离散混沌系统复杂度与密码学安全性的关系研究

发布时间：2018-04-03 06:48

本文选题：信息安全　切入点：密码学　出处：《华中科技大学》2014年硕士论文

【摘要】：混沌动力系统因其复杂的动力学特性被广泛应用于信息安全及其密码学领域。混沌系统具有对初始条件的敏感依赖性、类随机性以及短期可预测、长期不可预测的性质，这些良好的动力学性质与密码学中有关混淆与扩散等经典密码设计原则很好的吻合，混沌密码技术也成为备受关注的新型密码技术之一。混沌密码的安全性取决于混沌复杂的动力学特性。然而，混沌动力学复杂度高的系统并不能保证所设计的密码满足密码学复杂性的需求。混沌动力学复杂度与密码学复杂度的关系不明确，导致混沌密码缺乏相应的安全性理论评价体系。因此在混沌密码的研究中，动力学复杂度与密码学复杂度的关系是一个很有意义的课题，为构造满足密码学安全性要求的混沌密码系统，以及建立混沌密码系统的安全性理论奠定了基础。为此，，本文致力于研究混沌动力学与密码学复杂度的关系：研究建立了系统的Lyapunov指数与Lempel-Ziv复杂度，非线性复杂度等密码学复杂度指标的关系。研究结果表明两种复杂度之间存在着较强的相关性，且随着Lyapunov指数的增大，混沌系统生成的二元序列更加满足密码学复杂度的要求。在上述研究结果的基础上，本文设计了一类混沌伪随机序列发生器，实验结果表明所生成的伪随机序列满足密码学复杂度的要求，并验证了该伪随机序列具有良好的统计特性以及密钥空间。本文的研究成果将为建立混沌密码系统的安全性理论提供理论基础。
[Abstract]:Chaotic dynamical system is widely used in the field of information security and cryptography because of its complex dynamic characteristics.Chaotic systems have sensitive dependence on initial conditions, quasi-randomness, short-term predictability and long-term unpredictable properties. These good dynamical properties are in good agreement with the classical cryptographic design principles such as confusion and diffusion in cryptography.Chaotic cryptography has also become one of the new cryptographic technologies.The security of chaotic cryptography depends on the complex dynamics of chaos.However, the system with high complexity of chaotic dynamics can not guarantee that the cipher designed can meet the requirements of cryptography complexity.The relationship between chaotic dynamics complexity and cryptographic complexity is not clear, which leads to the lack of a corresponding security evaluation system for chaotic cryptography.Therefore, in the research of chaotic cryptography, the relationship between dynamics complexity and cryptography complexity is a very meaningful subject. In order to construct chaotic cryptosystem that meets the requirements of cryptography security,And the security theory of chaotic cryptosystem is established.Therefore, the relationship between chaotic dynamics and cryptographic complexity is studied. The relationship between Lyapunov exponent and Lempel-Ziv complexity, nonlinear complexity and other cryptographic complexity indexes is established.The results show that there is a strong correlation between the two kinds of complexity, and with the increase of Lyapunov exponent, the binary sequences generated by chaotic systems can meet the requirements of cryptographic complexity.Based on the above results, a kind of chaotic pseudorandom sequence generator is designed, and the experimental results are obtained.It is shown that the generated pseudorandom sequence meets the requirements of cryptographic complexity, and it is verified that the pseudorandom sequence has good statistical properties and key space.The research results in this paper will provide a theoretical basis for establishing the security theory of chaotic cryptosystem.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.1

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