a random diffusion strategy is used for embedding and accurate prediction is used to measure the smoothness. In 2014, [PERSON] and [PERSON] [20] proposed a different joint RDH system based on prediction error. However, the smoothness calculation from using prediction error fails to perform well. Nevertheless, in joint methods, the embedded data can only be extracted before image decryption. In other words, a receiver having a data-hiding key but no encryption key cannot extract any information. Moreover, when the payload is high, it is not possible to get error-free extracted bits with all these joint methods. To overcome these problems, a separable reversible data-hiding scheme is required. In separable methods [20; 21; 22; 23], with an encrypted image containing additional data, if a receiver has the data-hiding key, he can extract the additional bits from the marked encrypted image directly, while if the receiver has the encryption key, he can decrypt the received data which is similar to the original one. When, the receiver has both the data-hiding and encryption keys, he can extract the additional bits and recover the original image perfectly. However, in [20] prediction error is used for separable method too which causes worse performance. Moreover, in [21] data cannot be extracted precisely and the original image cannot be recovered perfectly especially when the payload is high. Beyond that, many parameters assumed in [21] make it a little complicated for implementation. [PERSON] et al. [22] proposed a novel scheme of RDH in encrypted images using distributed source coding (DSC) where the low-density parity check (LDPC) encoding and source decoding are used which make the system's complexity much higher. [PERSON] et al. [23] proposed a separable RDH technique in encrypted images based on pixel value ordering (PVO) where homomorphism encryption is used for image encryption. To solve the above-mentioned issues in both joint and separable methods, we propose an improved joint and separable RDH technique in this paper. For joint method, the encrypted image is divided into four sets, instead of blocks, and two sets can be used for data hiding. Therefore, the embedding capacity increases.