Lossless Data Hiding in Encrypted Images Compatible With Homomorphic Processing

Reversible data hiding in ciphertext has potential applications for privacy protection and transmitting extra data in a cloud environment. For instance, an original plain-text image can be recovered from the encrypted image generated after data embedding, while the embedded data can be extracted before or after decryption. However, homomorphic processing can hardly be applied to an encrypted image with hidden data to generate the desired image. This is partly due to that the image content may be changed by preprocessing or/and data embedding. Even if the corresponding plain-text pixel values are kept unchanged by lossless data hiding, the hidden data will be destroyed by outer processing. To address this issue, a lossless data hiding method called random element substitution (RES) is proposed for the Paillier cryptosystem by substituting the to-be-hidden bits for the random element of a cipher value. Moreover, the RES method is combined with another preprocessing-free algorithm to generate two schemes for lossless data hiding in encrypted images. With either scheme, a processed image will be obtained after the encrypted image undergoes processing in the homomorphic encrypted domain. Besides retrieving a part of the hidden data without image decryption, the data hidden with the RES method can be extracted after decryption, even after some processing has been conducted on encrypted images. The experimental results show the efficacy and superior performance of the proposed schemes.