# Reversible Data Hiding in Encrypted Image Based on Multi-MSB Embedding Strategy
## 1 Introduction
designed a method to embed secret bits through a public key mechanism. In the decoding processing, a powerful SVM (support vector machine) classifier with two classes is designed to distinguish encrypted and unencrypted image patches, so that the embedded bits and the original image can be decoded jointly. [PERSON] et al. [28] introduced an RDH method based on distributed source coding. After stream encryption of an image, a series of pixels is selected from the encrypted image for compression to vacate room for embedding data. However, the entropy value of the image after encryption will reach a maximum, which makes it difficult to vacate room to embed bits, so that the embedding rate is usually very low. For this case, some special encryption-based methods are proposed. [PERSON] et al. [29] designed a special encryption mode to encrypt the non-sampled interpolation error, and then used the improved histogram shifting and DE technology to embed data. [PERSON] et al. [30] divide the image into several crosses, the pixels of each cross are encrypted with the same key, and secret data is embedded by shifting the difference histogram of the encrypted image. [PERSON] et al. [31] encrypted the original image with key transmission and calculated two-layer pixel errors to generate an error histogram with three peak bins. Data hiding is performed by shifting the error histogram. In order to improve the embedding rate, [PERSON] et al. [32] first proposed a RRBE-based method. They exploited the traditional RDH method to achieve self-embedding before encryption so as to obtain room for data embedding. The embedding rate of [PERSON] et al. is higher than that of the previous methods. [PERSON] et al. [33] predicted some pixel values before encryption so that through histogram shifting to embed data in the predicted error, and a special encryption scheme is designed to encrypt the predicted error. [PERSON] et al. [34] increased the embedding rate through improving the method of [PERSON] et al. [33] by using half of the pixels in the original image to predict the other half of the pixels. In order to better utilize the correlation between adjacent pixels, [PERSON] et al. [35] considered a patch-level sparse representation which can reserve a large redundant room for embedding data in the encrypted image. [PERSON] et al. [36] encrypted the original image by using the public key encryption technology with homomorphism, and then embedded data into LSB of pixels in the encrypted image. In [37], a novel method of RDHEI was proposed, [PERSON] et al. first divided the pixels into smooth and complex regions according to the four neighborhood pixels of the pixels, and then encrypted the original image. The secret data is embedded in the median plane of the smooth pixels of the encrypted image. Compared with VRAE-based RDHEI methods, these RRBE-based RDHEI methods have improvedthe embedding capacity and the visual quality of decrypted images, but due to the limitation of the embedding method, the hiding capacity is not particularly large. Based on this, [PERSON] et al. [38] designed a new MSB-prediction based on a method which embeds data in the MSB of the pixels. In [38], two approaches are proposed, which are the CPE-HCRDH approach (high-capacity reversible data hiding approach with correction of prediction errors) and the EPE-HCRDH approach (high-capacity reversible data hiding approach with embedded prediction errors). In the CPE-HCRDH approach, the embedding rate can reach 1 bpp for every image, and in the EPE-HCRDH approach, the embedding rate is slightly lower, but still between 0.8 bpp and 1 bpp for most tested images. Subsequently, on the basis of method in [PERSON] et al. [38], [PERSON] et al. [39] further improved the maximum embedding rate by using the method of embedding data at the two-MSB of pixels. For most tested images, the embedding rate was larger than 1 bpp. Although [38; 39] achieving a high embedding rate, only one MSB and two MSBs are exploited in [38] and [39], respectively.