Study On Data Hiding In Encrypted Images From The Perspective Of Information Entropy

As an emerging topic, data hiding in encrypted images has drawn a lot of attentionsof the researchers recently. With the rapid development of the Internet, onlineapplications, cloud computing, and distributed processing, the privacy protection of theuser resources, especially the increasing amount of digital images, becomes more andmore important. Encryption is an effective way to protect the privacy of the image, anddata hiding aims to send secret information through the carrier, or is used for copyrightprotection, authentication, tamper detection, etc. Therefore, data hiding in encryptedimages, which can achieve effective management and control of the digital imageswhile protecting their privacy, has broad application prospects.Information theory is a discipline of applied mathematics that uses the methods ofprobability theory and mathematical statistics to study the issues of information,information entropy, communication system, data transmission, cryptology, datacompression, and so on. It is a guide to the research of digital signal processing.Encryption makes the entropy of the image become maximum. However, if we embedsome additional data into the carrier, the entropy must be increased. Therefore, weshould analyze the feasibility of data hiding in encrypted images from the perspective ofinformation entropy firstly. This would be helpful to our research.Based on the analysis of information entropy, according to the time of theprocessing of the encrypted image, the methods of data hiding in encrypted images canbe classified into three categories: data hiding by preprocessing the images beforeencryption, directly hiding data in the encrypted images, joint data hiding and imagedecryption. Since the application of the first method is limited, we mainly focus on therest two methods. The main contributions of this thesis are summarized below:①The classical reversible data hiding method in encrypted images is improved.To make full use of spatial correlation in natural images, the former idea of blockdivision is thoroughly abandoned, whereas the random diffusion strategy is used.Additionally, the fluctuation measurement of pixels containing embedded data isimproved by accurate prediction. In the latter improved version, we prove the feasibilityof full embedding, and design a new fluctuation measurement to get better performance.②As an efficient and effective technique, block compressed sensing is widelyused in the application of image sampling. By block compressed sensing, the image can be compressed and encrypted simultaneously. Based on the previous works, a novelreversible data hiding method is proposed to embed additional data into the blockcompressed sensing images.③By introducing homomorphic cryptosystem into the field, a data hiding method,which is directly processed in the encrypted domain, and equipped with reversibilityand commutativity simultaneously, is proposed. Two main problems in the existing realreversible data hiding algorithms are solved: one is that some algorithms are notprocessed in the encrypted domain; the other is that the reversibility which implies exactdata extraction and perfect image recovery cannot be ensured in some cases.④A novel commutative zero-watermarking and encryption scheme is proposed,in which the commutativity is equipped not only in the phases of watermarking andimage encryption, but also during the processes of watermark detection and imagedecryption. Moreover, the encryption of the protected image is complete, and thezero-watermarking will not cause any modification of the image so that the fidelity canbe preserved. However, the commutativity is not satisfactory in the existing relatedschemes. In some of them, watermarking and image encryption are commutative, butthe commutativity of watermark detection and image decryption has not beenconsidered. On the contrary, in other schemes, watermark detection and imagedecryption are commutative, but the order of watermarking and image encryption isfixed.⑤The joint fingerprinting and decryption scheme is attacked. The embeddedfingerprint can be replaced arbitrarily, and therefore the traitor tracing would fail.Besides, the intercepted encrypted image using the static key-trees based approach ofthe original scheme is also cracked. To make improvements, a new JFD method usingcodebook partition is proposed. Experiments and analysis show our proposed methodoutperforms the original one: the security is enhanced; both the robustness andfragileness are equipped; the fingerprint extraction is simplified; the distortion is limited;and at the same time, the computation and communication overheads are not increased.