Privacy-preserving reversible information hiding based on arithmetic of quadratic residues

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.