空间混沌及其在图像加密中的应用
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摘要
随着计算机技术与通信技术的迅猛发展,数字信息在世界范围内得到日益广泛的应用。然而,数字信息易于拷贝和发布给其应用带来了诸多安全问题。当前,数字信息在互联网和无线通信网络中的安全通信技术成为极具重要性的研究方向。
密码学是保护信息安全的最基本的手段。混沌理论和密码学之间有着天然的联系:如对初始条件和控制参数的敏感性、周期点集的稠密性和拓扑传递性,和密码学中的混淆与扩散特性。因此,基于混沌的密码技术在信息安全方面具有重要的地位。自二十世纪80年代以来,应用混沌系统构造新型密码系统受到了越来越多的关注,出现了不少充满希望的进展。然而,近期的研究表明,原来提出的被认为是实用性强和安全性高的混沌密码方案被分析,并被证实它们效率低、不安全和不可用。尤其对于信息量大和冗余度高的图像文件,大部分传统的基于混沌的密码系统不适合直接对它进行加密。如何通过细致的分析设计安全的混沌密码方案日渐成为急待解决的关键问题。
本文对高维混沌系统在图象加密中的应用做了深入研究,首次将空间混沌引入到密码学中,并设计了几种新的图像加密方案。此外,研究了分子轨道系统模型中的非线性行为,即从理论上证明了分子轨道中的空间混沌以及分岔现象的存在。论文的主要研究内容及创新之处有:
1.对当前混沌密码学的发展状况进行了详细的分析、归纳和总结,提出了目前存在的一些需要解决的关键问题;
2.从多方面对混沌理论基础作了详细的阐述。首先回顾了混沌理论的研究历史并给出了几种混沌的定义。其次简要概括了密码学的基本理论。然后阐述了混沌理论和混沌密码学的关系。最后介绍了几种混沌图像加密方法;
3.设计了一种利用高维混沌实现图像加密的加密方案。首先利用Arnoldcat映射混乱图像相素的位置,然后用Lorenz混沌系统进一步加密图像;
4.利用耦合映射格子进行数字图像的加密,设计加密/解密方案并进行了安全分析,获得了一个更安全、更适合数字图像的加密系统;
5.研究了具有矩形边界的方格子形共轭分子、直链和单环共轭分子结构的电子载波的运动形式,分析了分子轨道的非线性特性,如空间混沌、分岔和其他的非线性特性。另外,也讨论并给出了分子轨道和它的能量层的关系。从理论上证明了分子轨道中的空间混沌以及分岔现象的存在;
6.研究了由空间混沌系统生成的伪随机二进制序列的密码学特性,对这种伪随机二进制序列进行了密码学中众所周知的FIPS-140-1统计性测试,并进行了相关性分析,结果通过了所有的测试,说明这种伪随机二进制序列具有很好的密码学性能;
7.基于空间混沌,设计了两种图像加密方案,并且进行了安全性分析,实现了利用空间混沌对图像的加密/解密;
8.最后对论文工作进行了系统的全面总结并对今后的研究方向进行了展望。
对空间混沌以及空间混沌在图像加密中的应用的研究,不仅丰富了混沌保密通信的内容,而且也从另一角度对空间混沌有了新的认识和理解。因此对于空间混沌系统的深入认识和研究不仅具有重要的理论价值,而且具有广泛的实际应用价值。
With the rapid development and extensive applications of computer and communication technologies, digital information is being applied more and more widely in the world. Digital information is easy to copy and distribute, this also produces many security problems in its applications. As a result, the security and protection of digital information are becoming increasingly a key problem that must be solved urgently.
It's well known that cryptography is the fundamental method for information security. There is natural relationship between chaos and cryptography: such as the sensitive dependence on initial conditions and control parameters, the density of the set of all periodic points and topological transitivity which are related to some requirements such as confusion and diffusion in cryptography. Therefore, chaos-based encryption techniques play an increasing role in information security. Since 1980s, the idea of using chaotic systems to design new ciphers has attracted more and more attention, and much more contributions are made to get many promising achievements. However, recently, a majority of chaotic ciphers have been analyzed and proven not to be practicable, efficient and secure. Especially, for Encryption of images, it is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which are generally difficult to handle by traditional methods. How to design secure chaos-based encryption scheme in terms of detailed analysis is becoming a key problem that must be solved urgently.
In this dissertation, we study the image cryptosystems based on high-dimensional chaotic systems in detail. Spatial chaotic systems are firstly introduced to cryptography, and several image cryptosystems based on spatial chaotic systems are designed. In addition, the nonlinear characteristics of molecular orbit are studied, and the existence of spatial chaos and bifurcation are also proven. The main achievements and originality contained in this dissertation are as follows:
1. The research status and advances of chaotic ciphers has been summarized, analyzed and reviewed, and several existent key problems to be solved urgently have been pointed out;
2. Chaos theory is introduced in detail. First, the research history of chaos is reviewed. Second, the definition of chaos is proposed. Third, the definitions of cryptography are aggregated. Finally, the relationship between chaos theory and cryptography is compared in detail, and some image encryption methods are introduced;
3. Image encryption based on high-dimensional chaos has been suggested. This new scheme employs the Arnold cat map to shuffle the positions of image pixels and uses Lorenz chaotic map to confuse the relationship between the cipher-image and the plain-image;
4. Using couple map lattices to realize image encryption, and experimental tests and security analysis are carried out, the results show the image encryption scheme is secure and fit for digital image encryption;
5. The nonlinear motion forms of carrier wave functions for square-lattice conjugated molecules with rectangular boundary, straight-chain-conjugated molecules and monocyclic- ring-conjugated molecules are mainly studied. The nonlinear characteristics of molecular orbit, such as chaos, bifurcation, and other nonlinear properties, are studied. In addition, the relationship between molecular orbit and its energy level in the nonlinear dynamic system is also discussed, and the existence of spatial chaos and bifurcation are also proven;
6. A scheme for pseudo-random binary sequence generation based on the spatial chaotic map is proposed. In order to face the challenge of using the proposed PRBS in cryptography, the proposed PRBS is subjected to statistical tests which are the well-known FIPS-140-1 in the area of cryptography, and correlation properties of the proposed sequences are investigated. The proposed true random bit generator successfully passes all four statistical tests for every run. The results of the tests on the sequences show the perfect cryptographic performance;
7. Based on spatial chaos system, designing two image encryption methods, employing security analysis, and realizing image encryption/decryption using spatial chaos;
8. Finally, the research work of this dissertation is summarized, and the future research direction is indicated.
So investigating spatial chaos system and application in image encryption, it can not only enrich chaos secrecy communication, but also understand spatial chaos from another angle. Hence there are important the theory and practical values for the thorough understanding of spatial chaos system.
密码学是保护信息安全的最基本的手段。混沌理论和密码学之间有着天然的联系:如对初始条件和控制参数的敏感性、周期点集的稠密性和拓扑传递性,和密码学中的混淆与扩散特性。因此,基于混沌的密码技术在信息安全方面具有重要的地位。自二十世纪80年代以来,应用混沌系统构造新型密码系统受到了越来越多的关注,出现了不少充满希望的进展。然而,近期的研究表明,原来提出的被认为是实用性强和安全性高的混沌密码方案被分析,并被证实它们效率低、不安全和不可用。尤其对于信息量大和冗余度高的图像文件,大部分传统的基于混沌的密码系统不适合直接对它进行加密。如何通过细致的分析设计安全的混沌密码方案日渐成为急待解决的关键问题。
本文对高维混沌系统在图象加密中的应用做了深入研究,首次将空间混沌引入到密码学中,并设计了几种新的图像加密方案。此外,研究了分子轨道系统模型中的非线性行为,即从理论上证明了分子轨道中的空间混沌以及分岔现象的存在。论文的主要研究内容及创新之处有:
1.对当前混沌密码学的发展状况进行了详细的分析、归纳和总结,提出了目前存在的一些需要解决的关键问题;
2.从多方面对混沌理论基础作了详细的阐述。首先回顾了混沌理论的研究历史并给出了几种混沌的定义。其次简要概括了密码学的基本理论。然后阐述了混沌理论和混沌密码学的关系。最后介绍了几种混沌图像加密方法;
3.设计了一种利用高维混沌实现图像加密的加密方案。首先利用Arnoldcat映射混乱图像相素的位置,然后用Lorenz混沌系统进一步加密图像;
4.利用耦合映射格子进行数字图像的加密,设计加密/解密方案并进行了安全分析,获得了一个更安全、更适合数字图像的加密系统;
5.研究了具有矩形边界的方格子形共轭分子、直链和单环共轭分子结构的电子载波的运动形式,分析了分子轨道的非线性特性,如空间混沌、分岔和其他的非线性特性。另外,也讨论并给出了分子轨道和它的能量层的关系。从理论上证明了分子轨道中的空间混沌以及分岔现象的存在;
6.研究了由空间混沌系统生成的伪随机二进制序列的密码学特性,对这种伪随机二进制序列进行了密码学中众所周知的FIPS-140-1统计性测试,并进行了相关性分析,结果通过了所有的测试,说明这种伪随机二进制序列具有很好的密码学性能;
7.基于空间混沌,设计了两种图像加密方案,并且进行了安全性分析,实现了利用空间混沌对图像的加密/解密;
8.最后对论文工作进行了系统的全面总结并对今后的研究方向进行了展望。
对空间混沌以及空间混沌在图像加密中的应用的研究,不仅丰富了混沌保密通信的内容,而且也从另一角度对空间混沌有了新的认识和理解。因此对于空间混沌系统的深入认识和研究不仅具有重要的理论价值,而且具有广泛的实际应用价值。
With the rapid development and extensive applications of computer and communication technologies, digital information is being applied more and more widely in the world. Digital information is easy to copy and distribute, this also produces many security problems in its applications. As a result, the security and protection of digital information are becoming increasingly a key problem that must be solved urgently.
It's well known that cryptography is the fundamental method for information security. There is natural relationship between chaos and cryptography: such as the sensitive dependence on initial conditions and control parameters, the density of the set of all periodic points and topological transitivity which are related to some requirements such as confusion and diffusion in cryptography. Therefore, chaos-based encryption techniques play an increasing role in information security. Since 1980s, the idea of using chaotic systems to design new ciphers has attracted more and more attention, and much more contributions are made to get many promising achievements. However, recently, a majority of chaotic ciphers have been analyzed and proven not to be practicable, efficient and secure. Especially, for Encryption of images, it is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which are generally difficult to handle by traditional methods. How to design secure chaos-based encryption scheme in terms of detailed analysis is becoming a key problem that must be solved urgently.
In this dissertation, we study the image cryptosystems based on high-dimensional chaotic systems in detail. Spatial chaotic systems are firstly introduced to cryptography, and several image cryptosystems based on spatial chaotic systems are designed. In addition, the nonlinear characteristics of molecular orbit are studied, and the existence of spatial chaos and bifurcation are also proven. The main achievements and originality contained in this dissertation are as follows:
1. The research status and advances of chaotic ciphers has been summarized, analyzed and reviewed, and several existent key problems to be solved urgently have been pointed out;
2. Chaos theory is introduced in detail. First, the research history of chaos is reviewed. Second, the definition of chaos is proposed. Third, the definitions of cryptography are aggregated. Finally, the relationship between chaos theory and cryptography is compared in detail, and some image encryption methods are introduced;
3. Image encryption based on high-dimensional chaos has been suggested. This new scheme employs the Arnold cat map to shuffle the positions of image pixels and uses Lorenz chaotic map to confuse the relationship between the cipher-image and the plain-image;
4. Using couple map lattices to realize image encryption, and experimental tests and security analysis are carried out, the results show the image encryption scheme is secure and fit for digital image encryption;
5. The nonlinear motion forms of carrier wave functions for square-lattice conjugated molecules with rectangular boundary, straight-chain-conjugated molecules and monocyclic- ring-conjugated molecules are mainly studied. The nonlinear characteristics of molecular orbit, such as chaos, bifurcation, and other nonlinear properties, are studied. In addition, the relationship between molecular orbit and its energy level in the nonlinear dynamic system is also discussed, and the existence of spatial chaos and bifurcation are also proven;
6. A scheme for pseudo-random binary sequence generation based on the spatial chaotic map is proposed. In order to face the challenge of using the proposed PRBS in cryptography, the proposed PRBS is subjected to statistical tests which are the well-known FIPS-140-1 in the area of cryptography, and correlation properties of the proposed sequences are investigated. The proposed true random bit generator successfully passes all four statistical tests for every run. The results of the tests on the sequences show the perfect cryptographic performance;
7. Based on spatial chaos system, designing two image encryption methods, employing security analysis, and realizing image encryption/decryption using spatial chaos;
8. Finally, the research work of this dissertation is summarized, and the future research direction is indicated.
So investigating spatial chaos system and application in image encryption, it can not only enrich chaos secrecy communication, but also understand spatial chaos from another angle. Hence there are important the theory and practical values for the thorough understanding of spatial chaos system.
引文
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