Reversible Data Hiding in Homomorphic Encrypted Domain by Mirroring Ciphertext Group

Abstract

This paper proposes a novel reversible data hiding scheme for encrypted images by using homomorphic and probabilistic properties of Paillier cryptosystem. In the proposed method, groups of adjacent pixels are randomly selected, and reversibly embedded into the rest of the image to make room for data embedding. In each group, there are a reference pixel and a few host pixels. Least significant bits (LSBs) of the reference pixels are reset before encryption and the encrypted host pixels are replaced with the encrypted reference pixel in the same group to form mirroring ciphertext groups (MCGs). In such a way, the modification on MCGs for data embedding will not cause any pixel oversaturation in plaintext domain and the embedded data can be directly extracted from the encrypted domain. In an MCG, the reference ciphertext pixel is kept unchanged as a reference while data hider embeds the encrypted additional data into the LSBs of the host ciphertext pixels by employing homomorphic multiplication. On the receiver side, the hidden ciphertext data can be retrieved by employing a modular multiplicative inverse operation between the marked host ciphertext pixels and their corresponding reference ciphertext pixels, respectively. After that, the hidden data are extracted promptly by looking for a one-to-one mapping table from ciphertext to plaintext. Data extraction and image restoration can be accomplished without any error after decryption. Compared with the existing works, the proposed scheme has lower computation complexity, higher security performance, and better embedding performance. The experiments on the standard image files also certify the effectiveness of the proposed scheme.