Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bifurcation diagrams,the largest Lyapunov exponent plot,and the phase portraits are derived,respectively.Finally,with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem,we apply the discrete fractional map into color image encryption.After that,the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.

Dual Image Cryptosystem Using Henon Map and Discrete Fourier Transform

This paper introduces an efficient image cryptography system.The pro-posed image cryptography system is based on employing the two-dimensional(2D)chaotic henon map(CHM)in the Discrete Fourier Transform(DFT).The proposed DFT-based CHM image cryptography has two procedures which are the encryption and decryption procedures.In the proposed DFT-based CHM image cryptography,the confusion is employed using the CHM while the diffu-sion is realized using the DFT.So,the proposed DFT-based CHM image crypto-graphy achieves both confusion and diffusion characteristics.The encryption procedure starts by applying the DFT on the image then the DFT transformed image is scrambled using the CHM and the inverse DFT is applied to get the final-ly encrypted image.The decryption procedure follows the inverse procedure of encryption.The proposed DFT-based CHM image cryptography system is exam-ined using a set of security tests like statistical tests,entropy tests,differential tests,and sensitivity tests.The obtained results confirm and ensure the superiority of the proposed DFT-based CHM image cryptography system.These outcomes encourage the employment of the proposed DFT-based CHM image cryptography system in real-time image and video applications.

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.

An Integrable Symplectic Map Related to Discrete Nonlinear Schrdinger Equation

The method of nonlinearization of spectral problem is developed and applied to the discrete nonlinear Schr6dinger （DNLS） equation which is a reduction of the Ablowitz-Ladik equation with a reality condition. A new integable symplectic map is obtained and its integrable properties such as the Lax representation, r-matrix, and invariants are established.

Mapped Finite Element Discrete Variable Representation

Efficient numerical solver for the SchrSdinger equation is very important in physics and chemistry. The finite element discrete variable representation （FE-DVR） was first proposed by Rescigno and Mc-Curdy [Phys. Rev. A 62, 032706 （2000）] for solving quantum-mechanical scattering problems. In this work, an FE-DVR method in a mapped coordinate was proposed to improve the efficiency of the original FE-DVR method. For numerical demonstration, the proposed approach is applied for solving the electronic eigenfunctions and eigenvalues of the hydrogen atom and vibrational states of the electronic state 3E＋ of the Cs2 molecule which has long-range interaction potential. The numerical results indicate that the numerical efficiency of the original FE-DVR has been improved much using our proposed mapped coordinate scheme.

A Robust Image Watermarking Scheme Using Z-Transform, Discrete Wavelet Transform and Bidiagonal Singular Value Decomposition

Watermarking is a widely used solution to the problems of authentication and copyright protection of digital media especially for images,videos,and audio data.Chaos is one of the emerging techniques adopted in image watermarking schemes due to its intrinsic cryptographic properties.This paper proposes a new chaotic hybrid watermarking method combining Discrete Wavelet Transform(DWT),Z-transform(ZT)and Bidiagonal Singular Value Decomposition(BSVD).The original image is decomposed into 3-level DWT,and then,ZT is applied on the HH3 and HL3 sub-bands.The watermark image is encrypted using Arnold Cat Map.BSVD for the watermark and transformed original image were computed,and the watermark was embedded by modifying singular values of the host image with the singular values of the watermark image.Robustness of the proposed scheme was examined using standard test images and assessed against common signal processing and geometric attacks.Experiments indicated that the proposed method is transparent and highly robust.

Experiments of Reconstructing Discrete Atmospheric Dynamic Models from Data (I)

In this paper, we give some experimental results of our study in reconstructing discrete atmospheric dynamic models from data. After a great deal of numerical experiments, we found that the logistic map, xn +1= 1-uxn2 could be used in monthly mean temperature prediction when it was approaching the chaotic region, and its predictive results were in reverse states to the practical data. This means that the nonlinear developing behavior of the monthly mean temperature system is bifurcating back into the critical chaotic states from the chaotic ones.

Mapgis软件网格化效果比较

在物探等值线绘制中采用Mapgis的4种离散数据网格化方法,对物探规则网数据成图。经对比分析,使用距离幂函数反比加权法、泛克立格网格化方法绘制的等值线图与手工勾绘的等值线图异常形态基本一致,确定这两种方法作为物探等值线绘制的网格化模型。

A Hierarchy of Lax Integrable Lattice Equations, Liouville Integrability and a NewIntegrable Symplectic Map

A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discrete Hamiltonian systems. A new integrable symplectic map is given by binary Bargmann constraint of the resulting hierarchy. Finally, an infinite set of conservation laws is given for the resulting hierarchy.

Fractal structures in a generalized square map with exponential terms

Fractal structures in a generalized squared map with exponential terms are expanded in this paper. We describe how complex behaviors can arise as the parameters change. The appearances of different kinds of fractal structures, in both the attractive and the divergent regions, and most interestingly, on small regular islands embedded in the chaotic region, are manifested to have a variety of extraordinary geometries in the parameter plane.

A multiscale spatio-temporal framework to regionalize annual precipitation using k-means and self-organizing map technique

Determination of homogenous precipitation-based regions is a very important task in effective management of water resources. The present study tried to propose an effective precipitation-based regionalization methodology by conjugating both temporal pre-processing and spatial clustering approaches in a way to take advantage of multiscale properties of precipitation time series. Annual precipitation data of 51 years(1960-2010) for 31 rain gauges(RGs) were collected and used in proposed clustering approaches. Discreet wavelet transform(DWT) was used to capture the time-frequency attributes of the time series and multiscale regionalization was performed by using k-means and Self Organizing Maps(SOM) clustering techniques. Daubechies function(db) was selected as mother wavelet to decompose the precipitation time series. Also, proper boundary extensions and decomposition level were applied. Different combinations of the approximation(A) and detail(D) coefficients were used to determine the input dataset as a basis of spatial clustering. The proposed model's efficiency in spatial clustering stage was verified using three different indexes namely, Silhouette Coefficient(SC), Dunn index and Davis Bouldin index(DB). Results approved superior performance of k-means technique in comparison to SOM. It was also deduced that DWT-based regionalization methodology showed improvements in comparison to historical-based models. Cross mutual information was used to investigate the RGs of cluster 3's homogeneousness in DWT-k-means approach. Results of non-linear correlation approach verified homogeneity of cluster 3. Verifications based on mean annual precipitation values of rain gauges in each cluster also approved the capability of multiscale approach in precipitation regionalization.

A Hierarchy of Integrable Lattice Soliton Equations and New Integrable Symplectic Map

Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses discrete bi-Hamiltonian structure. A new integrable symplectic map and finite-dimensional integrable systems are given by nonlinearization method. The binary Bargmann constraint gives rise to a Biicklund transformation for the resulting integrable lattice equations. At last, conservation laws of the hierarchy are presented.

VBA和MapGIS在化探异常解释评价中的应用

化探异常下限的确定和图件的编制是化探异常解释评价工作最基础也是最关键的。笔者通过多年的探讨和实践,将VBA与MapGIS结合起来运用到化探异常解释评价工作中,取得了一些成效。文中,笔者以均值加2倍离差方法为例,探讨了运用VBA编程计算确定化探异常下限的基本思路和一般方法,详细介绍了离散点位数据图在MapGIS中直接成图的方法,指出了VBA与MapGIS在地矿行业中具有广阔的应用前景。

Generalized synchronization between different chaotic maps via dead-beat control

This paper presents a new scheme to achieve generalized synchronization（GS） between different discrete-time chaotic（hyperchaotic） systems.The approach is based on a theorem,which assures that GS is achieved when a structural condition on the considered class of response systems is satisfied.The method presents some useful features：it enables exact GS to be achieved in finite time（i.e.,dead-beat synchronization）;it is rigorous,systematic,and straightforward in checking GS;it can be applied to a wide class of chaotic maps.Some examples of GS,including the Grassi-Miller map and a recently introduced minimal 2-D quadratic map,are illustrated.

基于MapGIS的极值无偏地球化学等值线图生成方法

在MapGIS中自动生成地球化学等值线时,用三角剖分方法能最大程度地保留原始信息,但其图面可视化效果差,后期修改整饰的工作量巨大。用Gird网格化数据生成等值线,又会出现元素浓集中心和极值点位置存在一定程度的偏差和位移的情况,对后期的地球化学特征分析和异常查证工作带来了不便。经过研究发现,把离散采样点分析数据中的极值点提取出来,按照一定的阀值给极值点建立缓冲区,通过点对区空间分析,把规则网格数据中位置距离极值点较近,可能影响到三角剖分网优化效果的畸形网格节点剔除;再把离散的极值点数据和剔除了畸形网格节点的规则网格数据合并,进行三角剖分等值线追踪,很好地弥补了三角剖分生成等值线可视化效果差和网格化数据生成等值线出现浓集中心偏移的不足。该方法无需借助其他软件工具,在MapGIS中即可实现极值无偏移的地球化学等值线生成,既兼顾了制图精度,又满足了可视化效果,有很强的实用性。

基于MapGIS三角剖分数据扩边方法的探讨

由于1∶5万水系沉积物测量样品布设原则和采样条件的限制,我们无法把样品设计并采集到图幅的边沿上,导致后期数据处理成图时,用三角剖分勾绘出的平面等值线图周边呈现不规则锯齿状,且与图幅边沿有一定的距离,既不完整也不美观。利用MapGIS的离散数据网格化功能,先对离散分布的1∶5万水系沉积物测量原始分析数据进行网格化插值处理,用插值后的网格数据填充到图幅边沿的空缺部位,再进行三角剖分绘制平面等值线图,就可以科学合理的解决三角剖分绘制等值线图的扩边问题。

Bifurcation Analysis of Reduced Network Model of Coupled Gaussian Maps for Associative Memory

This paper proposes an associative memory model based on a coupled system of Gaussian maps. A one-dimensional Gaussian map describes a discrete-time dynamical system, and the coupled system of Gaussian maps can generate various phenomena including asymmetric fixed and periodic points. The Gaussian associative memory can effectively recall one of the stored patterns, which were triggered by an input pattern by associating the asymmetric two-periodic points observed in the coupled system with the binary values of output patterns. To investigate the Gaussian associative memory model, we formed its reduced model and analyzed the bifurcation structure. Pseudo-patterns were observed for the proposed model along with other conventional associative memory models, and the obtained patterns were related to the high-order or quasi-periodic points and the chaotic trajectories. In this paper, the structure of the Gaussian associative memory and its reduced models are introduced as well as the results of the bifurcation analysis are presented. Furthermore, the output sequences obtained from simulation of the recalling process are presented. We discuss the mechanism and the characteristics of the Gaussian associative memory based on the results of the analysis and the simulations conducted.

分数阶忆阻Henon映射的可控多稳定性及其视频加密应用

基于局部有源离散忆阻器构建一种能够产生任意数量共存吸引子的分数阶忆阻Henon映射.该映射的不动点数量由忆阻器内部参数控制,实现可控的同质多稳定性,适合基于混沌的工程应用.通过相图、分岔图、最大Lyapunov指数和吸引盆等方法揭示该映射的复杂动力学行为.数值模拟结果表明,该分数阶映射能够产生各种周期轨道、混沌吸引子和倍周期分岔等现象.随后使用ARM数字平台实现该系统,实验结果验证其物理可实现性.最后,基于该映射设计一种视频加密算法,并通过安全性分析验证该加密算法能够有效保证视频的安全传输.

离散色散光域傅里叶变换的延时和带宽扩展研究

光域傅里叶变换为射频频谱分析提供了一种新的解决方案。光域傅里叶变换主要受限于大的二阶色散的获得,而离散傅里叶变换只需要控制离散点的相位,理论上可以解决大色散的获得问题。文章利用光纤环作为离散色散器件,用线性调频信号作为待测信号,进行了光域离散傅里叶变换的研究。该系统是一个快速傅里叶变换系统,每次变换用时约2.07ns。用示波器观测线性调频信号变换前与变换后的波形延迟,可以测出该系统的变换延时,约为100ns,其延时大小主要取决于系统中的光纤长度。该系统可以实现对信号的不间断处理。为了扩展系统的瞬时带宽,对片上集成光微环组方案的可实现性进行了分析。

忆阻超混沌映射的可调控性设计及光纤保密通信系统构建

通过引入平方忆阻函数非线性反馈,构建离散超混沌映射,并实现超混沌序列的全局调幅、局部调幅以及直接偏置调控。混沌映射的可调控性通过离散忆阻的阻值函数和内部变量积分速度来实现。简易的忆阻约束关系同时赋予了直接偏置调控的可能性,通过额外引入常数项参数可实现一维状态变量的直接偏置调控。基于RISC-V单片机CH32V307实现了所提出的可调控超混沌映射,并通过美国国家标准与技术研究院测试证明了超混沌序列的伪随机属性。基于以上超混沌映射构建了正交啁啾复用-非正交多址接入物理层加密方案,实验完成了2 km弱耦合七芯光纤通信的误码率测试,进一步证明了基于离散忆阻构建的超混沌加密正交啁啾复用-非正交多址接入系统可实现数据的可靠传输和解密,有效保护数据安全。