混沌序列生成技术及其若干应用研究
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摘要
随着信息技术的发展和网络的普及，人们对于网络中信息的安全问题日益关注，如何保证信息的保密性、完整性和可用性成为信息技术普及和发展面临的一个基本问题，使得信息安全成为当前信息技术领域的研究热点之一。而在信息安全研究的各领域中，对密码理论和技术的研究处于核心的地位。
混沌是非线性动力学系统所特有的一种运动形式，是一种貌似无规则的运动，是在确定非线性系统中，不需要附加任何随机因素就可以实现的类随机行为。一般的混沌系统都具有以下基本特性：确定性、初值敏感性、遍历性、混合性、快速衰减的自相关性、长期不可预测性和伪随机性。而混沌系统所具有的初值敏感性、遍历性、伪随机性等特性与密码学中的基本要求相似，密码学的两个基本原则：混乱（Confusion）和扩散（Diffusion），在混沌系统中都可以找到相应的基本特性与之对应。混沌和密码学之间所具有的天然联系和结构上的某种相似性，为混沌理论在密码学中的应用提供了良好的基础。
本论文主要研究基于混沌系统的混沌序列生成方法和混沌序列的评价指标，同时研究了生成的混沌序列在Hash函数构造、图像分割技术和数字图像保护技术中的应用。具体包括以下工作：
1.分析了基于混沌系统的密码技术的研究现状，包括混沌的定义、混沌运动的特征、几种常见的混沌系统和研究混沌密码技术的相关准则。
2.研究了基于混沌系统产生的伪随机序列的性能评价指标，在此基础上，提出了一种混沌系统初值敏感性的评价指标――分叉迭代次数，并将其应用于混沌系统的评价，通过实验仿真，分析了该评价指标的有效性。
3.在对LFSR进行研究的基础上，结合混沌系统，设计了一种LFSR和混沌系统相结合的序列生成方法。鉴于LFSR和混沌系统相结合具有较大的密钥空间，采用LFSR产生选择函数来确定混沌系统的方式增加了密码分析攻击的难度，通过将LFSR的反馈值和生成的二进制序列反馈值进行异或运算的方式实现了对LFSR的随机扰动，使得生成序列具有良好的安全性和随机性。本方案不仅实现了二值伪随机序列的生成，而且实现了实值伪随机序列的生成。这两种伪随机序列产生过程通过对多个简单的混沌系统进行统一的循环迭代计算来达到，降低了计算过程的复杂性，也便于硬件实现。
4.在对Logistic和Tent混沌系统的相关性质进行研究的基础上，给出了一种分段Logistic映射构造方法，对其性能进行了实验分析。结果表明，定义的分段Logistic混沌映射生成的伪随机序列不仅具有良好的随机性、初值敏感性等性能，而且应用分段Logistic映射生成混沌序列的过程中，不需要增加相应的扰动过程，从而能够有效提高算法的效率。根据分段Logistic映射具有分岔速度快的特点，将其应用于Hash函数的构造方法中，设计了基于分段非线性混沌系统的Hash函数构造方法。
5.对Bernstein基函数的性质和Arnold混沌系统生成序列的分布情况进行了研究，在此基础上，设计了一种基于Bernstein基函数和混沌序列的伪随机序列生成方法，对产生的伪随机序列的相关性质进行了实验分析，结果表明，基于Bernstein基函数和插值运算得到的序列不仅具有随机分布的特点，而且其分布规律更适于基于混沌优化的图像分割算法。根据生成序列的分布特点，将其应用于基于混沌优化的图像分割算法中，取得了较好的分割效果。
6.研究了基于混沌系统的数字图像保护技术，包括基于混沌的自适应数字图像加密算法、能较好抵御剪切变换攻击的数字图像加密算法和基于图像融合技术的数字图像加密算法；基于混沌迭代结构的数字图像隐藏算法和基于图像融合实现不同大小图像隐藏的算法。
With the development of information and network technology, informationsecurity is getting much concern. As information technology is popularized anddeveloped, how to ensure the confidentiality, integrity and availability ofinformation is becoming a fundamental problem, which has made informationsecurity one of the hotspot in the current research field of information technology.In all the research areas of information security, cryptography theory andtechnology is at the core position.
Chaos is a unique movement appeared in nonlinear dynamic systems. It is aseemingly irregular movement form in the determination of nonlinear systems,which can be achieved in the class of random behavior without any additionalrandom factors. Chaotic systems have some properties in common: uncertainty,initial parameter sensitivity, ergodicity, mixing, rapid decay of the autocorrelation,long-term unpredictability and pseudo-randomness. The properties of initialparameter sensitivity, ergodicity and pseudo-randomness of chaotic system aresimilar to the requirements of cryptography, thus the two basic principles ofcryptography, confusion and diffusion will have some corresponding propertiesin the chaotic system. The natural connection and structural similarity betweenchaos and cryptography provide a good foundation for the application of chaosin cryptography.
Chaotic sequence generation methods based on chaotic systems and sequenceevaluation methods are studied in this dissertation. We also study Hash functionconstruction methods, image segmentation methods and digital imageprotection technologies based on chaotic systems. The specific work includesthe following aspects:
1. Current cryptography works based on chaotic system are summarized,including the definition of chaos, chaotic motion properties, several commonchaotic systems and related criteria of using chaos in cryptography.
2. Performance evaluation criteria of pseudo-random sequence generated bychaotic systems are studied, and a chaotic system initial parameter sensitivitycriterion, the number of bifurcation iteration, is proposed and applied into theevaluation of chaotic systems. The effectiveness of the evaluation is analyzed byexperimental simulations.
3. Combined with the properties of the LFSR and chaotic systems, a sequencegeneration method is designed based on LFSR and chaotic system. Since thecombination of LFSR and the chaotic system lead to a larger key space, thechaotic system that uses the LFSR generating selection function increases thedifficulty of cryptanalysis attacks. The feedback value of the LFSR and thefeedback value of the generated binary sequence are operated with XOR way, which can achieve operation of LFSR random disturbance and make thegenerated sequence have good safety and randomness. The method can notonly generate pseudo-random binary sequences, but also generate realpseudo-random sequences. The two pseudo-random sequence generationprocesses are achieved by several simple chaotic systems and repetitioniteration, which reduces complexity of the computation process, and facilitateshardware implementation as well.
4. Properties of Logistic and Tent chaotic systems are studied. On this basis, apiecewise Logistic map construction method is presented, and its performance isanalyzed by experimentations. Experimental results show that, pseudo-randomsequences generated by the piecewise Logistic chaotic map have goodrandomness, initial parameter sensitivity and other properties, and it does notrequire a corresponding disturbance in the process of generating chaoticsequence using piecewise Logistic map, which can effectively improve theefficiency of the algorithm. Because the piecewise Logistic map has goodbifurcation speed and can be used in Hash function construction method, a Hashfunction construction method based on piecewise nonlinear chaotic system ispresented.
5. The properties of Bernstein basis function and the distribution of sequencesgenerated by Arnold chaotic system are studied. On this basis, apseudo-random sequence generation method is designed based on Bernsteinbasis functions and the chaotic sequence. The related properties of thegenerated pseudo-random sequence are analyzed by simulations. Experimentalresults show that, sequences generated by Bernstein basis functions andinterpolation operations have the characteristics of random distribution, and itsdistribution is also more suitable for the image segmentation method based onchaotic optimization algorithm. According to the sequence distribution properties,the generated sequence is applied to image segmentation based on chaoticoptimization algorithm, and good segmentation results are achieved.
6. Digital image protection technologies based on chaotic system are studied,including an adaptive digital image encryption algorithm based on chaos, adigital image encryption algorithm that can withstand shear transform attacksbetter, and a digital image encryption algorithm based on image fusion technique,a digital image hiding algorithm based on chaotic iteration structure and animage hiding algorithm based on image fusion that can treat two images withdifferent sizes.
混沌是非线性动力学系统所特有的一种运动形式，是一种貌似无规则的运动，是在确定非线性系统中，不需要附加任何随机因素就可以实现的类随机行为。一般的混沌系统都具有以下基本特性：确定性、初值敏感性、遍历性、混合性、快速衰减的自相关性、长期不可预测性和伪随机性。而混沌系统所具有的初值敏感性、遍历性、伪随机性等特性与密码学中的基本要求相似，密码学的两个基本原则：混乱（Confusion）和扩散（Diffusion），在混沌系统中都可以找到相应的基本特性与之对应。混沌和密码学之间所具有的天然联系和结构上的某种相似性，为混沌理论在密码学中的应用提供了良好的基础。
本论文主要研究基于混沌系统的混沌序列生成方法和混沌序列的评价指标，同时研究了生成的混沌序列在Hash函数构造、图像分割技术和数字图像保护技术中的应用。具体包括以下工作：
1.分析了基于混沌系统的密码技术的研究现状，包括混沌的定义、混沌运动的特征、几种常见的混沌系统和研究混沌密码技术的相关准则。
2.研究了基于混沌系统产生的伪随机序列的性能评价指标，在此基础上，提出了一种混沌系统初值敏感性的评价指标――分叉迭代次数，并将其应用于混沌系统的评价，通过实验仿真，分析了该评价指标的有效性。
3.在对LFSR进行研究的基础上，结合混沌系统，设计了一种LFSR和混沌系统相结合的序列生成方法。鉴于LFSR和混沌系统相结合具有较大的密钥空间，采用LFSR产生选择函数来确定混沌系统的方式增加了密码分析攻击的难度，通过将LFSR的反馈值和生成的二进制序列反馈值进行异或运算的方式实现了对LFSR的随机扰动，使得生成序列具有良好的安全性和随机性。本方案不仅实现了二值伪随机序列的生成，而且实现了实值伪随机序列的生成。这两种伪随机序列产生过程通过对多个简单的混沌系统进行统一的循环迭代计算来达到，降低了计算过程的复杂性，也便于硬件实现。
4.在对Logistic和Tent混沌系统的相关性质进行研究的基础上，给出了一种分段Logistic映射构造方法，对其性能进行了实验分析。结果表明，定义的分段Logistic混沌映射生成的伪随机序列不仅具有良好的随机性、初值敏感性等性能，而且应用分段Logistic映射生成混沌序列的过程中，不需要增加相应的扰动过程，从而能够有效提高算法的效率。根据分段Logistic映射具有分岔速度快的特点，将其应用于Hash函数的构造方法中，设计了基于分段非线性混沌系统的Hash函数构造方法。
5.对Bernstein基函数的性质和Arnold混沌系统生成序列的分布情况进行了研究，在此基础上，设计了一种基于Bernstein基函数和混沌序列的伪随机序列生成方法，对产生的伪随机序列的相关性质进行了实验分析，结果表明，基于Bernstein基函数和插值运算得到的序列不仅具有随机分布的特点，而且其分布规律更适于基于混沌优化的图像分割算法。根据生成序列的分布特点，将其应用于基于混沌优化的图像分割算法中，取得了较好的分割效果。
6.研究了基于混沌系统的数字图像保护技术，包括基于混沌的自适应数字图像加密算法、能较好抵御剪切变换攻击的数字图像加密算法和基于图像融合技术的数字图像加密算法；基于混沌迭代结构的数字图像隐藏算法和基于图像融合实现不同大小图像隐藏的算法。
With the development of information and network technology, informationsecurity is getting much concern. As information technology is popularized anddeveloped, how to ensure the confidentiality, integrity and availability ofinformation is becoming a fundamental problem, which has made informationsecurity one of the hotspot in the current research field of information technology.In all the research areas of information security, cryptography theory andtechnology is at the core position.
Chaos is a unique movement appeared in nonlinear dynamic systems. It is aseemingly irregular movement form in the determination of nonlinear systems,which can be achieved in the class of random behavior without any additionalrandom factors. Chaotic systems have some properties in common: uncertainty,initial parameter sensitivity, ergodicity, mixing, rapid decay of the autocorrelation,long-term unpredictability and pseudo-randomness. The properties of initialparameter sensitivity, ergodicity and pseudo-randomness of chaotic system aresimilar to the requirements of cryptography, thus the two basic principles ofcryptography, confusion and diffusion will have some corresponding propertiesin the chaotic system. The natural connection and structural similarity betweenchaos and cryptography provide a good foundation for the application of chaosin cryptography.
Chaotic sequence generation methods based on chaotic systems and sequenceevaluation methods are studied in this dissertation. We also study Hash functionconstruction methods, image segmentation methods and digital imageprotection technologies based on chaotic systems. The specific work includesthe following aspects:
1. Current cryptography works based on chaotic system are summarized,including the definition of chaos, chaotic motion properties, several commonchaotic systems and related criteria of using chaos in cryptography.
2. Performance evaluation criteria of pseudo-random sequence generated bychaotic systems are studied, and a chaotic system initial parameter sensitivitycriterion, the number of bifurcation iteration, is proposed and applied into theevaluation of chaotic systems. The effectiveness of the evaluation is analyzed byexperimental simulations.
3. Combined with the properties of the LFSR and chaotic systems, a sequencegeneration method is designed based on LFSR and chaotic system. Since thecombination of LFSR and the chaotic system lead to a larger key space, thechaotic system that uses the LFSR generating selection function increases thedifficulty of cryptanalysis attacks. The feedback value of the LFSR and thefeedback value of the generated binary sequence are operated with XOR way, which can achieve operation of LFSR random disturbance and make thegenerated sequence have good safety and randomness. The method can notonly generate pseudo-random binary sequences, but also generate realpseudo-random sequences. The two pseudo-random sequence generationprocesses are achieved by several simple chaotic systems and repetitioniteration, which reduces complexity of the computation process, and facilitateshardware implementation as well.
4. Properties of Logistic and Tent chaotic systems are studied. On this basis, apiecewise Logistic map construction method is presented, and its performance isanalyzed by experimentations. Experimental results show that, pseudo-randomsequences generated by the piecewise Logistic chaotic map have goodrandomness, initial parameter sensitivity and other properties, and it does notrequire a corresponding disturbance in the process of generating chaoticsequence using piecewise Logistic map, which can effectively improve theefficiency of the algorithm. Because the piecewise Logistic map has goodbifurcation speed and can be used in Hash function construction method, a Hashfunction construction method based on piecewise nonlinear chaotic system ispresented.
5. The properties of Bernstein basis function and the distribution of sequencesgenerated by Arnold chaotic system are studied. On this basis, apseudo-random sequence generation method is designed based on Bernsteinbasis functions and the chaotic sequence. The related properties of thegenerated pseudo-random sequence are analyzed by simulations. Experimentalresults show that, sequences generated by Bernstein basis functions andinterpolation operations have the characteristics of random distribution, and itsdistribution is also more suitable for the image segmentation method based onchaotic optimization algorithm. According to the sequence distribution properties,the generated sequence is applied to image segmentation based on chaoticoptimization algorithm, and good segmentation results are achieved.
6. Digital image protection technologies based on chaotic system are studied,including an adaptive digital image encryption algorithm based on chaos, adigital image encryption algorithm that can withstand shear transform attacksbetter, and a digital image encryption algorithm based on image fusion technique,a digital image hiding algorithm based on chaotic iteration structure and animage hiding algorithm based on image fusion that can treat two images withdifferent sizes.
引文
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