基于多目标遗传算法的8×8 S盒的优化设计方法

混沌系统具有非线性、伪随机性、初始值敏感等特性,为基于动力系统构造性能良好的S盒提供了基础,进一步保证了分组加密算法安全性.目前,基于混沌构造S盒的方法大多数针对单个性能指标进行优化,难以获得全面的性能提升.针对此问题,结合混沌映射与多目标遗传算法,提出了一种新的S盒设计方法.首先,利用混沌映射的特性产生初始S盒种群;然后,以S盒的非线性度和差分均匀性为优化目标,基于遗传算法框架对上述两指标进行优化.针对S盒的特点,在优化算法中引入了交换操作,设计了新的变异操作以及非支配序集计算,有效提升了S盒的非线性度和差分均匀性.实验结果表明该算法产生的S盒其差分均匀度为6,非线性度值至少为110,有效提升了S盒的综合性能.

Adaptive generalized synchronization between Chen system and a multi-scroll chaotic system

Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is designed, by which the controlled Chen system can be synchronized with a multi-scroll chaotic system including unknown parameters. The Lyapunov direct method is exploited to prove that the synchronization error and parameter identification error both converge to zero. Numerical simulation results verify the feasibility of the proposed method further.

Chaotic Motion Analysis for a Coupled Magnetic-Flow-Mechanical Model of the Rectangular Conductive Thin Plate

The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin plate theory,considering geometric nonlinearity and using the principle of virtualwork,the nonlinearmotion partial differential equation of the rectangular conductive thin plate is deduced.Using the separate variable method and Galerkin’s method,the system motion partial differential equation is converted into the general equation of the Duffing equation;the Hamilton system is introduced,and the Melnikov function is used to analyze the Hamilton system,and obtain the critical surface for the existence of chaos.The bifurcation diagram,phase portrait,time history response and Poincarémap of the vibration system are obtained by numerical simulation,and the correctness is demonstrated.The results showthatwhen the ratio of external excitation amplitude to damping coefficient is higher than the critical surface,the system will enter chaotic state.The chaotic motion of the rectangular conductive thin plate is affected by different magnetic field distributions and airflow.

具有稚虫迁徙机制的S型自适应混沌蜉蝣算法

针对蜉蝣优化算法(MA)全局搜索能力较弱,对子代优秀个体有效信息利用不够充分的缺点,以及在计算中后期易陷入局部收敛,进而影响优化效果的问题,提出一种具有稚虫迁徙机制的S型自适应混沌蜉蝣优化算法(S-AMA)。S-AMA算法首先采用Logistic混沌映射产生蜉蝣种群,增加算法初期种群的多样性;随后,将蜉蝣生命周期进行数学建模,并引入S型生命系数替换原有的重力惯性系数,动态调整算法探索能力和开发能力间的平衡性;最后,根据蜉蝣在缺氧环境下的种群活动,引入稚虫迁徙机制强化子代优秀个体摆脱局部最优的能力,进而更加充分地搜索最优解附近的区域,以增强算法的收敛精度。实验部分将S-AMA应用于标准函数测试集,并分别进行优化对比实验、Wilcoxon秩和检验。结果表明:与对比算法相比,S-AMA算法具有更好的寻优能力、收敛速度及鲁棒性。

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.

Chaotic attractor transforming control of hybrid Lorenz-Chen system

Based on passive theory, this paper studies a hybrid chaotic dynamical system from the mathematics perspective to implement the control of system stabilization. According to the Jacobian matrix of the nonlinear system, the stabilization control region is gotten. The controller is designed to stabilize fast the minimum phase Lorenz-Chen chaotic system after equivalently transforming from chaotic system to passive system. The simulation results show that the system not only can be controlled at the different equilibria, but also can be transformed between the different chaotic attractors.

Hybrid Synchronization of a Chen Hyper-Chaotic System with Two Simple Linear Feedback Controllers

This paper brings attention on the hybrid synchronization of the Chen hyper-chaotic system by using some simple controllers. We give the sufficient conditions for achieving the goal by using the Lyapunov stability theory, and we verify our conclusion by numerical simulations.

一种基于广义Chen's混沌系统的图像加密新算法

根据高维混沌系统具有更高安全性的特点,提出一种基于三维Chen s混沌系统的数字图像加密新算法,通过置乱图像像素的空间位置和改变像素值来混淆密文图像和明文图像之间的关系。利用Chen s混沌系统的二维序列置乱图像像素的空间位置;然后,由Chen s混沌系统输出的三维混沌序列得到适合灰度图像或真彩色图像加密的密钥序列,利用混沌密钥序列对置乱图像进行逐像素加密。研究结果表明,该算法具有良好的像素值混淆、扩散性能和较大抵抗强力攻击的密钥空间,加密图像像素值具有类随机均匀分布特性,且相邻像素值具有零相关特性,所提出的方案具有较高安全性。

Chen’s混沌动力系统的控制

为了研究Chen’s混沌动力系统的混沌控制问题,通过双线性反馈方法将混沌控制在不稳定的平衡点,给出了非反馈周期信号控制混沌系统在不稳定周期轨道上(UPO)的方法。应用Lya-punov定理和Routh-Hurwitz判据分析了被控系统的稳定条件,数字仿真结果证明了控制方法的正确性、有效性。给出了控制Chen’s混沌动力系统到每一个平衡点的具体方法和稳定条件,得出了运用周期信号控制Chen’s混沌动力系统到高周期轨道的判定方法,解决了Chen’s混沌动力系统的控制问题。

基于Chen超混沌系统的改进AES算法的实现

本文针对传统AES算法存在的S盒迭代周期短问题,采用新的仿射变换对进行改进;针对密钥扩展过程中轮密钥与种子密钥之间存在强关联性的缺陷,充分考虑超混沌系统特性与流密码优点的结合,应用在AES算法上对密钥扩展过程进行优化。实验及安全性分析的结果表明:基于Chen超混沌系统的改进AES算法能够更有效的保障数据安全。

非线性复杂动力系统——Chen’s系统的混沌控制

主要介绍了Chen’s混沌系统,并对其控制作了研究,提出了3种利用线性反馈控制Chen’s系统到平衡点的方法和1种利用非线性反馈控制系统到周期轨的方法,并给出了相应的证明及数值仿真。

Chen's混沌系统的同步控制

主要对非线性复杂动力系统——Chen's系统的同步控制作出了研究,主要利用驱动-响应同步原理,设计了4种不同的非线性反馈控制器来控制2个初始条件不同的Chen's系统达到同步。

Chen’s系统混沌行为负反馈控制

研究了Chen’s系统的非线性动力学行为及稳定性 ,采用负反馈控制方法对Chen’s系统的混沌行为进行控制 ,把该系统控制到指定的平衡态和希望的振荡周期轨道上 .并对控制方法的混沌控制过程进行理论分析与数值研究 ,得到了一致的结果 .

基于Chen系统的DSP混沌图像加密

介绍了在DSP基础上,实现数字图像的混沌加密及硬件实现方法。根据离散化和数字化处理技术,对三维Chen混沌系统作离散化处理,用C语言和DSP技术产生三维Chen混沌迭代序列,分别对数字图像进行混沌加密和解密。基于芯片型号为TMS32 0VC5509A的DSP开发平台,以灰度图像为例,设计了Chen混沌序列对数字图像进行加密与解密算法,给出了DSP硬件实现结果表明,改善了安全性、提高了速度、满足了实时性要求。

Synchronization of chaotic systems with different orders

A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state wriables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.

四维Chen系统耦合改进的S盒的图像加密算法

为了克服传统AES加密算法生成的固定S盒所带来的不足,提出了一种四维Chen系统耦合改进的S盒图像加密算法.改进的S盒生成结合了超混沌序列,使其具有优良的正交性及复杂性等特征.首先,由超混沌序列排列组合成S盒,分别替换彩色图像的三基色灰度值.然后,利用不同初始值形成的混沌序列分别对替换后的三基色灰度值进行置乱操作.最后,将置乱后的灰度值进行二进制按位异或运算,完成图像的加密.仿真实验验证了此算法的优越性.

Adaptive synchronization of a critical chaotic system

This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory,a novel adaptive control law is derived for the synchronization of a new chaotic system with known or unknown system parameters.Theoretical analysis and numerical simulations showthe effectiveness and feasibility of the proposed schemes.

A novel study on the impulsive synchronization of fractional-order chaotic systems

The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. The synchronization criterion is suitable for the case of the order 0 〈 q ≤ 1. It is more general than those of the known results. Simulation results are given to show the effectiveness of the proposed synchronization criterion.

Applying and Comparison of Chaotic-Based Permutation Algorithms for Audio Encryption

This research presents,and claries the application of two permutation algorithms,based on chaotic map systems,and applied to a le of speech signals.They are the Arnold cat map-based permutation algorithm,and the Baker’s chaotic map-based permutation algorithm.Both algorithms are implemented on the same speech signal sample.Then,both the premier and the encrypted le histograms are documented and plotted.The speech signal amplitude values with time signals of the original le are recorded and plotted against the encrypted and decrypted les.Furthermore,the original le is plotted against the encrypted le,using the spectrogram frequencies of speech signals with the signal duration.These permutation algorithms are used to shufe the positions of the speech les signals’values without any changes,to produce an encrypted speech le.A comparative analysis is introduced by using some of sundry statistical and experimental analyses for the procedures of encryption and decryption,e.g.,the time of both procedures,the encrypted audio signals histogram,the correlation coefcient between specimens in the premier and encrypted signals,a test of the Spectral Distortion(SD),and the Log-Likelihood Ratio(LLR)measures.The outcomes of the different experimental and comparative studies demonstrate that the two permutation algorithms(Baker and Arnold)are sufcient for providing an efcient and reliable voice signal encryption solution.However,the Arnold’s algorithm gives better results in most cases as compared to the results of Baker’s algorithm.