Histogram shifting in encrypted images with public key cryptosystem for reversible data hiding

Histogram shifting is an effective reversible data hiding (RDH) approach in processing digital images. When the host image is encrypted for privacy protection in some open environments including the cloud, RDH has to be processed in the encrypted domain accordingly. However, the performance of the existing RDH schemes in encrypted images is generally not satisfactory due to the fact that signal processing in encrypted domain is a challenging problem. In this paper, an effective RDH technique in encrypted images is proposed. Specifically, the histogram of the image is first expanded by applying the homomorphic multiplication in the encrypted domain based on the public key cryptosystem, and the histogram shifting is achieved by using the homomorphic addition in the encrypted domain in order to embed the additional data into the host images. The embedded additional data can be extracted accurately, and the host images can be recovered perfectly. Extensive experiment results are illustrated that the data embedding rate is up to 1 bit per pixel (bpp) or even 1016 bpp regardless of the different pixel distributions of natural images. The performance of the proposed RDH approach is largely improved in encrypted images, which shows the effectiveness of the proposed method.