目的 随着云计算和云存储场景中用户隐私保护的需求日益增加，密文域图像可逆信息隐藏（reversibledata hiding in encrytpted images，RDHEI）受到了广泛关注。然而大多数RDHEI算法以提升嵌入率和保障图像加密安全性为目的，复杂化图像的预处理操作。为此，提出一种基于可变预测和多MSB（most significant bit）替换的密文域图像可逆信息隐藏算法。方法 提出可变预测位平面翻转策略，用相邻像素值迭代预测当前像素值的多位最高有效位。若预测值比翻转值更接近目标像素值，则当前预测位平面可以用于信息隐藏，将其比特值修改为0。同时，用位置图自适应地标记可嵌入像素点。所生成的位置图具有稀疏特征，可以使用算术编码无损压缩。最后，对预留空间后的图像进行加密，通过多MSB替换的策略嵌入隐秘信息和压缩位置图。结果 经实验测试，本文算法在BOWS-2（break our watermarking system 2nd）数据集上平均嵌入率为2.953 bit/像素，并记录了1 000幅图像在预处理前后的每个位平面信息熵，其中最高位平面的信息熵比原始MSB下降了0.76，说明可变预测位平面翻转将多个高位平面翻转为0，使其处于稀疏状态，有效增加了嵌入空间。结论 本文算法利用明文图像的空间相关性，对高位平面进行翻转与替换，从而为隐秘信息预留了更多的嵌入空间。所提方法可无损恢复原始图像，且无差错提取隐秘信息。

Objective With the growing demand of users for privacy protection in cloud computing and cloud storage scenarios，reversible data hiding in encrypted images（RDHEI）has gained widespread attention. RDHEI has three independent roles，namely，image holder，service provider，and image receiver. Before uploading the images to the cloud，the holder encrypts it，and the service provider embeds some necessary information into the encrypted image for management and other purposes in the cloud server. After obtaining the marked encrypted image，the receiver can opt to extract the embedded data or recover the image according to its own secret key. The existing RDHEI schemes can be divided into two categories：vacating room after encryption（VRAE）and reserving room after encryption（RRBE）. The largest difference between two types of methods lies in the different processes before and after the encryption phase. For RRBE，before uploading the encrypted image to the service provider，essential preprocessing needs to be operated by the image holder for reserving the data space. For VRAE，the image holder can upload the encrypted image directly，and the service provider conducts the data space for the preparation of the subsequent embedding. The operation of vacating room in two types of methods is a redundant processing of images. The core is to select the point to use pixel correlation，and it is also a compromise between embedded capacity and transmission security. However，most RDHEI algorithms complicate the preprocessing of images to improve the embedding rate and ensure the security of image encryption. This paper proposes a reversible data hiding algorithm based on variable prediction and multi-most significant bit（MSB）replacement in encrypted images. Method The proposed algorithm mainly consists of the following parts：image preprocessing，exclusive encryption，data embedding，data extraction，and image recovery. This paper proposes a variable prediction bit-plane inversion（VPBI） strategy，which aims to make full use of the whole relevance of the image. First，VPBI is designed to predict iteratively multiple relevant bit-planes of the current pixel value with adjacent pixel values. When the prediction value is closer to the target pixel than the inverted value，the prediction is accurate. The current prediction bit-plane can be used for data hiding and modify its bit value to zero. Because the method of VPBI works from the second row and second column of the image， to increase the number of embeddable pixels as much as possible，the linear prediction method is designed to obtain the prediction error in the first row and column except for the first pixel. The positive and negative signs of the prediction error are stored in the last bit of its binary sequence with one bit，which means the absolute value of the prediction error cannot be greater than 127 or -127. Then，a sign indication map is designed to record this type of prediction error. At the same time，the location map is used to mark adaptively the embeddable position，which is sparse and can be lossless compressed using arithmetic coding. After reserving space，the image is XOR-encrypted by the image holder，and the holder inserts the side information such as the compressed location map，sign indication map，and the first MSB back into the first MSB bit-plane. At the data embedding phase，the service provider embeds the secret data and the compressed location map through the multiMSB replacement strategy. Finally，the extraction of secret data and the recovery of image are reverse processes. Therefore，if the image receiver holds the corresponding key，the secret data can be extracted without loss or the original image can be recovered perfectly. Result To evaluate the performance of the proposed algorithm，experiments compare the proposed algorithm with five other state-of-the-art RDHEI algorithms on six common grayscale images and one public database：Break our watermarking system 2nd（BOWS-2）. The information entropy，embedding capacity，embedding rate，peak signal-to-noise ratio（PSNR），and structure similarity index measure（SSIM）are used as the quantitative evaluation metrics. First，the experiment tests the information entropy of each bit-plane of 1 000 images before and after preprocessing. The information entropy of the highest bit-plane is 0. 76 lower than that of the original MSB，and the second， third，fourth，and fifth bit-planes decrease by 0. 25，0. 45，0. 61，and 0. 75，respectively，indicating VPBI generates more zeros for multiple significant bit-planes，makes them sparse，and effectively increases the embedded space. Experimental results show the average embedding rates of the proposed algorithm on the BOWS-2 reach 2. 953 bit/pixel，which is 0. 423 bit/pixel higher than the latest algorithm. The secret data can be extracted without error，and the PSNR and SSIM are constant values that equal to ∞ and 1，respectively，which show the proposed algorithm is reversible. Conclusion In this paper，a reversible data hiding algorithm in encrypted images based on variable prediction and multiMSB replacement is proposed. By using the redundancy between pixels and reducing the space occupation of sign indication map，VPBI is proposed to deal the multiMSB planes. The comparison of the variable prediction value，the inverse value of the target pixel，and the target pixel can provide considerable spaces to embed data. In the embedding stage，the method of multiMSB replacement is used to hide secret data. The adaptive location map and other side information are saved to the highest bit-plane to ensure no additional data are required when the image is transmitted to the cloud server. Experiments show the proposed method has high embedding rate and can ensure reversibility and security. In the future，an effective scheme for optimizing high-texture images will be further developed.