Reversible data hiding in compressed and encrypted images by using Kd-tree

In this paper, a joint scheme and a separable scheme for reversible data hiding (RDH) in compressed and encrypted images by reserving room through Kd-tree were proposed. Firstly, the plain cover image was losslessly compressed and encrypted with lifting based integer wavelet transform (IWT) and set partition in hierarchical tree (SPIHT) encoding. Then, several shift operations were performed on the generated SPIHT bit-stream. The shifted bit-stream was restructured into small chunks and packed in the form of a large square matrix. The binary square matrix was exposed to Kd-tree with random permutations and reserving uniform areas of ones and zeros for secret data hiding. After that, a joint or a separable RDH scheme can be performed in these reserved spaces. In the joint RDH scheme, the secret data were embedded in the reserved spaces before encrypting with multiple chaotic maps. Thus, secret data extraction and cover image recovery were achieved together. In the separable RDH scheme, the secret data were embedded in the reserved spaces after encrypting with multiple chaotic maps. Since message extraction and cover image recovery are performed separately, anyone who has the embedding key can extract the secret message from the marked encrypted copy, while cannot recover the cover image. A complete encoding and decoding procedure of RDH for compressed and encrypted images was elaborated. The imperceptibility analysis showed that the proposed methods bring no distortion to the cover image because there was no change to the original cover image. The experimental results showed that the proposed schemes can perform better for secret data extraction and can restore the original image with 100% reversibility with much more embedding capacity and security. The proposed schemes significantly outperform the state-of-the-art RDH methods in the literature on compressed and encrypted images.