混沌图像编码加密及Hash函数构造研究
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摘要
随着互联网技术和无线技术的发展，图像、语音和视频等多媒体数据可以通过各种移动社会网络系统方便、快捷、实时地传输与拷贝。为保护个人的切身利益，密码技术研究受到人们的高度重视，而加密算法和Hash函数是密码学研究中的两项基本技术，它们在保证信息安全的过程中发挥了重要的作用。
基于非线性科学的混沌理论，以其遍历性、轨迹不可预测性和对初值或参数极度敏感的特性，被广泛应用于控制、信号处理、通信、计算机密码学等领域，混沌密码学就是其中一个重要的研究热点。非线性科学和信息科学的深入研究也推动了混沌密码学的不断发展，并取得了大量的理论和应用成果。但是，由于混沌理论研究还不够成熟，现有的一些研究结果在安全性或效率方面依然存在诸多不足。本文在现有混沌密码学研究成果的基础上，主要致力于基于数字化混沌理论与编码理论的信息安全研究，包括基于混沌理论的图像编码加密算法设计和Hash函数构造。本文的主要工作体现在以下几个方面：
1.对当前混沌密码学的发展现状进行了详细地分析、归纳和总结，并对现有的基于混沌理论的图像加密算法和Hash函数构造方法进行了系统的概括，指出了目前存在的一些需要解决的关键问题。
2.为改善Logistic映射吸引子中存在的大量周期窗口及其迭代输出序列呈现不均匀分布的情况，利用耦合映象格子模型结构简单动力学特性却复杂的优点，提出基于空间混沌的数字图像加密算法。算法实现过程中通过耦合映象格子间的耦合作用增强系统的混淆和扩散程度，并通过密钥根据明文相关选取提高抵制已知/选择明文攻击能力。实验仿真结果说明，算法的安全性高。
3.根据遍历矩阵的概念及性质，利用时空混沌复杂的动力学特性，提出了一种基于块处理的图像加密算法。首先，利用混沌系统的内随机性，设计基于时空混沌的伪随机序列矩阵，因其具有良好的密码学特性，可用于构造图像加密的遍历矩阵。其次，对数字图像的二维矩阵进行分块，使用设计得到的标准遍历矩阵对每个小块作代数扩散和置乱混淆。其中，设计的加密算法的密钥与明文密切相关，实现了类似“一次一密”的密钥体制，提高了加密算法的安全性。实验测试了加密算法的安全性能，仿真结果说明加密算法对密钥和明文极度敏感，能满足现有图像加密的各种安全特性。
4.针对JPEG数据结构的特征，研究了JPEG图像加密算法。结合JPEG图像编码原理，提出一种基于JPEG的混沌图像选择加密算法。利用离散余弦变换量化后的图像信息主要集中于DC系数的特性，提取DC系数并对它进行置乱和扩散，并对加密后的DCT系数进行熵编码得到传输数据流。理论分析和实验仿真说明，该算法既保证了JPEG图像的压缩率不变又安全地加密了图像信息。
5.利用小波分析所具有的时域和频域的良好局部化性质，提出了两种基于小波变换和混沌序列的图像加密算法。它们的基本思想是将图像信号分解为高频部分和低频部分，利用图像的纹理和边缘信息集中在高频部分而低频逼近部分集中了图像的大部分能量的特点，主要对低频部分进行加密，保证了加密算法的鲁棒性和有效性。此外，为提高算法的抗攻击能力，密钥流与明文/密文紧密相关，而且在对图像进行混沌加密的同时扰动混沌映射的系统参数和初始值，从而实现加密过程的自适应处理，使之拥有更好的扩散效果。仿真实验验证两种算法具有较好的安全性和实时性，对常见的破解攻击还具有良好的鲁棒性。
6.研究了分数阶混沌系统的数值计算方法，并分析了分数阶混沌系统产生的伪随机序列的统计特性，发现它们满足Golomb关于理想伪随机序列假设的三条准则，适合应用于图像加密设计，以分数阶Chen系统为例完成了图像加密设计，并通过实验仿真验证了系统的安全性和有效性。
7.根据传统Hash函数的定义和一般结构，在现有的典型的设计方案的基础上，运用时空混沌系统设计了一种新的Hash函数构造方法，并对它进行了理论分析和实验仿真，该方法很好地达到了Hash函数对于扩散性、防伪造性、不可逆性和密钥敏感性的要求，且可操作性强，实际推广应用的潜力较大。此外，通过FPGA技术实现了时空混沌HASH编码系统的硬件设计，以电力集中抄表系统为例，将其应用于智能电网的消息认证。实验结果表明该编码系统能够承担数据消息的频繁认证，并且硬件占用资源少，认证速度快，能够有效加强智能电网消息传递的安全性。
With the development of Internet and wireless technology, it becomes very convenient,fast and real-time to transmit and duplicate image, voice, video and other multimedia datathrough a variety of mobile social network systems. In order to protect privacy, cryptologyhas become a hot research area, where encryption algorithm and Hash function are two basictechnologies, and play an important role to ensure the information security.
Due to its track ergodicity, unpredictability and the sensitive dependence on initialconditions or control parameters, chaos theory based on nonlinear science is widely used inthe fields of control theory, signal processing, communication, computer cryptography etc.Among them, chaotic cryptology is an important research branch. The study of nonlinearscience and information science promotes the further development of chaotic cryptology sothat lots of research findings have been achieved. However, current approaches have theweaknesses in terms of safety and efficiency as chaos theory has not been completelyinvestigated at present. Based on the current research results of chaotic cryptology, this thesisis to investigate information security strategies based on digital chaos and coding theory,including the design of image coding encryption algorithm and the construction of Hashfunction based on chaos theory. Specifically, the main contributions and achievements of thisdissertation are as follows:
1. Current research findings and advantages of chaotic cryptology are summarized,analyzed and reviewed, in particular focused on image encryption algorithm and constructionof Hash function based on chaos theory. The weaknesses of current approaches and the aimsof the research are also outlined.
2. There are lots of periodic windows and its iteration sequences appear unevendistribution in Logistic mapping attractor. To enhance the ability, a spatial chaos-based imageencryption algorithm is proposed using the advantages of coupled map lattice model, such assimple structure and complex dynamic characteristics. The cryptosystem gains confusion anddiffusion by the coupling effect among coupled map lattices. In addition, the relation to thekey and plaintext can effectively resist known/chosen plaintext attack. Experimentalsimulation results show that the algorithm is of high safety.
3. On the basis of the concept and properties of the ergodic matrix, a block-based imageencryption algorithm is proposed using the complex dynamics characteristic of spatiotemporalchaos. Firstly, the pseudorandom matrix is generated by iterating spatiotemporal chaos, whichobtains good randomness and cryptographic properties. Secondly, each image sub-block is diffused and confused through algebraic and scrambling operations using standard ergodicmatrices. Especially, the key is closely related to plaintext, and it makes encryption schemesimilar to “once a secret” cryptosystem, which improves the security of the encryptionalgorithm. Theoretical analysis and computer simulation results show that the proposedscheme is extremely sensitive to the key and plaintext, and can satisfy all kinds of existingimage encryption security requirements.
4. According to the characteristics of JPEG image, combined with the JPEG codingprinciple, a chaos-based JPEG image encryption algorithm is proposed. The information ofimage is mainly focused on DC coefficients after discrete cosine transform, so only DCcoefficients are extracted and further encrypted, then the encrypted DCT coefficient is entropycoded and consequently the transmission data flow is generated. Theoretical analysis andexperimental simulation results show that the algorithm not only remains compression rateunchanged but also securely encrypts the image information.
5. By using time and frequency domain properties of wavelet analysis, two imageencryption algorithms based on wavelet transform and chaotic sequence are proposed. Thebasic idea is to decompose original image into low and high frequency sub-bands, and the lowfrequency sub-band contains basic information of original image. Based on this characteristic,only the lowest frequency sub-band is encrypted to increase the encryption robustness andeffectiveness. Additionally, key stream is closely related to plaintext/cipher-text to improvethe ability to resist traditional attacks. Moreover, initial values and parameters of chaossystem are disturbed, which make the algorithm have better diffusion effect. Simulationexperiments verified that both two algorithms are safe and real-time, and have goodrobustness to common cracking attack.
6. Studied on the statistical features of pseudo-random sequence generated fromfractional order chaotic systems, the results show that the statistical features satisfy theGolomb’s principles. So the fractional order chaotic system is suitable for image encryptionapplication. Taking fractional order Chen system as an example, experimental simulationresults verified the encryption scheme is safe and effective.
7. According to the traditional definition and general structure of Hash function, a newspatiotemporal chaos-based Hash function construction method is proposed. Compared withthe existing chaotic Hash functions, the proposed method improves computationalperformance of Hash system. The theoretical analysis and experimental simulation prove thatthe method meets the Hash function requirements of invasive, forgery prevention,irreversibility and key sensitivity. Moreover, the maneuverability of the system is strong, and can be applied to industrial applications. In addition, the hardware implementation of thecorresponding HASH coding system is designed based on FPGA platform. It is applied to theSmart Power Grids for message authentication in the Integrated Meter Reading System.Experimental results show that this system has a high computing speed, can completemessage authentication quickly even for frequent requests, occupy minimal hardwareresources, and effectively strengthen the security of message transmission.
基于非线性科学的混沌理论，以其遍历性、轨迹不可预测性和对初值或参数极度敏感的特性，被广泛应用于控制、信号处理、通信、计算机密码学等领域，混沌密码学就是其中一个重要的研究热点。非线性科学和信息科学的深入研究也推动了混沌密码学的不断发展，并取得了大量的理论和应用成果。但是，由于混沌理论研究还不够成熟，现有的一些研究结果在安全性或效率方面依然存在诸多不足。本文在现有混沌密码学研究成果的基础上，主要致力于基于数字化混沌理论与编码理论的信息安全研究，包括基于混沌理论的图像编码加密算法设计和Hash函数构造。本文的主要工作体现在以下几个方面：
1.对当前混沌密码学的发展现状进行了详细地分析、归纳和总结，并对现有的基于混沌理论的图像加密算法和Hash函数构造方法进行了系统的概括，指出了目前存在的一些需要解决的关键问题。
2.为改善Logistic映射吸引子中存在的大量周期窗口及其迭代输出序列呈现不均匀分布的情况，利用耦合映象格子模型结构简单动力学特性却复杂的优点，提出基于空间混沌的数字图像加密算法。算法实现过程中通过耦合映象格子间的耦合作用增强系统的混淆和扩散程度，并通过密钥根据明文相关选取提高抵制已知/选择明文攻击能力。实验仿真结果说明，算法的安全性高。
3.根据遍历矩阵的概念及性质，利用时空混沌复杂的动力学特性，提出了一种基于块处理的图像加密算法。首先，利用混沌系统的内随机性，设计基于时空混沌的伪随机序列矩阵，因其具有良好的密码学特性，可用于构造图像加密的遍历矩阵。其次，对数字图像的二维矩阵进行分块，使用设计得到的标准遍历矩阵对每个小块作代数扩散和置乱混淆。其中，设计的加密算法的密钥与明文密切相关，实现了类似“一次一密”的密钥体制，提高了加密算法的安全性。实验测试了加密算法的安全性能，仿真结果说明加密算法对密钥和明文极度敏感，能满足现有图像加密的各种安全特性。
4.针对JPEG数据结构的特征，研究了JPEG图像加密算法。结合JPEG图像编码原理，提出一种基于JPEG的混沌图像选择加密算法。利用离散余弦变换量化后的图像信息主要集中于DC系数的特性，提取DC系数并对它进行置乱和扩散，并对加密后的DCT系数进行熵编码得到传输数据流。理论分析和实验仿真说明，该算法既保证了JPEG图像的压缩率不变又安全地加密了图像信息。
5.利用小波分析所具有的时域和频域的良好局部化性质，提出了两种基于小波变换和混沌序列的图像加密算法。它们的基本思想是将图像信号分解为高频部分和低频部分，利用图像的纹理和边缘信息集中在高频部分而低频逼近部分集中了图像的大部分能量的特点，主要对低频部分进行加密，保证了加密算法的鲁棒性和有效性。此外，为提高算法的抗攻击能力，密钥流与明文/密文紧密相关，而且在对图像进行混沌加密的同时扰动混沌映射的系统参数和初始值，从而实现加密过程的自适应处理，使之拥有更好的扩散效果。仿真实验验证两种算法具有较好的安全性和实时性，对常见的破解攻击还具有良好的鲁棒性。
6.研究了分数阶混沌系统的数值计算方法，并分析了分数阶混沌系统产生的伪随机序列的统计特性，发现它们满足Golomb关于理想伪随机序列假设的三条准则，适合应用于图像加密设计，以分数阶Chen系统为例完成了图像加密设计，并通过实验仿真验证了系统的安全性和有效性。
7.根据传统Hash函数的定义和一般结构，在现有的典型的设计方案的基础上，运用时空混沌系统设计了一种新的Hash函数构造方法，并对它进行了理论分析和实验仿真，该方法很好地达到了Hash函数对于扩散性、防伪造性、不可逆性和密钥敏感性的要求，且可操作性强，实际推广应用的潜力较大。此外，通过FPGA技术实现了时空混沌HASH编码系统的硬件设计，以电力集中抄表系统为例，将其应用于智能电网的消息认证。实验结果表明该编码系统能够承担数据消息的频繁认证，并且硬件占用资源少，认证速度快，能够有效加强智能电网消息传递的安全性。
With the development of Internet and wireless technology, it becomes very convenient,fast and real-time to transmit and duplicate image, voice, video and other multimedia datathrough a variety of mobile social network systems. In order to protect privacy, cryptologyhas become a hot research area, where encryption algorithm and Hash function are two basictechnologies, and play an important role to ensure the information security.
Due to its track ergodicity, unpredictability and the sensitive dependence on initialconditions or control parameters, chaos theory based on nonlinear science is widely used inthe fields of control theory, signal processing, communication, computer cryptography etc.Among them, chaotic cryptology is an important research branch. The study of nonlinearscience and information science promotes the further development of chaotic cryptology sothat lots of research findings have been achieved. However, current approaches have theweaknesses in terms of safety and efficiency as chaos theory has not been completelyinvestigated at present. Based on the current research results of chaotic cryptology, this thesisis to investigate information security strategies based on digital chaos and coding theory,including the design of image coding encryption algorithm and the construction of Hashfunction based on chaos theory. Specifically, the main contributions and achievements of thisdissertation are as follows:
1. Current research findings and advantages of chaotic cryptology are summarized,analyzed and reviewed, in particular focused on image encryption algorithm and constructionof Hash function based on chaos theory. The weaknesses of current approaches and the aimsof the research are also outlined.
2. There are lots of periodic windows and its iteration sequences appear unevendistribution in Logistic mapping attractor. To enhance the ability, a spatial chaos-based imageencryption algorithm is proposed using the advantages of coupled map lattice model, such assimple structure and complex dynamic characteristics. The cryptosystem gains confusion anddiffusion by the coupling effect among coupled map lattices. In addition, the relation to thekey and plaintext can effectively resist known/chosen plaintext attack. Experimentalsimulation results show that the algorithm is of high safety.
3. On the basis of the concept and properties of the ergodic matrix, a block-based imageencryption algorithm is proposed using the complex dynamics characteristic of spatiotemporalchaos. Firstly, the pseudorandom matrix is generated by iterating spatiotemporal chaos, whichobtains good randomness and cryptographic properties. Secondly, each image sub-block is diffused and confused through algebraic and scrambling operations using standard ergodicmatrices. Especially, the key is closely related to plaintext, and it makes encryption schemesimilar to “once a secret” cryptosystem, which improves the security of the encryptionalgorithm. Theoretical analysis and computer simulation results show that the proposedscheme is extremely sensitive to the key and plaintext, and can satisfy all kinds of existingimage encryption security requirements.
4. According to the characteristics of JPEG image, combined with the JPEG codingprinciple, a chaos-based JPEG image encryption algorithm is proposed. The information ofimage is mainly focused on DC coefficients after discrete cosine transform, so only DCcoefficients are extracted and further encrypted, then the encrypted DCT coefficient is entropycoded and consequently the transmission data flow is generated. Theoretical analysis andexperimental simulation results show that the algorithm not only remains compression rateunchanged but also securely encrypts the image information.
5. By using time and frequency domain properties of wavelet analysis, two imageencryption algorithms based on wavelet transform and chaotic sequence are proposed. Thebasic idea is to decompose original image into low and high frequency sub-bands, and the lowfrequency sub-band contains basic information of original image. Based on this characteristic,only the lowest frequency sub-band is encrypted to increase the encryption robustness andeffectiveness. Additionally, key stream is closely related to plaintext/cipher-text to improvethe ability to resist traditional attacks. Moreover, initial values and parameters of chaossystem are disturbed, which make the algorithm have better diffusion effect. Simulationexperiments verified that both two algorithms are safe and real-time, and have goodrobustness to common cracking attack.
6. Studied on the statistical features of pseudo-random sequence generated fromfractional order chaotic systems, the results show that the statistical features satisfy theGolomb’s principles. So the fractional order chaotic system is suitable for image encryptionapplication. Taking fractional order Chen system as an example, experimental simulationresults verified the encryption scheme is safe and effective.
7. According to the traditional definition and general structure of Hash function, a newspatiotemporal chaos-based Hash function construction method is proposed. Compared withthe existing chaotic Hash functions, the proposed method improves computationalperformance of Hash system. The theoretical analysis and experimental simulation prove thatthe method meets the Hash function requirements of invasive, forgery prevention,irreversibility and key sensitivity. Moreover, the maneuverability of the system is strong, and can be applied to industrial applications. In addition, the hardware implementation of thecorresponding HASH coding system is designed based on FPGA platform. It is applied to theSmart Power Grids for message authentication in the Integrated Meter Reading System.Experimental results show that this system has a high computing speed, can completemessage authentication quickly even for frequent requests, occupy minimal hardwareresources, and effectively strengthen the security of message transmission.
引文
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