Abstract: Information hiding ensures necessary security of massive data in the cloud and Internet of things environments. Although traditional encryption can protect the privacy of the image effectively, it cannot protect the image in other aspects such as copyright and integrity. Therefore, information hiding in encrypted domain is required and challenged. An information hiding scheme in homomorphic encrypted domain is proposed. Firstly, the homomorphism of compressive sensing is explored, and it is found that doubling the measurements obtained by compressive sensing is equivalent to directly extending the original signal before compressive sensing. Secondly, by using homomorphic addition, information hiding in the compressive sensing encrypted domain is realized based on differential extension. The experimental simulation results show that the proposed algorithm has satisfactory performances in both privacy protection and information hiding, and the embedding capacity is higher than the related state of art works. 

Key words: compressive sensing, homomorphic encryption, differential extension, information hiding