忆容器混沌系统及其在邮件加密中的应用研究

发布时间：2018-08-06 19:28

【摘要】：早在20世纪70年代就提出了忆阻器的概念,但是直到2008年,HP实验室才证明了忆阻元件的存在。忆阻器是具有记忆功能的非线性元件,在非易失性阻抗存储器(RRAM)及神经网络研究等领域具有重要的应用价值。2009年,广义忆阻器、广义忆容器及广义忆感器被提出,忆容器特性研究才逐渐开展。目前,关于忆容器的研究仍以数学模型及等效电路为主,来探索忆容器在非线性电路中的特性。本文主要研究了荷控忆容器与磁控忆容器的数学模型及其等效电路实现,并基于荷控忆容器设计了一个混沌振荡器。分析了荷控忆容器混沌系统受参数和初值影响的动力学特性。设计了降阶系统的模拟电路,得到了一种混沌吸引子。最后,利用忆容器混沌序列替换DES密钥序列,设计了混沌-DES加密算法,并用于电子邮件安全软件设计。研究内容包括如下几个方面:(1)介绍了忆阻器、忆容器、忆感器的数学定义以及HP实验室TiO_2忆阻器的端口特性。分析了荷控忆容器的光滑三次曲线模型和压控忆容器的光滑二次曲线模型,并分别设计了相应的等效电路验证其紧滞回线特性。(2)分析了典型的一维离散Logistic映射与连续的Lorenz混沌系统,介绍了混沌系统的分析方法。提出了一个新的三维连续混沌系统,通过平衡点、分岔图、Lyapunov指数进行系统混沌系统特性分析,并通过动力学地图分析系统的状态分布情况。研究结果表明该系统最大的特点是具有共存吸引子,即系统参数固定,不同的变量初始值组合,导致系统轨迹最终收敛于不同的吸引子。(3)根据荷控忆容器构造了一个自治的混沌振荡系统,通过动力学地图、分岔图及Lyapunov指数分析了在参数变化过程中系统的动力学特性。另外,在固定系统参数的情况下,分析了初值变化的分岔图及Lyapunov指数谱。分析发现,该忆容器混沌系统具有共存振荡特性,存在多种共存吸引子。对四阶混沌系统进行积分处理,得到降阶系统,发现共存吸引子类型减少,说明系统的共存振荡特性被削弱。利用实际器件设计了三阶混沌系统模拟电路,得到了共存混沌吸引子中的一种。(4)为研究混沌系统在通信领域的应用价值,分析了混沌系统与密码学的关系,介绍了传统DES加密算法。忆容器混沌序列通过了NIST所有测试指标,说明忆容器混沌信号具有良好的随机性。利用忆容器混沌序列替换传统DES密钥,设计了混沌-DES加密算法。基于该算法设计了一款电子邮件安全软件。
[Abstract]:The concept of a resistive device was put forward in the 1970s, but it was not until 2008 that the existence of the resistive element was proved by HP Labs. The memory resistor is a nonlinear element with memory function, which has important application value in the field of non-volatile impedance memory (RRAM) and neural network. In 2009, the generalized memory device, the generalized memory container and the generalized memory sensor were proposed. The research on the characteristics of receptacles was carried out gradually. At present, mathematical models and equivalent circuits are still used to study the characteristics of memory vessels in nonlinear circuits. This paper mainly studies the mathematical model and equivalent circuit realization of charge controlled memory vessel and magnetic memory container, and designs a chaotic oscillator based on charge controlled memory vessel. The dynamic characteristics of the chaotic system affected by parameters and initial values are analyzed. An analog circuit of reduced order system is designed and a chaotic attractor is obtained. Finally, a chaotic encryption algorithm is designed by replacing the DES key sequence with the chaotic sequence of the memory container, and it is used in the design of the email security software. The contents of the research are as follows: (1) the mathematical definition of the resistive device, the memory container, the memory sensor and the port characteristics of the HP Labs TiO_2 resistor are introduced. The smooth cubic curve model of the charge controlled memory vessel and the smooth quadratic curve model of the pressure controlled memory vessel are analyzed. The corresponding equivalent circuits are designed to verify the properties of the tight hysteretic loop. (2) the typical one-dimensional discrete Logistic maps and continuous Lorenz chaotic systems are analyzed and the analytical methods of the chaotic systems are introduced. In this paper, a new three-dimensional continuous chaotic system is proposed. The characteristic of the chaotic system is analyzed by the equilibrium point, the bifurcation diagram and Lyapunov exponent, and the state distribution of the system is analyzed by the dynamic map. The results show that the main characteristic of the system is the coexisting attractor, that is, the system parameters are fixed, and the initial values of different variables are combined. As a result, the trajectory of the system eventually converges to different attractors. (3) an autonomous chaotic oscillation system is constructed according to the charge controlled memory vessel. The dynamic characteristics of the system are analyzed by means of dynamic maps, bifurcation diagrams and Lyapunov exponents. In addition, the bifurcation diagram and Lyapunov exponent spectrum of initial values are analyzed under the condition of fixed system parameters. It is found that the chaotic system has the characteristics of coexistence oscillation and multiple coexisting attractors. By integrating the fourth order chaotic system, the reduced order system is obtained. It is found that the coexisting attractor type is reduced, which indicates that the coexistence oscillation characteristic of the system is weakened. A third order chaotic system simulation circuit is designed by using practical devices, and one of the coexisting chaotic attractors is obtained. (4) in order to study the application value of chaotic system in the field of communication, the relationship between chaotic system and cryptography is analyzed. This paper introduces the traditional DES encryption algorithm. The chaotic sequence of the vessel has passed all the test indexes of NIST, which shows that the chaotic signal of the container has good randomness. The chaotic-des encryption algorithm is designed by replacing the traditional DES key with the chaotic sequence of the memory container. Based on this algorithm, an e-mail security software is designed.
【学位授予单位】：杭州电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN60;O415.5

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