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 k U+2082 and k U+2083, 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 U+0028 XOR U+0029 encryption algorithm. The encryption scheme could increase randomness and improve speed of encryption. © 2017 Chinese Association of Automation.

Rucklidge-based memristive chaotic system:Dynamic analysis and image encryption

A new four-dimensional(4D)memristive chaotic system is obtained by introducing a memristor into the Rucklidge chaotic system,and a detailed dynamic analysis of the system is performed.The sensitivity of the system to parameters allows it obtains 16 different attractors by changing only one parameter.The various transient behaviors and excellent spectral entropy and C0 complexity values of the system can also reflect the high complexity of the system.A circuit is designed and verified the feasibility of the system from the physical level.Finally,the system is applied to image encryption,and the security of the encryption system is analyzed from multiple aspects,providing a reference for the application of such memristive chaotic systems.

A new image encryption algorithm based on the fractional-order hyperchaotic Lorenz system

We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded in the proposed algorithm to enhance the security. Such an algorithm is detailed in terms of security analyses, including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. The experimental results demonstrate that the proposed image encryption scheme has the advantages of large key space and high security for practical image encryption.

A New Study in Encryption Based on Fractional Order Chaotic System

In this paper, we introduce a novel approach to achieve the data encryption. The fractional order Lorenz chaotic system is used to generate the chaotic sequence and the characteristics of the chaotic sequence are studied. Some examples concerned with text and image encryption are also presented in the paper, which show exciting results by the approach we introduced.

A general method for synchronizing an integer-order chaotic system and a fractional-order chaotic system

This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By intro- ducing fractional-order operators into the controllers, the addressed problem is transformed into a synchronization one among integer-order systems. A novel general method is presented in the paper with rigorous proof. Based on this method, effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order, and for the synchronization between an integer-order Chen system and a fractional-order Liu system. Numerical results, which agree well with the theoretical analyses, are also given to show the effectiveness of this method.

Control of fractional chaotic and hyperchaotic systems based on a fractional order controller

We present a new fractional-order controller based on the Lyapunov stability theory and propose a control method which can control fractional chaotic and hyperchaotic systems whether systems are commensurate or incommensurate. The proposed control method is universal, simple, and theoretically rigorous. Numerical simulations are given for several fractional chaotic and hyperchaotic systems to verify the effectiveness and the universality of the proposed control method.

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.

No-chattering sliding mode control in a class of fractional-order chaotic systems

A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.

Circuit realization of the fractional-order unified chaotic system

This paper studies the chaotic behaviours of the fractional-order unified chaotic system. Based on the approximation method in frequency domain, it proposes an electronic circuit model of tree shape to realize the fractional-order operator. According to the tree shape model, an electronic circuit is designed to realize the 2.7-order unified chaotic system. Numerical simulations and circuit experiments have verified the existence of chaos in the fraction-order unified system.

Prescribed performance synchronization for fractional-order chaotic systems

In this paper the synchronization for two different fractional-order chaotic systems, capable of guaranteeing synchronization error with prescribed performance, is investigated by means of the fractional-order control method. By prescribed performance synchronization we mean that the synchronization error converges to zero asymptotically, with convergence rate being no less than a certain prescribed function. A fractional-order synchronization controller and an adaptive fractional-order synchronization controller, which can guarantee the prescribed performance of the synchronization error,are proposed for fractional-order chaotic systems with and without disturbances, respectively. Finally, our simulation studies verify and clarify the proposed method.

Control of a fractional chaotic system based on a fractional-order resistor-capacitor filter

We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional- order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed control method is simple, robust, and theoretically rigorous, and its anti-noise performance is satisfactory. Numerical simulations are given for several fractional chaotic systems to verify the effectiveness and the universality of the proposed control method.

An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree

This paper proposes an image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree.Firstly,other programming software is used to perform the middle order traversal,and the plaintext image is sorted according to the middle order traversal sequence on the permutation.Secondly,the chaotic sequence is generated using the coupled map lattice to set the chaotic interference value.Finally,the XOR operation between the adjacent pixel values of the replacement image is completed to generate the ciphertext matrix.The simulation and experimental results show that the proposed algorithm can resist typical attacks and has good robustness.

Robust Finite-time Synchronization of Non-identical Fractional-order Hyperchaotic Systems and Its Application in Secure Communication

This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.

Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application

Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link.In this paper,considering the complex network with uncertain parameters,new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization(FTCPS).In addition,based on fractional-order Lyapunov functional method and finite-time stability theory,the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters.Meanwhile,numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters.Finally,the network is applied to image encryption,and the security analysis is carried out to verify the correctness of this method.

A medical image encryption algorithm based on synchronization of time-delay chaotic system

This paper presents a new synchronization method of the time-delay chaotic system and its application in medical image encryption. Compared with the existing techniques, the error system is greatly simplified because many coupled items can be considered zero items. An improved image encryption scheme based on a dynamic block is proposed. This scheme divides the image into dynamic blocks, and the number of blocks is determined by a previous block cipher. Numerical simulations are provided to illustrate the effectiveness of the proposed method.

An improved image encryption algorithm based on chaotic maps

Recently, two chaotic image encryption schemes have been proposed, in which shuffling the positions and changing the grey values of image pixels are combined. This paper provides the chosen plaintext attack to recover the corresponding plaintext of a given ciphertext. Furthermore, it points out that the two schemes are not sufficiently sensitive to small changes of the plaintext. Based on the given analysis, it proposes an improved algorithm which includes two rounds of substitution and one round of permutation to strengthen the overall performance.

A Cross-Plane Color Image Encryption Algorithm Based on 1D-SLM

With the rapid development of 5G technology,it has become fast and easy for people to transmit information on the Internet.Digital images can express information more intuitively,so transmitting information through images has excellent applications.This paper uses a new chaotic system called 1D-Sin-Logistic-Map(1D-SLM).1D-SLM has two control parameters,which can provide larger parameter space,and the parameter space in the chaotic state is continuous.Through Lyapunov exponent analysis(LE),bifurcation diagrams analysis,spectral entropy analysis(SE),and 0-1 test,it is verified that 1D-SLM has complex dynamic behavior and is very suitable for cryptography.Compared with other 1D chaotic systems,the 1D-SLM has a larger Lyapunov exponent(LE)and spectral entropy(SE).For color image encryption algorithms,only relying on chaotic mapping is not enough to ensure security.So combined with 1D-SLM,we design a color image encryption algorithm,which is implemented by plane expansion,which reduces the correlation between the three channels of color images.The experimental results show that the proposed cross-plane color image encryption algorithm is safe and resistant to common attack methods.

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.

Image encryption based on a delayed fractional-order chaotic logistic system

A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system.In the process of generating a key stream,the time-varying delay and fractional derivative are embedded in the proposed scheme to improve the security.Such a scheme is described in detail with security analyses including correlation analysis,information entropy analysis,run statistic analysis,mean-variance gray value analysis,and key sensitivity analysis.Experimental results show that the newly proposed image encryption scheme possesses high security.

A new color image encryption scheme based on chaos synchronization of time-delay Lorenz system

In this paper, a new image encryption scheme is presented based on time-delay chaos synchronization. Compared with existing methods, a new method is pro- posed and a lot of coupled items can be taken as zero items to simplify the whole system. A simple linear controller is introduced to realize time-delay chaos synchronization and image encryption. The positions of the image pixels are firstly shuffled and then be hidden in the cartier image. The address codes of the chaotic sequences are adopted to avoid the disturbances induced by the initial value and computer accuracy error. Simulation results for color image are provided to illustrate the effectiveness of the proposed method. It can be seen clearly that the system can converge quickly and the image can be encrypted rapidly.