Reversible data hiding in encrypted images using cross division and additive homomorphism

•Host image is divided into crosses.•Homomorphic encryption is with no data expansion.•Data hiding is directly processed in encrypted domain.•Real reversibility is realized.•Difference histogram is shifted several rounds.

There are three problems in the existing reversible data hiding (RDH) algorithms in encrypted images: one is that some algorithms are not processed in the encrypted domain; another is that the reversibility which implies exact data extraction and perfect image recovery cannot be ensured in some cases; the last is that data expansion occurs when probabilistic public-key cryptosystem is used for image encryption in some homomorphic schemes. In this paper, a complete RDH in encrypted images is proposed. By using the idea of cross division and additive homomorphism, we solve all of the problems. Experimental results verify the superiority of the proposed method, which will have a good potential for practical applications of multimedia privacy protection.