# Reversible Data Hiding in Encrypted Image Based on Multi-MSB Embedding Strategy
## 1 Introduction  
Image encryption and data hiding are two main means for data security. The former aims to transform the meaningful image into a noise-like one to prevent image content leakage [1; 2; 3; 4], while the latter embeds secret data into a cover image imperceptibly. In image encryption, the original image is the one to be protected, while, in data hiding, the secret data is the information that should be undisclosed. Traditional data hiding technology is usually irreversible, and the embedding process will bring permanent distortion to the original carrier, which is not accepted in some cases such as military images, medical images, and judicial evidence collection where the original carrier needs to be restored without distortion. Take into account requirements of lossless recovery of the original carrier, reversible data hiding (RDH) was proposed. RDH technology has made great progress in the past decade. For example, early reversible data hiding technologies losslessly compress the least significant bit (LSB) planes or quantization residuals to accommodate for secret bits [5; 6; 7; 8]. Later, [PERSON] [9] proposed an RDH method using difference expansion (DE). This method divides an image into a series of pixel pair and embeds a secret bit into a pair of pixels by expanding the difference of this pixel pair. Based on the DE method, some improved reversible data hiding algorithms were proposed in [10; 11; 12; 13]. Another classic reversible data-hiding algorithm is histogram shifting (HS) [14; 15; 16; 17; 18; 19; 20; 21]. HS methods aim to generate a sharp histogram by counting pixel values [14], pixel difference [15; 16], or prediction errors [17; 18; 19; 20; 21]. The peak bin is expanded for data embedding, and the other bins need to be shifted for reversibility. Among these methods, HS-based methods can achieve better embedding performance. Nowadays, RDHEI has received increasing attention in the research community, in which both the original image and secret data need to be protected. In RDHEI, image encryption and data embedding are accomplished by different users separately. The content-owner first encrypts the original image to a noise-like one according to encryption key, then the data hider embeds secret data into the encrypted image using a data-hiding key without knowing its original content. The receiver can perform different operations according to the available keys. This can be applied in many scenarios such as Cloud storage, medical image management system. In general, RDHEI can be divided into two categories, namely, vacating room after encryption (VRAE) [22; 23; 24; 25; 26; 27; 28; 29; 30; 31] or reserving room before encryption (RRBE) [32; 33; 34; 35; 36; 37; 38; 39]. [PERSON] et al. [22] used an AES (advanced encryption standard) encryption algorithm to encrypt the original image, and then randomly selected a location in each 4\(\times\)4 pixel block to embed the secret bits. In order to extract secret bits during the decryption phase, they performed a local standard deviation analysis of the marked image. The embedding rate (ER) of this method is very small, i.e., only 0.0625 bpp. [PERSON] [23] encrypted the original image using the stream cipher firstly and then divided the encrypted image into blocks and each pixel block was divided into two parts. In one part, the three LSBs of each pixel were flipped to embed a secret bit. On the receiver side, a fluctuation function was designed for data extraction and image recovery. [PERSON] et al. [24] improves the method of [PERSON] et al. [23], so that the visual quality of decrypted images is improved. [PERSON] et al. [25] adopted a prediction error to introduce two RDH methods in the encryption domain, namely, joint method and separable method. In order to make full use of the spatial correlation in the original image, [PERSON] et al. [26] abandoned the idea of block segmentation and adopted the strategy of random diffusion, and the performance is better than that of [PERSON] [23]. In [27], [PERSON] et al.