基于TD-ERCS混沌系统的伪随机数发生器及其统计特性分析

为了进一步分析切延迟椭圆反射腔映射系统(TD-ERCS)混沌系统的密码学意义上的安全性， 采用TD-ERCS并行方式构造了一个结构简单的伪随机序列发生器.用户密码不再是固定不变的 ，可在［2⁶⁴，2⁶⁷²］区域内任意取值.对所产生的二值伪随机 序列（即TD-ERC S序列）进行了均衡性、游程特性、相关性等基本统计特性初步测试，并与m序列、logistic 序列、Chebyshev混沌序列、SCQC序列作了对比分析.实验表明，TD-ERCS序列有更好的统计 特性. 关键词： 混沌 TD-ERCS PRNG 统计特性     

Logistic混沌系统的熵特性研究

作为形式上相对较为简单的一维混沌函数,Logistic系统在很多领域有着重要的应用.本文主要分析了Logistic系统的熵稳定特性,对不同参数μ和系统初值形成的Logistic序列,进行了统计分类,得到了一系列的熵值,并详细分析了熵的分布情况.数值仿真结果表明,Logistic系统的熵由参数μ决定,而与系统初值基本无关,且当参数μ取值接近上界(μ=4)时,序列分布越趋于均匀,熵也接近理论极限值.     

TD-ERCS离散混沌伪随机序列的复杂性分析

采用相空间直接观察法和行为复杂性算法,系统地分析了新型TD-ERCS离散混沌系统产生的伪随机序列的复杂性,得出了其复杂性变化规律.在Kolmogorov复杂性基础上,应用经典的Limpel-Ziv算法,ApEn算法和PE算法,从一维时间序列到多维相空间重构两方面计算了TD-ERCS离散混沌伪随机序列的复杂度大小.计算结果表明,TD-ERCS系统的行为复杂性高,而且该系统的复杂性大小随系统参数改变的变化范围小,是一个复杂性非常稳定的全域性离散混沌系统,其产生的混沌伪随机序列适合于信息加密或扩频通信. 关键词： 混沌 混沌伪随机序列 TD-ERCS系统 复杂度     

共轭Chen混沌系统的分岔分析及基于该系统的超混沌生成研究

分析了一个三维自治混沌系统的Hopf分岔现象,该系统的混沌吸引子属于共轭Chen混沌系统.通过引入一个控制器,基于该混沌系统构建了一个四维自治超混沌系统.该超混沌系统含有一个单参数,在一定的参数范围内呈现超混沌现象.通过Lyapunov指数和分岔分析,随着参数的变化该系统轨道呈现周期轨道、准周期轨道、混沌和超混沌的演化过程. 关键词： 混沌 超混沌生成 Hopf分岔 分岔分析     

基于非线性电阻的RLC混沌电路实验分析

给出了一种含非线性电阻的RLC混沌电路,并通过实验分析了电路中的“双涡卷”混沌现象,使学生更深入地了解电路中的混沌概念。     

Lorenz混沌系统的分析与电路实现

利用Matlab的数值计算和Multisim的电路模型分析和实现著名的Lorenz混沌系统,观察Lorenz混沌吸引子,加深对混沌现象的认识,可将混沌理论与实验引入到大学物理实验教学项目中。     

一种基于Logistic混沌系统和奇异值分解的零水印算法

改变了传统通过修改图像内容进行版权保护的做法,描述了一种基于混沌理论和奇异值分解（singular value decomposing,SVD）的零水印方案;利用了Logistic混沌系统的初值敏感性映射信息隐藏的位置,增强了算法的安全性;采用了奇异值的不变特性构造注册中心的水印,保证了在不改变宿主图像任何信息的同时进行有效地版权保护;将有意义的二值图像作为水印图像,解决了零水印方案水印为无意义二值序列的问题;同时深入分析了水印容量和算法安全性之间的关系.通过对标准测试图像、卡通、医学、风景、遥感、诗画等 关键词： 零水印 混沌系统 Logistic系统 奇异值分解     

T混沌系统的动力学分析与同步及其电路仿真

针对一类T混沌系统,对系统平衡点的稳定性进行了分析,并对系统的分岔,Lyapunov指数,Poincare截面进行了数值分析.同时,针对参数己知和未知两种情形,研究其同步控制问题,利用Lyapunov函数设计并证明了系统的反馈控制器.最后运用Multisim软件设计实现了T混沌系统同步的混沌电路,验证了所提出同步方法的有效性和可实现性.     

基于改进Logistic混沌映射的数字图像加密算法研究

混沌序列具有伪随机性、遍历性、对初始条件极其敏感性以及具备白噪声的统计特性等特点;文章利用Logistic混沌映射的改进算法产生的混沌序列所具有的这些特性,对数字图像进行空域像素进行位置置乱,然后对置乱后的图像序列按照一定的方法进行异或处理得到加密图像;实验在图像的竖直、水平、对角线方向,随机选择像素点,利用其灰度值,图像像素个数,计算数学期望,方差,协方差,相关系数;结果表明文章算法扰乱了图像像素间的相关性,使得加密图像能够抵抗明文统计的攻击,且密钥空间大,运算速度快,具有非常好的加密效果。     

Coullet混沌系统的演化和控制实验

构建了Coullet混沌系统的硬件实验电路,改变系统的参数,可以从示波器上观察系统从稳定周期状态演变到混沌状态的分岔过程.采用非线性反馈控制方法实现了对Coullet混沌系统的有效控制,改变反馈控制增益,可以将Coullet系统从混沌状态控制到稳定的周期状态.     

一种基于TD-ERCS的生物特征密钥产生算法

提出了一种新的思路,即由生物特征直接生成系统所需的密钥,从而降低了系统的成本和复杂性,并方便用户操作.为了保证该方法的安全性,采用改进后的切延迟椭圆反射腔混沌系统（TD-ERCS）对生物特征进行处理.实验结果表明该算法具有极高的运算速度,良好的生物特征敏感性、抗碰撞性和随机性,可实际用于生物特征密码系统. 关键词： 混沌 切延迟椭圆反射腔系统 生物特征密码系统 密钥产生算法     

Cryptanalysis of a color image encryption algorithm based on chaos

A novel image encryption algorithm based on logistic map is proposed recently. In this paper, a chosen plaintext attack on this algorithm is presented and some other flaws of the algorithm are pointed out. Theoretical analysis and experimental simulation indicate that the plain image can be recovered exactly from the cipher image without secret key. Therefore, this algorithm is not secure enough for practical applications. An improvement is proposed to enhance the security of the original algorithm. Simulation results and theoretical analysis show that the improved scheme has expected cryptographic properties and is more secure than the original algorithm.     

Effects of randomness on chaos and order of coupled logistic maps

Natural systems are essentially nonlinear being neither completely ordered nor completely random. These nonlinearities are responsible for a great variety of possibilities that includes chaos. On this basis, the effect of randomness on chaos and order of nonlinear dynamical systems is an important feature to be understood. This Letter considers randomness as fluctuations and uncertainties due to noise and investigates its influence in the nonlinear dynamical behavior of coupled logistic maps. The noise effect is included by adding random variations either to parameters or to state variables. Besides, the coupling uncertainty is investigated by assuming tinny values for the connection parameters, representing the idea that all Nature is, in some sense, weakly connected. Results from numerical simulations show situations where noise alters the system nonlinear dynamics.     

Optical image encryption using improper Hartley transforms and chaos

We propose a new method for image encryption using improper Hartley transform and chaos theory. Improper Hartley transform is a Hartley transform in which the phase between the two Fourier transforms is a fractional multiple of π/2. This fractional order is called fractional parameter and serves as a key in the image encryption and decryption process. Four types of chaos functions have been used. These functions are the logistic map, the tent map, the Kaplan-Yorke map and the Ikeda map. Random intensity masks have been generated using these chaotic functions and are called chaotic random intensity masks. The image is encrypted by using improper Hartley transform and two chaotic random intensity masks. The mean square error has been calculated. The robustness of the proposed technique in terms of blind decryption has been tested. The computer simulations are presented to verify the validity of the proposed technique.     

Optical image encryption using fractional Fourier transform and chaos

We propose a new method for image encryption using fractional Fourier transform and chaos theory. Random phase masks are generated using iterative chaos functions. The input image is combined with the first random phase mask at the object plane and is then transformed using the fractional Fourier transform. After the first fractional Fourier transform, the second random phase mask, again generated by using the chaos functions, is used at the fractional plane. The second fractional Fourier transform operation is then carried out to obtain the encrypted image. Three types of chaos functions have been used: the logistic map, the tent map and the Kaplan–Yorke map. The mean square error and the signal-to-noise ratio between the decrypted image and the input image for the correct order and the incorrect order of the fractional Fourier transform have been calculated. The computer simulations are presented to verify the validity of the proposed technique.     

Deep-learning-based cryptanalysis of two types of nonlinear optical cryptosystems

The two types of nonlinear optical cryptosystems (NOCs) that are respectively based on amplitude-phase retrieval algorithm (APRA) and phase retrieval algorithm (PRA) have attracted a lot of attention due to their unique mechanism of encryption process and remarkable ability to resist common attacks. In this paper, the securities of the two types of NOCs are evaluated by using a deep-learning (DL) method, where an end-to-end densely connected convolutional network (DenseNet) model for cryptanalysis is developed. The proposed DL-based method is able to retrieve unknown plaintexts from the given ciphertexts by using the trained DenseNet model without prior knowledge of any public or private key. The results of numerical experiments with the DenseNet model clearly demonstrate the validity and good performance of the proposed the DL-based attack on NOCs.     

基于切延迟的椭圆反射腔离散混沌系统及其性能研究

根据椭圆反射腔物理模型， 提出了一种改变系统演化轨道的切延迟操作方法，导出了基于该方法的一类离散混沌映射系 统.实验表明，这类离散混沌系统最大Lyapunov指数恒大于零,状态变量等概率分布且与参 数和初值无关,全域零相关性，切延迟1单位时存在一个稳定不变的方形吸引子，切延迟大于 1单位时走向各态遍历.这类离散混沌系统可以产生两个独立的伪随机序列，其特殊性质和 复杂的动力学行为极具密码学应用价值. 关键词： 混沌 切延迟 Lyapunov指数 TD-ERCS 吸引子     

基于强度统计算法的混沌序列复杂度分析

为了分析混沌序列的复杂度,文中采用强度统计复杂度算法分别对离散混沌系统(TD-ERCS)和连续混沌系统(简化Lorenz系统)进行复杂度分析,计算了混沌序列随参数变化的复杂度,分析了连续混沌系统产生的伪随机序列分别进行m序列和混沌伪随机序列扰动后的复杂度.研究表明,强度统计复杂度算法是一种有效的复杂度分析方法,离散混沌序列复杂度大于连续混沌序列复杂度,但对连续混沌系统的伪随机序列进行m序列和混沌伪随机序列扰动后可大大增加复杂度,为混沌序列在信息加密中的应用提供了理论依据. 关键词： 强度统计复杂度算法 TD-ERCS系统 简化Lorenz系统 序列扰动