目的 密文域可逆信息隐藏是一种可以在加密图像中嵌入秘密信息、保证秘密信息可以无错提取以及明文图像可以无损恢复的技术，越来越受到研究者们的关注，并广泛应用于云服务器端的用户隐私保护。针对密文域可逆信息隐藏算法中嵌入率不高的问题，提出一种联合定长编码和哈夫曼编码的密文域可逆信息隐藏算法。方法 使用定长编码与哈夫曼编码相结合的分组编码方式对原始明文图像高位平面进行压缩，通过重排列将空出空间排放在低位平面中，并使用流密码加密重排后的图像。然后将秘密信息嵌入密文图像低位平面的空出空间中。合法接收方可分离地实现秘密信息的无错提取以及原始明文图像的无损恢复。结果 实验结果表明，所提算法的嵌入率在UCID(an uncompressed color image database)、BOSSBase(Break Our Steganographic System)和BOWS-2(Break Our Watermarking System 2nd)这3个数据集上达到2.123 4 bit/像素、2.410 7 bit/像素和2.380 3 bit/像素，分别比同类算法高出0.246 6 bit/像素、0.088 1 bit/像素和0.135 6 bit/像素。结论 所提算法利用自然图像相邻像素间的相关性，对具有比特连续性的高位平面进行编码、压缩，从而为秘密信息的嵌入腾出更多空间，提升了嵌入率。

可逆信息隐藏; 密文域; 定长编码; 哈夫曼编码; 分离的

Objective Reversible data hiding in encrypted images (RDHEI) aims to embed secret data in the encrypted images to protect users' privacy on cloud storage. It has attracted increasing attention recently since the original plaintext image and the secret data can be restored and extracted lossless. Data differentiation hiding in plaintext images, encrypted images have no correlation between adjacent pixels subject to low image redundancy. The embedding capacity levels of encrypted images have been improving due to its high practical value. The high embedding rate of the plaintext image depends on the image compression algorithm intensively. In terms of the high redundancy between adjacent pixels, more space can be vacated for embedding secret data via the plaintext image compressing. It is difficult to obtain higher compression space in the encrypted domain for the image compression algorithm. Current reversible data hiding algorithms in encrypted images can be divided into three frameworks as belows: vacating room after encryption (VRAE), vacating room by encryption(VRBE) and reserving room before encryption (RRBE). For VRAE, space is vacated via using a compression algorithm in encrypted images directly. This framework is difficult to obtain a high embedding rate in common. For VRBE, more attentions are paid to the impact of the encryption algorithm for the image processing. Customized encryption algorithms make the encrypted images maintain spatial correlation in adjacent pixels locally and make the compression algorithms have high performance in encrypted images as well. However, the current design of the encryption algorithm is relatively reduntant and time-consuming. RRBE is an efficient reversible data hiding framework in encrypted images, reserving room for secret data before the image is encrypted and ensuring high embedding rate and security accuracy both. RRBE is suitable for reversible data hiding in privacy protection. To obtain more compression room and improve the embedding rate of RRBE, this research has proposed a reversible data hiding method in encrypted images based on multi-most significant bit (MSB) planes compression coding. Method First, a new bit-plane joint compression algorithm is designed. The bits in the MSB planes are rearranged to bit-streams that have long consecutive sequences of 0 or 1. The rearrangement scheme is based on block MSB planes and uses four types of scanning(row by row, row by column, column by row, column by column). The four rearranged bit-streams are respectively compressed via the combination of fixed-length coding and Huffman coding. Fixed-length coding takes full advantage of the correlation between bits in MSB planes and compresses the bits that the length of consecutive sequences of 0 or 1 equal to or greater than L_s. It is an extended run-length coding that uses a batch of L_fix bits to represent the length of the consecutive sequence, one bit for the type of this kind of code, and one bit for sequence content. Huffman coding addresses the issue of additional bits originated from the discontinuous short bit-sequence that the length of consecutive sequence of 0 or 1 less than L_s. It uses the Huffman algorithm to construct a codebook of short bit-sequences with the shortest average code length. Next, the shortest compressed bit-stream and the auxiliary information (L_s, L_fix, block size, type of scanning, the length of compressed bit-stream, and codebook) will be the demonstration of the original bit-planes. The content owner can reserve high-capacity room for data hider benefited from this compression algorithm. In order to divide the secret data extraction and image recovery, the vacated room is rearranged into LSB (least significant bit) planes. Then stream cipher with encryption key is utilized to encrypt the rearranged image, the vacated room in LSB planes of the encrypted image can embed secret data in accordance with data hiding key. At last, the receiver can directly extract secret data from LSB planes without compression information in MSB planes and recover the plaintext image without the information of LSB planes directly as well. Legitimate receivers achieve error-free secret data extraction based on data hiding key and lossless recovery of the original plaintext image by encryption key separately. Result To evaluate the performance of the proposed algorithm, experiments compare the proposed algorithm with four state-of-the-art RDHEI algorithms on five standard test images and three public datasets (an uncompressed color image database(UCID), Break Our Steganographic System(BOSSBase), and Break Our Watermarking System 2nd(BOWS-2)) and use the embedding rate, PSNR, and SSIM as the quantitative evaluation metrics. First of all, several experiments are replicated on five standard test images to pick the best parameters(L_s, L_fix, and the block size) of the proposed algorithm. Meanwhile, the parameters in the four state-of-the-art RDHEI algorithms are set for their best performance. Experimental results show that the average embedding rates of the proposed algorithm on the three datasets of UCID, BOSSBase, and BOWS-2 reach 2.123 4 bit/pixel, 2.410 7 bit/pixel and 2.380 3 bit/pixel respectively, which are 0.246 6 bit/pixel, 0.088 1 bit/pixel and 0.135 6 bit/pixel higher than the best state-of-the-art algorithm. The PSNR and SSIM are constant values that equal to +∞ and 1 respectively, which show that the proposed algorithm is reversible. Conclusion This paper proposes a reversible data hiding algorithm in encrypted images based on joint fixed-length coding and Huffman coding with a high compression ratio. By using the correlation between adjacent pixels of a natural image, the multi-MSB planes of the image can be effectively compressed to reserve high-capacity room for embedding secret data. Based on this compression algorithm, a RRBE(reserving room before encryption) method of RDHEI is designed. Experimental results show that the proposed method achieves high embedding rate and separable reversible data hiding in encrypted images with its own priority. Although the embedding rate of the proposed method has been increased compared with the same type of RDHEI methods, the compression ratio is highly correlated with the smoothness of the original plaintext image. Non-smooth images embedding capacity improvement has been further to develop in the future.

reversible data hiding; encrypted domain; fixed-length coding; Huffman coding; separately