一种混沌伪随机序列复杂度分析法

分析了已有的序列线性复杂度分析方法，提出了用近似熵算法计算混沌运动的测度熵，作为衡量混沌伪随机序列复杂度的标准.理论研究表明，利用较短的观察序列，该方法能够准确地反映混沌系统和混沌伪随机序列复杂度的大小，可以作为判断利用混沌系统产生的伪随机序列的复杂度准则.实验结果表明该方法的有效性和理论结果的正确性. 关键词： 混沌 伪随机序列 熵     

一种确定混沌伪随机序列复杂度的模糊关系熵测度

将模糊关系的概念引入混沌伪随机序列复杂度的测度方法之中,提出了一种新的混沌伪随机序列复杂度测度方法——模糊关系熵(fuzzy relationship entropy,简记为F-REn)测度方法,并推导了F-REn的两个基本性质.仿真结果表明,该测度方法能够有效测度混沌伪随机序列的复杂度,与近似熵(ApEn)测度方法和符号熵测度方法相比,F-REn测度具有更加好的对序列符号空间的适用性、更加小的对测量维度的敏感性和更加强的对分辨率参数的鲁棒性. 关键词： 混沌伪随机序列 模糊理论 复杂度     

混沌伪随机序列的谱熵复杂性分析

为了准确分析混沌伪随机序列的结构复杂性,采用谱熵算法对Logistic映射、Gaussian映射和TD-ERCS系统产生的混沌伪随机序列复杂度进行了分析.谱熵算法具有参数少、对序列长度N(惟一参数)和伪随机进制数K鲁棒性好的特点.采用窗口滑动法分析了混沌伪随机序列的复杂度演变特性,计算了离散混沌系统不同初值和不同系统参数条件下的复杂度.研究表明,谱熵算法能有效地分析混沌伪随机序列的结构复杂度;在这三个混沌系统中,TD-ERCS系统为广域高复杂度混沌系统,复杂度性能最好;不同窗口和不同初值条件下的混沌系统复杂度在较小范围内波动.为混沌序列在信息安全中的应用提供了理论和实验依据.     

基于复合符号混沌的伪随机数生成器及加密技术

提出了复合符号混沌序列的概念;并以符号动力学的揉序列为基础,将已知的伪随机数与揉序列规则下的短序列复合后得到新的符号混沌序列,再转换成二进制序列,从而得到长度随迭代次数成几何级数增加的伪随机序列(PRN).理论与实证分析都表明这是一个有效的伪随机生成器.为应用到图像的加解密技术中,建立了一个新型元胞自动机.该元胞自动机能有效地避免数据膨胀,加密效率高,并能产生显著的"雪崩效应",提高了加密技术的安全性. 关键词： 复合符号混沌序列 符号动力学 伪随机序列 元胞自动机     

基于符号动力学的开关变换器时间不可逆性分析

本文提出了一种采用符号动力学和相对熵理论分析开关变换器非线性特性的新方法.根据迭代映射描述的开关变换器非线性系统得到离散数值序列,基于拓扑共轭理论将其转化为符号序列,通过前向序列和后向序列概率计算该符号序列的相对熵.文中以一阶电压反馈DCM Boost变换器为例,研究结果表明,开关变换器存在时间不可逆性,相对熵数值能够量化开关变换器处于混沌状态时离开平衡点的距离,从而得到一种新的可量化的开关变换器非线性动力学行为指标.     

DC-DC变换器的符号时间序列描述及模块熵分析

本文提出了一种采用符号时间序列和熵理论分析DC-DC变换器非线性行为的方法.该方法首先用离散时间序列描述非线性连续系统,然后将其转换为由简单字符构成的符号序列,再用信息学方法计算出该符号序列的模块熵,从而得到一种新的可量化的非线性动力学行为统计指标.文中以一阶电压反馈DCM和二阶电流反馈CCM Boost变换器为例进行研究.研究结果表明,模块熵这种粗粒化的统计分析方法,能够量化DC-DC变换器的倍周期分岔和混沌行为,且能够准确地确定混沌行为的发生,是一种尚未在DC-DC变换器中提出的简单、实用的分析方法. 关键词： 符号时间序列 符号动力学 模块熵 Lyapunov指数     

级联混沌及其动力学特性研究

初值敏感性是混沌的本质,混沌的随机性来源于其对初始条件的高度敏感性,而Lyapunov指数又是这种初值敏感性的一种度量.本文的研究发现,混沌系统的级联可明显提高级联混沌的Lyapunov指数,改善其动力学特性.因此,本文研究了混沌系统的级联和级联混沌对动力学特性的影响,提出了混沌系统级联的定义及条件,从理论上证明了级联混沌的Lyapunov指数为各个级联子系统Lyapunov指数之和;适当的级联可增加系统参数、扩展混沌映射和满映射的参数区间,由此可提高混沌映射的初值敏感性和混沌伪随机序列的安全性.以Logistic映射、Cubic映射和Tent映射为例,研究了Logistic-Logistic级联、Logistic-Cubic级联和Logistic-Tent级联的动力学特性,验证了级联混沌动力学性能的改善.级联混沌可作为伪随机数发生器的随机信号源,用以产生初值敏感性更高、安全性更好的伪随机序列.     

基于线性反馈移位寄存器和混沌系统的伪随机序列生成方法

结合线性反馈移位寄存器（LFSR）和混沌理论各自的优点,采用循环迭代结构,给出一种将LFSR和混沌理论相结合的伪随机序列生成方法.首先根据LFSR的计算结果产生相应的选择函数,通过选择函数确定当前迭代计算使用的混沌系统,应用选择的混沌系统进行迭代计算产生相应的混沌序列;然后把生成的混沌序列进行数制转换,在将得到的二进制序列作为产生的伪随机序列输出的同时将其作为反馈值与LFSR的反馈值进行相应的运算,运算结果作为LFSR的最终反馈值,实现对LFSR生成序列的随机扰动.该方法既可生成二值伪随机序列,也可生成实值伪随机序列.通过实验对生成的伪随机序列进行了分析,结果表明,产生的序列具有良好的随机性和安全性. 关键词： 线性反馈移位寄存器 混沌系统 伪随机序列 随机性     

一种新的分段非线性混沌映射及其性能分析

结合线性反馈移位寄存器（LFSR）和混沌理论各自的优点,采用循环迭代结构,给出一种将LFSR和混沌理论相结合的伪随机序列生成方法.首先根据LFSR的计算结果产生相应的选择函数,通过选择函数确定当前迭代计算使用的混沌系统,应用选择的混沌系统进行迭代计算产生相应的混沌序列;然后把生成的混沌序列进行数制转换,在将得到的二进制序列作为产生的伪随机序列输出的同时将其作为反馈值与LFSR的反馈值进行相应的运算,运算结果作为LFSR的最终反馈值,实现对LFSR生成序列的随机扰动.该方法既可生成二值伪随机序列,也可生成实值伪随机序列.通过实验对生成的伪随机序列进行了分析,结果表明,产生的序列具有良好的随机性和安全性.     

混沌伪随机序列的复杂度的稳定性研究

增强统计复杂度能反映混沌伪随机序列的随机本质,在此基础上提出了k错增强统计复杂度的定义,用来衡量混沌伪随机序列复杂度的稳定性,并证明了其两个基本特性.以Logistic,Henon,Cubic,Chebyshev和Tent映射产生的混沌伪随机序列为例,说明了该方法的应用.仿真结果表明,该方法能区分不同混沌伪随机序列的稳定性,是一种衡量混沌序列稳定性的有效方法. 关键词： 稳定性 k错增强统计复杂度')" href="#">k错增强统计复杂度 混沌 伪随机序列     

将混沌序列变换成均匀伪随机序列的普适算法

提出了一种将混沌序列变换成均匀伪随机序列的普适算法.这种算法基于计算机浮点数表示的bit位操作,不针对任何具体对象,可将任意连续或分段连续分布的实型随机变量转换成均匀分布的随机变量.理论分析表明,这种算法源于实型随机变量中普遍存在着的沿bit位以指数规律增强的均匀化趋势.任何实型的混沌序列,不论来自混沌映射系统还是混沌微分动力系统,都可以在同一个标准算法下变换成均匀分布的伪随机序列,因而是混沌伪随机数发生器标准化模块设计和硬件实现的关键技术基础. 关键词： 混沌 伪随机序列 均匀分布函数     

A novel hyperchaotic map with sine chaotification and discrete memristor

Discrete memristor has become a hotspot since it was proposed recently. However, the design of chaotic maps based on discrete memristor is in its early research stage. In this paper, a memristive seed chaotic map is proposed by combining a quadratic discrete memristor with the sine function. Furthermore, by applying the chaotification method, we obtain a high-dimensional chaotic map. Numerical analysis shows that it can generate hyperchaos. With the increase of cascade times, the generated map has more positive Lyapunov exponents and larger hyperchaotic range. The National Institute of Standards and Technology (NIST) test results show that the chaotic pseudo-random sequence generated by cascading two seed maps has good unpredictability, and it indicates the potential in practical application.     

一个二次多项式混沌系统的均匀化及其熵分析

利用已有理论给出了一个二次多项式混沌系统,证明了该系统与Tent映射拓扑共轭,给出了该混沌系统的概率密度函数;并根据此概率密度函数,得到了轨道均匀分布的反三角函数映射;对均匀化前后的混沌系统在不同参数下产生序列的信息熵、Kolmogorov熵、离散熵的特性进行了分析,结果显示均匀化后产生的混沌序列混沌程度不改变且具有更好的均匀性.     

A new perturbation method to the Tent map and its application

Disturbance imposed on the chaotic systems is an effective way to maintain its chaotic good encryption features. This paper proposes a new perturbation method to the Tent map. First it divides the Tent map domain into 2^N parts evenly and selects a particular part from them, then proliferates the Tent map mapping trajectory of this particular part, which can disturb the entire system disturbance. The mathematical analysis and simulated experimental results prove that the disturbed Tent map has uniform invariant distribution and can produce good cryptographic properties of pseudo-random sequence. These facts avoid the phenomenon of short-period caused by the computer's finite precision and reducing the sequence's dependence on the disturbance signal, such that effectively compensate for the digital chaotic system dynamics degradation.     

Dynamical analysis,circuit realization,and application in pseudorandom number generators of a fractional-order laser chaotic system

A new five-dimensional fractional-order laser chaotic system (FOLCS) is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system. Dynamical behavior of the system, circuit realization and application in pseudorandom number generators are studied. Many types of multi-stable states are discovered in the system. Interestingly, there are two types of state transition phenomena in the system, one is the chaotic state degenerates to a periodical state, and the other is the intermittent chaotic oscillation. In addition, the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm. Moreover, a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit. Finally, a pseudo-random sequence generator is designed using the FOLCS, and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22. This study enriches the research on the dynamics and applications of FOLCS.     

Dynamics analysis of chaotic maps: From perspective on parameter estimation by meta-heuristic algorithm

Chaotic encryption is one of hot topics in cryptography, which has received increasing attention. Among many encryption methods, chaotic map is employed as an important source of pseudo-random numbers(PRNS). Although the randomness and the butterfly effect of chaotic map make the generated sequence look very confused, its essence is still the deterministic behavior generated by a set of deterministic parameters. Therefore, the unceasing improved parameter estimation technology becomes one of potential threats for chaotic encryption, enhancing the attacking effect of the deciphering methods. In this paper, for better analyzing the cryptography, we focus on investigating the condition of chaotic maps to resist parameter estimation. An improved particle swarm optimization(IPSO) algorithm is introduced as the estimation method. Furthermore, a new piecewise principle is proposed for increasing estimation precision. Detailed experimental results demonstrate the effectiveness of the new estimation principle, and some new requirements are summarized for a secure chaotic encryption system.     

A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism

A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.