The Switching Fractional Order Chaotic System and Its Application to Image Encryption

Many studies on fractional order chaotic systems and secure communications have been carried out, however, switching fractional order chaotic system and its application to image encryption have not been explored yet. In this paper, a new switching fractional order chaotic system is proposed, containing fractional order Chen system and the other two fractional order chaotic systems. Chaotic attractors and dynamical analysis including Lyapunov exponent, bifurcation diagram, fractal dimension, dissipation, stability and symmetry are shown firstly. After that, some circuit simulations through Multisim are presented. By controlling switch k₁ and k₂, switching among the three fractional order chaotic subsystems can be realized. Finally, we apply the switching fractional order chaotic system to image encryption using exclusive or (XOR) encryption algorithm. The encryption scheme could increase randomness and improve speed of encryption.      

基于离散分数余弦变换的图像加密算法研究*

为了提高图像加密的效率和安全性,采用态函数线性组合法构造了一种离散分数余弦变换函数,利用其良好的正交性能及具有分数阶参数和周期参数的特点,提出了一种基于离散分数余弦变换的图像加密新方法。该加密算法采用了图像分块（图元）的方法。将图像分成大小不同的图元,使用离散分数余弦变换对每个图元分别进行行变换和列变换,从而完成对图像的加密。实验结果分析表明,该算法的加密效果、效率和抗穷举攻击能力是令人满意的。     

分数阶Duffing系统在图像加密中的应用

混沌图像加密技术是近年来发展起来的一种新的图像加密技术,但目前采用的混沌系统大都是整数阶的一维、二维或三维混沌系统,很少使用分数阶的混沌系统。以Duffing系统为例,对分数阶Duffing系统和整数阶Duffing系统进行分析,当两个系统取相同参数并都达到混沌状态时,对混沌序列的伪随机性进行分析比较,可得到分数阶的混沌系统的伪随机性更强,并且分数导数的阶数也可以作为密钥,理论上比整数阶系统的密钥空间大得多,分数阶Duffing系统更适用于图像加密,并具有很好的加密效果。     

二维离散分数阶Fourier变换的双混沌图像加密算法

针对现今分数阶Fourier变换和传统混沌加密的不足,提出了一种基于二维离散分数阶Fourier变换的双混沌图像加密算法。该算法首先借助明文图像信息生成辅助密钥矩阵与输入密钥相结合得到混沌序列,再将生成的中间密文作为二维离散分数阶Fourier变换输入,最后进行置乱操作,使得明文信息得到很好的隐藏。通过实验仿真表明,该算法不仅能有效抵抗统计特征攻击、差分攻击,而且大大改善经传统分数阶Fourier变换后直方图像不平滑的缺点,达到很好的加密效果。     

混沌密钥调制DFRFT旋转因子的视频加密

现有分数阶傅里叶变换（FRFT）由于旋转因子的单一性很少应用于视频实时加密,而当前单纯混沌加密算法的安全性又存在着诸多缺陷。为此,提出一种新的视频实时加密算法——混沌密钥调制DFRFT旋转因子。该算法将混沌加密与分数阶傅里叶变换进行了有机结合。首先将离散分数阶傅里叶变换（DFRFT）的旋转因子用混沌密钥进行调制,然后用调制后的旋转因子对视频数据进行分数阶傅里叶变换,最终完成了对视频数据的加密系统。该加密系统在技术上实现了视频数据在客户端的实时采集、实时加密;密文在网络上的实时传输、密文在接收端的接收、实时解密和播放。实验结果表明,加、解密效果很好,满足了实时性与安全性的要求。对实验结果的理论、安全性分析表明,该算法简单易行、安全性高。该算法的安全性优于单纯的混沌加密算法或单纯傅里叶视频加密算法,且满足了实时性要求。为解决实时性与安全性冲突问题提供了一条新的途径。     

基于分数阶Fourier的双混沌加密算法

图像加密在生活中有着重要地位。针对传统的自然混沌系统安全性较低的问题,提出了改进的H-L双混沌和分数阶Fourier变换的图像加密算法。 以穷举法解出的 最优解序列的顺序为基础,将混沌映射与分数阶Fourier变换结合起来, 实现了空间域和频域的置乱,使明文信息得到了隐藏。仿真实验结果表明,通过改进的算法达到了较好的加密效果,其密钥空间大、计算复杂度低、敏感性强,能有效地抵抗统计攻击等,在图形信息安全方面有一定的应用价值。     

基于级联混沌系统的分数域语音加密算法

为保证语音信号在通信传输中的安全性,提出一种基于级联混沌系统的分数域语音加密算法。首先,对语音信号进行分组;其次,利用混沌系统获取分数傅里叶变换的阶次,各组数据对应的阶次呈动态变化;然后,采用具有较低计算复杂度的采样型分数傅里叶离散变换得到各组对应的分数域谱数据;最后,利用级联混沌系统依次对各组分数域进行数据加密,从而实现语音信号的整体加密。实验结果表明,所提算法对密钥具有极大的敏感度,得到的加密信号与原信号相比波形和分数域谱分布更均匀、相关性更小;同时与频域加密和固定阶次的分数域加密方法相比,该算法能有效增大密钥空间,同时降低计算复杂度。可见所提算法能够有效满足语音信号的实时安全传输要求。     

基于小波变换和FRFT的图像加密算法

为了提高图像的安全性,增强图像的加密效果,提出一种基于离散小波和分数阶傅里叶变换（FRFT）的图像加密算法。首先利用离散小波变换使图像信号稀疏化,然后对稀疏化处理后的图像进行离散FRFT处理,得到最终加密图像。MATLAB的仿真结果表明,和单一的小波变换相比,该算法的加密和解密效果较好,能够较好地隐藏图片的信息。     

基于分数阶Rossler混沌序列的图像加密

图像加密在当前信息安全堪忧的背景下显得尤为重要。传统加密方法是利用整数阶混沌序列或者其它低维离散序列的一个或者多个系数作为密钥对图像信息进行加密,由于加密序列相对简单且密钥空间较小,导致安全性不佳。本文提出基于分数阶Rossler混沌序列的图像加密算法,该算法以分数阶Rossler混沌系统的阶次和系统参数作为密钥,增大了密钥空间,而分数阶混沌系统特有的记忆特性,有效地增加了混沌序列的复杂性,使其在图像加密上更具安全性。     

Bit-level color image encryption algorithm based on coarse-grained logistic map and fractional chaos

A novel color image encryption algorithm based on coarse-grained fractional chaotic system signals is proposed in this paper. First, color images are divided into three channels, which are encrypted based on the corresponding three states of the chaotic system. Second, the chaotic systems are defined as fractional chaotic, in which the fractional order enlarges the parameter space. Third, the fractional chaotic signals are handled with unfixed coarse-grained methods instead of being utilized directly. In addition, the original image and the chaotic signals are divided into bit signals from the pixel values, and the high and low bits are encrypted, respectively. To demonstrate the effectiveness and robustness of the proposed color image encryption algorithm, its properties, including the key space, information entropy, correlation analysis, key sensitivity, and resistance to differential attacks, are provided using a numerical simulation.

     

The multistage homotopy analysis method: application to a biochemical reaction model of fractional order

In this paper, a new reliable algorithm called the multistage homotopy analysis method (MHAM) based on an adaptation of the standard homotopy analysis method (HAM) is presented to solve a time-fractional enzyme kinetics. This enzyme–substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The new algorithm is only a simple modification of the HAM, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding systems. Numerical comparisons between the MHAM and the classical fourth-order Runge–Kutta method in the case of integer-order derivatives reveal that the new technique is a promising tool for nonlinear systems of integer and fractional order.     

基于随机分数梅林变换的非线性图像加密算法

为了消除线性加密系统的安全隐患,提出了一种基于随机分数梅林变换的非线性图像加密算法。结合对数—极坐标变换和随机分数傅里叶变换构造了随机分数梅林变换,随机化过程用到的实对称随机矩阵由线性同余函数生成。输入的实值图像经随机分数梅林变换非线性加密,得到便于存储和传输的实值密文。该算法增加了线性同余函数的3个参数作为密钥,与分数梅林变换相比,随机分数梅林变换的分数阶密钥的敏感性更强。数值模拟表明该算法有较强的抗攻击能力,密钥灵敏度高,具有良好的安全性     

一种混沌流密码算法设计与实现

提出了一种基于Logistic混沌映射的流密码算法,该算法利用混沌本身所具有的随机特性,提出了一种新的对混沌系统扰动的方法。通过编码算法以及在混沌随机序列数字化的基础上引入一种新的非线性变换算法,以抵抗对混沌流密码系统的各种攻击。经统计测试和相关分析,密钥序列具有较高的线性复杂度和良好的密码学特性。整个加密系统的周期性大、灵活性好,加密模型还可以推广到其他混沌系统。     

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

This paper presents a new algorithm for computation of controllability and observability Gramians for an expanded state space form of integer‐order approximator to linear time‐invariant discrete‐time noncommensurate fractional‐order systems. The introduced methodology can significantly reduce the time complexity of the Gramians' calculation, being the main computational burden in modeling of discrete‐time fractional‐order systems by means of a high integer‐order expanded state space approximator and the balanced truncation reduction method. Simulation experiments illustrate an efficiency of the introduced methodology, in particular for low‐dimension fractional‐order systems and high implementation lengths.     

A numerical estimation of the fractional-order Liouvillian systems and its application to secure communications

This paper introduces a method for the numerical estimation of the fractional derivative of a signal, a smoothed sliding modes state observer is used to make the estimation. As application for the estimator a color image encryption algorithm is given, the algorithm is based on the synchronisation of fractional chaotic Liouvillian systems and its main characteristics are the capability to keep data safe from the most common types of cryptanalysis and handling large colour images while producing no data loss.     

State space approximation for general fractional order dynamic systems

Approximations for general fractional order dynamic systems are of much theoretical and practical interest. In this paper, a new approximate method for fractional order integrator is proposed. The poles of the approximate model are unrelated to the order of integrator. This feature shows benefits on extending the algorithm to the systems containing various fractional orders. Then a unified approximate method is derived for general fractional order linear or nonlinear dynamic systems via combining the proposed new method with the distributed frequency model approach. Numerical examples are given to show the wide applicability of our method and to illustrate the acceptable accuracy for approximations as well.     

基于主动控制的三维自治混沌系统的异结构反同步

分析了三维自治混沌系统之间的异结构反同步问题,并采用主动控制方法实现了一类三维自治混沌系统,如Lorenz系统,Chen系统和L櫣系统之间的两两反同步.数值仿真试验验证了该控制方案的有效性.     

AES加密算法在不停车收费系统中的应用

为了解决不停车收费系统中的数据安全问题,对数据加密过程进行了分析,介绍了AES加密算法的结构和几种变换的过程,围绕AES加密算法现阶段的安全性进行了探讨,选择出AES加密算法对系统中的敏感信息进行加密并通过语言实现;提出了各种加密算法都有一个有效期,为保证计算机系统安全稳定运行,要随着科学发展,对选择的加密算法进行更新。     

分数微积分理论在非线性车辆悬架滑模控制中的应用

基于分数微积分理论,提出分数阶”天棚”阻尼控制概念,并以它控制的悬架为参考模型,提出一个控制效果理想、鲁棒性好的悬架滑模控制的新策略,并应用于非线性悬架的动力学控制中．文中给出了一种精度较高,收敛稳定的分数阶系统的数值算法,最后对非线性悬架的滑模主动控制进行数值仿真,验证了新控制策略优良的控制效果．     

一类分数傅里叶变换图像加密算法的安全分析

从分数阶傅里叶变换的性质出发,对一类分数阶傅里叶变换图像加密算法进行分析。对原有算法结果图进行肉眼判断,提取图像中间结果数据进行对比分析,可知算法的密钥具有不敏感性,并且解密图具有很大失真。对分数傅里叶变换进行理论上的分析和讨论。分析及实验结果表明,直接使用分数阶傅里叶变换进行加密的算法对密钥并不敏感,存在安全隐患。为实现密文图像的显示和传输而引入的RGB映射将导致解密图像像素值失真。