基于动力学特性的混沌密码算法研究
发布时间：2019-01-05 21:17
【摘要】：自1965年美国气象学家Lorenz发现混沌现象以来，混沌理论受到越来越多的关注。混沌系统因具有对初始值和系统参数的敏感依赖性、遍历性和存在周期无限长的轨道的性质，这些是理想的密码系统所追求的性质。一个简单的混沌动力系统却有着非常复杂的行为，这些复杂行为有着很好的密码学性质，这正是混沌密码学的价值所在。另一方面，建立在数论、代数及算法复杂性理论基础之上传统密码算法正遭遇各种挑战，随着密码分析方法和研究手段的不断成熟，DES，MD5，SHA1等原来被认为安全的系统最近接连被破解，量子计算的发展也对非对称密码算法造成了巨大威胁。新的密码设计理论正成为一种迫切的需求，而从全新角度进行设计的混沌密码算法正是一种良好的替代方案。 然而，现存的混沌密码算法还存在诸多问题，他们往往因为动力学特性差或者是算法结构设计存在问题而被破译，现有的混沌密码算法还没有一个得到了广泛的应用。针对上述问题，本文从以下几个方面进行了研究： （1）研究了混沌系统动力学特性对密码算法的影响。通过对Lyapunov指数谱的计算可以明确混沌系统在哪些参数区域是非混沌的，并且可以衡量初始时刻相邻轨道随时间变化分离的快慢程度.具有恒正的Lyapunov指数谱在密码学中是比较理想的性质。混沌系统的极限点集表明了系统长时间运行后应该保持的稳定的性质，在密码学中理想的系统其极限状况应该尽量保持均匀以免泄露系统的特征。复杂度的研究可以表明系统生成的序列的随机的程度，复杂度高的系统产生的序列往往更难以预测。 （2）在分析了上述动力学性质后，提出了一类低维的具有Markov分割性质的混沌系统T(x, p, sigma)。其将区间级别的变换作为分析的基础，可利用符号动力学对其做详细的研究。可以从理论上证明它有恒正的Lyapunov指数，而且其极限分布是均匀分布。通过参数的调整，在近似熵和符号熵的评价标准下它的复杂度可以远高于Logistic映射和Tent映射，利用它产生的序列具有更好的随机性。 （3）进一步的，，分析了现有混沌图像加密算法结构存在的问题。现有的混沌图像加密算法大多是基于Fridrich结构的，它有两个部分组成，一个置乱矩阵，一个扩散函数。通过对被破译的混沌算法进行分析，发现其扩散函数的设计结构过于简单易破解，而置乱矩阵是可逆矩阵，这样一来，通过选择明文攻击可以分析出算法的密钥流，进而可以破解出原始明文图像。 （4）设计了一种新的图像加密算法。利用本文所构造的新的混沌系统去设计一个新的密钥生成函数，因具备理想的动力学性质，其产生的密钥比较理想；另外，通过采用不同群中的加法混合运算改进了图像加密算法的扩散函数使其难以破解。通过对算法基本性质的测试可以看出本文设计的算法可以通过目前图像加密算法的所有测试，另外算法可以抵抗通常的攻击。 （5）在FPGA的平台上实现了本文的混沌图像加密算法。给出了算法的实现方法，利用FPGA的平台特性优化了算法的可并行执行部分，并利用流水线技术做了进一步优化，使其在资源消耗不多的情况下有不错的计算速度。 研究结果表明，本文采用的混沌系统具有比较理想的动力学特性，这些理想的特性使得此系统特别适合用于密码算法的设计。本文设计的图像加密算法安全性高，计算效率好具有不错的应用前景。
[Abstract]:Since 1965, the American meteorologist, Lorenz, has been more and more concerned about the mix-up theory. the hybrid system is of the nature of an ideal cryptographic system due to the nature of the orbit having an infinite length of sensitivity, ergodic, and existence of the initial value and system parameters. A simple hybrid power system has very complex behavior, and these complex behaviors have very good cryptographic properties, which is the value of the hybrid cryptography. On the other hand, the traditional cryptographic algorithm based on the theory of number theory, algebra and algorithm complexity is faced with various challenges, and with the development of the password analysis method and the research means, the systems of DES, MD5, SHA1, etc., which are originally thought to be safe, are recently cracked, The development of quantum computation also poses a great threat to the asymmetric cryptographic algorithm. The new design theory of the code is becoming an urgent need, and the mixed-code algorithm designed from the new angle is a good alternative. However, there are many problems in the existing hybrid cryptographic algorithms, which are often deciphered because of the poor dynamic characteristics or the problems of the structural design of the algorithm, and the existing hybrid cryptographic algorithm has not been widely used. In the light of the above problems, this paper makes a research on the following aspects In this paper, the dynamic characteristics of the hybrid system and the code algorithm are studied in this paper. The influence of the time-varying separation of the adjacent tracks in the initial time can be measured by the calculation of the Lyapunov exponent spectrum. Slow degree. The Lyapunov exponent spectrum with constant positive is more ideal in cryptography The limit point set of the hybrid system shows the stable property that should be kept after the system is running for a long time. The limit condition of the ideal system in cryptography should be kept as uniform as possible in order to avoid the leakage system. The study of complexity can indicate the random degree of the system generated by the system, and the sequence generated by the system with high complexity tends to be more difficult. In this paper, a class of low-dimensional hybrid system T (x, p, s) with Markov-splitting properties is proposed after analyzing the dynamic properties. igma). It uses the transformation of the interval level as the basis for the analysis and can be done using the symbolic dynamics In this paper, we can theoretically prove that it has a constant positive Lyapunov exponent and its limit distribution It is a uniform distribution. By adjusting the parameters, its complexity can be much higher than the Logistic mapping and the Tent mapping under the evaluation criteria of the approximate entropy and the symbol entropy. good randomness. (3) Further, the existing hybrid image encryption algorithm is analyzed The existing hybrid image encryption algorithm is based on the Fridrich structure, which consists of two parts, a scrambling matrix, It is found that the design structure of the diffusion function is too simple and easy to crack, and the scrambling matrix is a reversible matrix, so that the key stream of the algorithm can be analyzed by selecting the plaintext attack, which can then be cracked. The original plain text image is shown. (4) It is designed In this paper, a new key generation function is designed by using the new hybrid system constructed in this paper. Because of the ideal dynamic property, the key generated by the new key generation function is ideal; in addition, the expansion of the image encryption algorithm is improved by using the addition and mixing operation in different groups. The hash function makes it difficult to crack. By testing the basic properties of the algorithm, it can be seen that the algorithm designed in this paper can pass all the tests of the current image encryption algorithm, and the other algorithms can resist the usual attack. (5) It is implemented on the platform of the FPGA In this paper, the hybrid image encryption algorithm is given. The implementation method of the algorithm is given. The executable part of the algorithm is optimized by using the platform characteristics of the FPGA, and further optimization is made by using the pipeline technology, so that it is not much consumed in the resource consumption. The results show that the hybrid system used in this paper has the ideal dynamic characteristics, and these ideal characteristics make the system It is especially suitable for the design of the cipher algorithm. The security of the image encryption algorithm designed in this paper is high,
【学位授予单位】：中国科学院研究生院(长春光学精密机械与物理研究所)
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN918.4;O415.5
[Abstract]:Since 1965, the American meteorologist, Lorenz, has been more and more concerned about the mix-up theory. the hybrid system is of the nature of an ideal cryptographic system due to the nature of the orbit having an infinite length of sensitivity, ergodic, and existence of the initial value and system parameters. A simple hybrid power system has very complex behavior, and these complex behaviors have very good cryptographic properties, which is the value of the hybrid cryptography. On the other hand, the traditional cryptographic algorithm based on the theory of number theory, algebra and algorithm complexity is faced with various challenges, and with the development of the password analysis method and the research means, the systems of DES, MD5, SHA1, etc., which are originally thought to be safe, are recently cracked, The development of quantum computation also poses a great threat to the asymmetric cryptographic algorithm. The new design theory of the code is becoming an urgent need, and the mixed-code algorithm designed from the new angle is a good alternative. However, there are many problems in the existing hybrid cryptographic algorithms, which are often deciphered because of the poor dynamic characteristics or the problems of the structural design of the algorithm, and the existing hybrid cryptographic algorithm has not been widely used. In the light of the above problems, this paper makes a research on the following aspects In this paper, the dynamic characteristics of the hybrid system and the code algorithm are studied in this paper. The influence of the time-varying separation of the adjacent tracks in the initial time can be measured by the calculation of the Lyapunov exponent spectrum. Slow degree. The Lyapunov exponent spectrum with constant positive is more ideal in cryptography The limit point set of the hybrid system shows the stable property that should be kept after the system is running for a long time. The limit condition of the ideal system in cryptography should be kept as uniform as possible in order to avoid the leakage system. The study of complexity can indicate the random degree of the system generated by the system, and the sequence generated by the system with high complexity tends to be more difficult. In this paper, a class of low-dimensional hybrid system T (x, p, s) with Markov-splitting properties is proposed after analyzing the dynamic properties. igma). It uses the transformation of the interval level as the basis for the analysis and can be done using the symbolic dynamics In this paper, we can theoretically prove that it has a constant positive Lyapunov exponent and its limit distribution It is a uniform distribution. By adjusting the parameters, its complexity can be much higher than the Logistic mapping and the Tent mapping under the evaluation criteria of the approximate entropy and the symbol entropy. good randomness. (3) Further, the existing hybrid image encryption algorithm is analyzed The existing hybrid image encryption algorithm is based on the Fridrich structure, which consists of two parts, a scrambling matrix, It is found that the design structure of the diffusion function is too simple and easy to crack, and the scrambling matrix is a reversible matrix, so that the key stream of the algorithm can be analyzed by selecting the plaintext attack, which can then be cracked. The original plain text image is shown. (4) It is designed In this paper, a new key generation function is designed by using the new hybrid system constructed in this paper. Because of the ideal dynamic property, the key generated by the new key generation function is ideal; in addition, the expansion of the image encryption algorithm is improved by using the addition and mixing operation in different groups. The hash function makes it difficult to crack. By testing the basic properties of the algorithm, it can be seen that the algorithm designed in this paper can pass all the tests of the current image encryption algorithm, and the other algorithms can resist the usual attack. (5) It is implemented on the platform of the FPGA In this paper, the hybrid image encryption algorithm is given. The implementation method of the algorithm is given. The executable part of the algorithm is optimized by using the platform characteristics of the FPGA, and further optimization is made by using the pipeline technology, so that it is not much consumed in the resource consumption. The results show that the hybrid system used in this paper has the ideal dynamic characteristics, and these ideal characteristics make the system It is especially suitable for the design of the cipher algorithm. The security of the image encryption algorithm designed in this paper is high,
【学位授予单位】：中国科学院研究生院(长春光学精密机械与物理研究所)
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN918.4;O415.5
【参考文献】
相关期刊论文 前10条
1 蔡军辉;雷仲魁;孙继如;;基于FPGA的数字视频加解密系统设计[J];信息化研究;2009年11期
2 章明朝;于晓;李佩s
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