Robust and reversible image watermarking in homomorphic encrypted domain

Abstract This paper proposes a robust and reversible watermarking scheme for the encrypted image by using Paillier cryptosystem. In the proposed method, the original image is divided into a number of non-overlapping blocks sized by 8 × 8 and Paillier cryptosystem is applied to encrypt the pixels in each block. Firstly, a data hider can calculate the statistical values of encrypted blocks by employing modular multiplicative inverse (MMI) method and looking for a mapping table. Then a watermark sequence can be embedded into the encrypted image by shifting the histogram of the statistical values. On the receiver side, the shifted histogram can be obtained from both the encrypted image and the decrypted image. Furthermore, the embedded watermark can be extracted from the shifted histogram. The encrypted original image can be restored by employing inverse operations of histogram shifting. This is followed by a decryption operation to restore the original image. In the proposed method, the hidden bits can still be extracted correctly under some typical content-preserving operations, such as JPEG/JPEG2000 compression and additive Gaussian noise. Compared with the previous reversible watermarking methods in plaintext domain, the proposed method has satisfactory performance in image quality and robustness. Experimental results have shown the validity of the proposed method.