Efficient reversible data hiding in encrypted image with public key cryptosystem

This paper proposes a new reversible data hiding scheme for encrypted images by using homomorphic and probabilistic properties of Paillier cryptosystem. The proposed method can embed additional data directly into encrypted image without any preprocessing operations on original image. By selecting two pixels as a group for encryption, data hider can retrieve the absolute differences of groups of two pixels by employing a modular multiplicative inverse method. Additional data can be embedded into encrypted image by shifting histogram of the absolute differences by using the homomorphic property in encrypted domain. On the receiver side, legal user can extract the marked histogram in encrypted domain in the same way as data hiding procedure. Then, the hidden data can be extracted from the marked histogram and the encrypted version of original image can be restored by using inverse histogram shifting operations. Besides, the marked absolute differences can be computed after decryption for extraction of additional data and restoration of original image. Compared with previous state-of-the-art works, the proposed scheme can effectively avoid preprocessing operations before encryption and can efficiently embed and extract data in encrypted domain. The experiments on the standard image files also certify the effectiveness of the proposed scheme.