信息熵视角下的密文图像信息隐藏研究
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摘要
密文图像信息隐藏是一个崭新的研究领域，近年来吸引了众多研究者。随着计算机网络、在线应用、云计算以及分布式处理等技术的发展，关于用户资源尤其是越来越多的数字图像资源的隐私保护问题变得尤为突出。加密是一种可以有效保护图像隐私的技术，而信息隐藏又可以在图像中传递秘密信息，或者用于实现版权保护、防伪认证、篡改检测等功能，因此，在加密后的图像上进行信息隐藏能够在保证图像隐私性的同时对图像数据进行有效管理和控制，具有良好的应用前景。
信息论是运用概率论与数理统计的方法研究信息、信息熵、通信系统、数据传输、密码学、数据压缩等问题的应用数学学科，是现代科学技术基础理论之一，对数字信号处理的研究有着更高层面的指导意义。因为密文图像的一个显著特点就是信息熵趋于最大化，而在数据大小不变的情况下，信息量的增加必然会导致数据本身信息熵的增大，所以，要在密文图像中再增加额外信息，我们需要首先从信息熵的角度分析其可行性，进而提出问题的解决之道。从更高的层面着手，由抽象到具体，使我们能够在研究中找准切入点，提高科研效率。
本论文在基于信息熵问题分析的基础之上，按照密文图像信息隐藏过程中对密文图像进行处理的时间先后，分别从加密前对图像进行预处理、直接在密文图像上进行操作以及在图像解密的同时进行操作这三个方面对密文图像信息隐藏的实现方法进行研究。其中，通过加密前对图像进行预处理实现密文图像信息隐藏的方法在实际应用中有太多的局限性，不作为我们研究的重点。我们的工作主要集中在以下几个方面：
①改进了直接在密文图像上进行信息隐藏的典型算法。改进方案打破了原方案对图像分块的思想，取而代之的是一种随机扩散的思想。此外，通过精确预测的方法提高了波动函数的精确性。在进一步的改进方案中，我们证明了在图像中所有像素都嵌入信息的可行性，并设计了更适合的波动函数，取得了性能上的进一步提高。
②块压缩感知是一种对图像进行有效采样的技术，并且具有对图像同时进行压缩和加密的双重效果。结合已有的工作，我们提出了一种基于块压缩感知图像的直接在密文图像上进行信息隐藏的算法。
③提出了基于同态加密机制的、能同时保证可逆性和可交换性的、直接在密文域上进行的信息隐藏算法。解决了两个现有方案中难以克服的问题：一是直接在完全的密文域中进行信息隐藏；二是可逆性，即嵌入信息能够准确无误地提取并且宿主图像也能够完美地恢复。
④提出了一种新的可交换零水印机制。不仅水印嵌入和图像加密可交换，而且水印提取和图像解密也可交换。水印信息隐藏可以直接在完全加密的图像上进行，而且不会对图像质量有任何影响。而在其它相关方案中，要么水印嵌入和图像加密不满足交换性，要么水印提取和图像解密不满足交换性。
⑤攻击了基于矢量量化图像的解密同时嵌入指纹信息的方案：随意更换图像中隐藏的指纹信息，使叛徒追踪无法成功；破解了基于静态密钥树的方法，使密文图像在没有解密密钥的情况下可以直接解密。在此基础上，基于码书划分的思想，提出了新的能在解密的同时进行指纹信息隐藏的方案。新方案具有如下特点：安全；兼具鲁棒性与脆弱性；指纹提取方便；图像失真有限；同时，计算和通信开销都没有增大。
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.
信息论是运用概率论与数理统计的方法研究信息、信息熵、通信系统、数据传输、密码学、数据压缩等问题的应用数学学科，是现代科学技术基础理论之一，对数字信号处理的研究有着更高层面的指导意义。因为密文图像的一个显著特点就是信息熵趋于最大化，而在数据大小不变的情况下，信息量的增加必然会导致数据本身信息熵的增大，所以，要在密文图像中再增加额外信息，我们需要首先从信息熵的角度分析其可行性，进而提出问题的解决之道。从更高的层面着手，由抽象到具体，使我们能够在研究中找准切入点，提高科研效率。
本论文在基于信息熵问题分析的基础之上，按照密文图像信息隐藏过程中对密文图像进行处理的时间先后，分别从加密前对图像进行预处理、直接在密文图像上进行操作以及在图像解密的同时进行操作这三个方面对密文图像信息隐藏的实现方法进行研究。其中，通过加密前对图像进行预处理实现密文图像信息隐藏的方法在实际应用中有太多的局限性，不作为我们研究的重点。我们的工作主要集中在以下几个方面：
①改进了直接在密文图像上进行信息隐藏的典型算法。改进方案打破了原方案对图像分块的思想，取而代之的是一种随机扩散的思想。此外，通过精确预测的方法提高了波动函数的精确性。在进一步的改进方案中，我们证明了在图像中所有像素都嵌入信息的可行性，并设计了更适合的波动函数，取得了性能上的进一步提高。
②块压缩感知是一种对图像进行有效采样的技术，并且具有对图像同时进行压缩和加密的双重效果。结合已有的工作，我们提出了一种基于块压缩感知图像的直接在密文图像上进行信息隐藏的算法。
③提出了基于同态加密机制的、能同时保证可逆性和可交换性的、直接在密文域上进行的信息隐藏算法。解决了两个现有方案中难以克服的问题：一是直接在完全的密文域中进行信息隐藏；二是可逆性，即嵌入信息能够准确无误地提取并且宿主图像也能够完美地恢复。
④提出了一种新的可交换零水印机制。不仅水印嵌入和图像加密可交换，而且水印提取和图像解密也可交换。水印信息隐藏可以直接在完全加密的图像上进行，而且不会对图像质量有任何影响。而在其它相关方案中，要么水印嵌入和图像加密不满足交换性，要么水印提取和图像解密不满足交换性。
⑤攻击了基于矢量量化图像的解密同时嵌入指纹信息的方案：随意更换图像中隐藏的指纹信息，使叛徒追踪无法成功；破解了基于静态密钥树的方法，使密文图像在没有解密密钥的情况下可以直接解密。在此基础上，基于码书划分的思想，提出了新的能在解密的同时进行指纹信息隐藏的方案。新方案具有如下特点：安全；兼具鲁棒性与脆弱性；指纹提取方便；图像失真有限；同时，计算和通信开销都没有增大。
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.
引文
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