The phenomenal advances of cloud computing technology have given rise to the research area of privacy-preserving signal processing, which aims to preserve information privacy even when the signals are processed in an insecure environment. Privacy-preserving information hiding is a multidisciplinary study that has opened up a great deal of intriguing real-life applications, such as data exfiltration prevention, data origin authentication, and electronic data management. Information hiding is a practice of embedding intended messages into carrier signals through imperceptible alterations. In view of some content-sensitive scenarios, however, the ability to preserve perfect copies of signals is of crucial importance, for instance, considering the inadequate robustness of recent artificial intelligence-aided automated systems against noise perturbations. Reversibility of information hiding systems is a valuable property that permits recovery of original carrier signals if desired. In this paper, we propose a novel privacy-preserving reversible information hiding scheme inspired by the mathematical concept of quadratic residues. A quadratic residue has four (not necessarily distinct) square roots, which enables payloads to be encoded in a dynamic fashion. Furthermore, a predictive model based upon the projection theorem is devised to assist carrier signal recovery. The experimental results showed significant improvements over the state-of-the-art methods with regard to capacity, fidelity, and reversibility.

For vacating-room-after-encryption reversible data hiding in encrypted images (VRAE RDHEI), an essential problem is how to address potential errors in data extraction and image recovery. This problem significantly limits the capacities of the existing VRAE RDHEI methods. To solve the problem while losing as little capacity as possible, in this paper, a novel method is proposed that uses the ideas of noisy channel model and channel code. By designing the data hiding mechanism appropriately, the embedding and extraction of data in the proposed method can be equivalent to the input and output of a virtual binary symmetric channel (BSC) model, so that the errors in data extraction are equivalent to the bit transitions in BSC. Based on the virtual BSC model, polar code is used to encode the secret data in the data hider's side. With the help of polar code, the receiver can decode the extracted bits containing errors to obtain correct secret data, then recover the error-free original image based on the corrected secret data. The experimental results proved that, compared with the existing VRAE methods, the proposed method can significantly improve the capacity and the quality of the decrypted images under the premise of complete reversibility.

In this paper, we proposed a novel reversible data hiding method in encrypted image (RDHEI), which is based on the compression of pixel differences. In the proposed method, at the content owner’ side the image is divided into non-overlapping blocks, and a block-level image encryption scheme is used to generate the encrypted image, which partially retains spatial correlation in the blocks. Due to the spatial correlation, in each block the pixels are highly likely to be similar. Therefore, the pixel differences in all blocks are concentrated in a small range and can be compressed. By the compression of pixel differences, the data hider can vacate the room to accommodate secret data in the encrypted image without losing information. At the receiver’s side, the receiver can obtain secret data or retrieve the original image using different keys with no error. The experimental results demonstrate that, compared with existing methods, the proposed method can achieve a higher capacity and visual quality.