Reversible Data Hiding Algorithm in Fully Homomorphic Encrypted Domain

This paper proposes a reversible data hiding scheme by exploiting the DGHV fully homomorphic encryption, and analyzes the feasibility of the scheme for data hiding from the perspective of information entropy. In the proposed algorithm, additional data can be embedded directly into a DGHV fully homomorphic encrypted image without any preprocessing. On the sending side, by using two encrypted pixels as a group, a data hider can get the difference of two pixels in a group. Additional data can be embedded into the encrypted image by shifting the histogram of the differences with the fully homomorphic property. On the receiver side, a legal user can extract the additional data by getting the difference histogram, and the original image can be restored by using modular arithmetic. Besides, the additional data can be extracted after decryption while the original image can be restored. Compared with the previous two typical algorithms, the proposed scheme can effectively avoid preprocessing operations before encryption and can successfully embed and extract additional data in the encrypted domain. The extensive testing results on the standard images have certified the effectiveness of the proposed scheme.