Hyperchaotic Lorenz System Research Articles

Image Encryption Based on Dynamic Filtering and Bit Cuboid Operations

As one of the most widely used media types, images play an important role in the era of the Internet. And hence how to enhance the security of images has become a hot topic in the field of information security. However, due to some intrinsic characteristics of images, image security is still a challenging task. For the purpose of coping with this issue, in this paper, we propose a novel algorithm that combines a hyperchaotic system, dynamic filtering, and bit cuboid operations, namely, DFBC, for image encryption. Specifically, the proposed DFBC consists of four steps: firstly, a 7D Lorenz hyperchaotic system is utilized to generate a pseudorandom sequence; secondly, variable 1D filters are derived from the pseudorandom sequence, and dynamic filtering is conducted on each pixel of an image; thirdly, a diffusion scheme is performed and then the image is transformed to a bit cuboid; and, finally, various types of permutation (rearranging, symmetry, rotation, zigzag, and global bit permutation) are performed on the bit cuboid. The experiments on several testing images demonstrate that the DFBC achieves state‐of‐the‐art results in terms of several evaluation criteria, showing that the DFBC is promising for image encryption.

Function-based hybrid synchronization types and their coexistence in non-identical fractional-order chaotic systems

This paper presents new results related to the coexistence of function-based hybrid synchronization types between non-identical incommensurate fractional-order systems characterized by different dimensions and orders. Specifically, a new theorem is illustrated, which ensures the coexistence of the full-state hybrid function projective synchronization (FSHFPS) and the inverse full-state hybrid function projective synchronization (IFSHFPS) between wide classes of three-dimensional master systems and four-dimensional slave systems. In order to show the capability of the approach, a numerical example is reported, which illustrates the coexistence of FSHFPS and IFSHFPS between the incommensurate chaotic fractional-order unified system and the incommensurate hyperchaotic fractional-order Lorenz system.

A novel plaintext-related image encryption scheme using hyper-chaotic system

A novel and secure plaintext-related image encryption scheme is given in this paper using hyper-chaotic Lorenz system and hash function. In our scheme, we used the classical encryption architecture: permutation and diffusion. The initial conditions of hyper-chaotic Lorenz system which is employed in permutation and key stream generation algorithms are generated by information of the original image and initial key. Therefore, the encryption process has a strong relationship with plain image in the proposed scheme. So, our work performs excellently on resisting the known-plaintext attack. In addition, results of many widely used security analyses and comparisons with other works show that our work has outstanding security performance for the digital image communication.

A quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections

In this paper, a quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections is proposed. Firstly, in order to enhance the complexity of trajectory, three impulse signals values are injected into coupled hyper-chaotic Lorenz system during iterations. Then, six sequences generated from this system are used to encrypt red, green and blue components of the quantum color original image by XOR operations and right cyclic shift operations. Six initial values and three impulse signals values are used as keys, which could reduce the burden of keys transmission and make the cryptosystem own a key space large enough to resist exhaustive attack, even the attack from a quantum computer. Numerical simulations demonstrate that the proposed encryption scheme has a good feasibility and effectiveness for protecting quantum color images and is more secure in comparison with other encryption algorithms.

A Weak Signal Detection Application Based on Hyperchaotic Lorenz System

A Weak Signal Detection Application Based on Hyperchaotic Lorenz System

Secure communication for non-ideal channel via robust TS fuzzy observer-based hyperchaotic synchronization

This paper proposes a novel hyperchaotic secure communication scheme for non-ideal communication channels. The proposed approach employs Takagi–Sugeno (TS) fuzzy model and linear matrix inequality (LMI) technique to design a controller which synchronizes the hyperchaotic transmitter and receiver systems. In the presented method, only few numbers of states are needed to be transformed which is consistent with the practical limitations of a non-ideal channel and highly secure communication. Therefore, a robust fuzzy observer is proposed to estimate the other states of the transmitter at the receiver side. Furthermore, since the channel is non-ideal, H∞ performance criterion is employed to derive robust observer and controller against the external disturbance and noise. In order to make the proposed approach more applicable, the sufficient controller and observer design conditions are formulated in terms of linear matrix inequalities (LMIs) which can be solved by convex optimization techniques. In addition, to further remove the effect of the noise on the information recovery, a moving average filter is utilized. Finally, to show the effectiveness and advantages of the proposed approach, the hyperchaotic Lorenz system is considered and the signal is analyzed at the transmitter and receiver sides. Then, the results obtained show the superiority and effectiveness of the proposed method compared with those of the existing approaches.

Coexistence of identical synchronization, antiphase synchronization and inverse full state hybrid projective synchronization in different dimensional fractional-order chaotic systems

The topic related to the coexistence of different synchronization types between fractional-order chaotic systems is almost unexplored in the literature. Referring to commensurate and incommensurate fractional systems, this paper presents a new approach to rigorously study the coexistence of some synchronization types between nonidentical systems characterized by different dimensions and different orders. In particular, the paper shows that identical synchronization (IS), antiphase synchronization (AS), and inverse full state hybrid projective synchronization (IFSHPS) coexist when synchronizing a three-dimensional master system with a fourth-dimensional slave system. The approach, which can be applied to a wide class of chaotic/hyperchaotic fractional-order systems in the master-slave configuration, is based on two new theorems involving the fractional Lyapunov method and stability theory of linear fractional systems. Two examples are provided to highlight the capability of the conceived method. In particular, referring to commensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Rössler system of order 2.7 and the hyperchaotic four-dimensional Chen system of order 3.84. Finally, referring to incommensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Lü system of order 2.955 and the hyperchaotic four-dimensional Lorenz system of order 3.86.

Hidden attractors in a new complex generalised Lorenz hyperchaotic system, its synchronisation using adaptive contraction theory, circuit validation and application

Objectives of the paper are (1) to design two new real and complex no equilibrium point hyperchaotic systems, (2) to design synchronisation technique for the new systems using the contraction theory and (3) to validate the results by using circuit realisation. First a new no equilibrium point hyperchaotic system is developed using a 3-D generalised Lorenz system; then using the new system a new complex no equilibrium point hyperchaotic system is reported. Both the new systems have hidden chaotic attractors. Various dynamical behaviours are observed in the new systems like chaotic, periodic, quasi-periodic and hyperchaotic. Both the systems have inverse crisis route to chaos with the variation of parameter a and crisis route to chaos with the variation of parameters $$b,\ c$$ and d. These phenomena along with hidden attractors in a complex hyperchaotic system are not seen in the literature. Synchronisation between the identical new hyperchaotic systems is achieved using the contraction theory. Further the synchronisation between the identical new complex hyperchaotic systems is achieved using adaptive contraction theory. The proposed synchronisation strategies are validated using the MATLAB simulation and circuit implementation results. Further, an application of the proposed system is shown by transmitting and receiving an audio signal.

A one-time pad color image cryptosystem based on SHA-3 and multiple chaotic systems

A novel image encryption algorithm is proposed that combines the SHA-3 hash function and two chaotic systems: the hyper-chaotic Lorenz and Chen systems. First, 384 bit keystream hash values are obtained by applying SHA-3 to plaintext. The sensitivity of the SHA-3 algorithm and chaotic systems ensures the effect of a one-time pad. Second, the color image is expanded into three-dimensional space. During permutation, it undergoes plane-plane displacements in the x, y and z dimensions. During diffusion, we use the adjacent pixel dataset and corresponding chaotic value to encrypt each pixel. Finally, the structure of alternating between permutation and diffusion is applied to enhance the level of security. Furthermore, we design techniques to improve the algorithm's encryption speed. Our experimental simulations show that the proposed cryptosystem achieves excellent encryption performance and can resist brute-force, statistical, and chosen-plaintext attacks.

A Chaotic System Based Image Encryption Scheme with Identical Encryption and Decryption Algorithm

A new symmetric key image encryption scheme based on hyper-chaotic Lorenz system is proposed. The encryption process and the decryption process are identical in the proposed scheme. They both include two diffusion operations, one plaintext-related scrambling operation and three matrix rotating 180 degrees operations. The hyper-chaotic Lorenz system is employed to generate the secret code streams to encrypt the plain image, and to implement the diffusion process with XOR operation. The plaintext-related scrambling is used in this scheme to make different plain images correspond to different secret code streams even when the secret keys are the same, so that the scheme can fight against the chosen/known plaintext attacks. Simulation results show that the proposed scheme has the merits of high encryption speed, large key space, strong key sensitivity, strong plaintext sensitivity, good statistical properties of cipher-text, and etc., and can be used in practical communications.

FPGA implementation of fractional-order chaotic systems

This paper presents the digital implementation of fractional-order (FO) chaotic systems on Field Programmable Gate Array (FPGA). In the proposed work Simulink model of each chaotic system is first realized using HDL coder of MATLAB, wherein each coefficient and signal is represented using a fixed number of bits. The construced design is translated into VHDL code using hardware generation block. This code is further translated into bitstream file using Quartus software. The chaotic system is implemented by downloading the obtained bitstream file into Altera FPGA Cyclone IV E (EP4CE11529C7N) chip. A methodology has been developed to construct FO chaotic system using HDL coder. Five different FO chaotic systems, viz., Lorenz, Chen, Lü, Arneodo, and Lorenz Hyperchaotic system have been presented in the paper to illustrate the methodology. The systems have been implemented on FPGA platform. Analysis of each chaotic system is carried out on the basis of hardware resource utilization, static power analysis and synthesis frequency on FPGA. The results show that FPGA provides high-speed realizations with the desired accuracy and low power consumption for FO chaotic systems.

Dynamic analysis of a 5D fractional-order hyperchaotic system

In this paper, the fractional-order 5D hyperchaotic system is proposed based on the hyperchaotic Lorenz system. Fractional-order chaotic systems are often three- or four-dimensional. There are few results about high dimension fractional-order systems. For this 5D hyperchaotic system, the stability of equilibrium points is analyzed by means of the stability theory of fractional systems. Then the fractional bifurcation is investigated. It is found that the system admits bifurcations with varying fractional-order and parameters, respectively. Under different bifurcation parameters, some conditions ensuring the bifurcations are presented. Finally, numerical simulations are presented to confirm the given analytical results.

Modified function projective combination synchronization of hyperchaotic systems

In this work, a novel combination synchronization scheme in which synchronization of a new combination hyperchaotic drive system formed by combining state variables of the original drive system with appropriate scaling factors with a response hyperchaotic system is considered. A self-combination system is constructed from hyperchaotic Lorenz system by combining state variables of the Lorenz system with appropriate scaling factors. Modified function projective synchronization between the newly constructed combination hyperchaotic Lorenz system and hyperchaotic Lu system is investigated using adaptive method. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two systems as modified function projective synchronized. Numerical simulations are done to show the validity and effectiveness of the proposed synchronization scheme.

A Novel Image Encryption Algorithm Based on a Fractional-Order Hyperchaotic System and DNA Computing

In the era of the Internet, image encryption plays an important role in information security. Chaotic systems and DNA operations have been proven to be powerful for image encryption. To further enhance the security of image, in this paper, we propose a novel algorithm that combines the fractional-order hyperchaotic Lorenz system and DNA computing (FOHCLDNA) for image encryption. Specifically, the algorithm consists of four parts: firstly, we use a fractional-order hyperchaotic Lorenz system to generate a pseudorandom sequence that will be utilized during the whole encryption process; secondly, a simple but effective diffusion scheme is performed to spread the little change in one pixel to all the other pixels; thirdly, the plain image is encoded by DNA rules and corresponding DNA operations are performed; finally, global permutation and 2D and 3D permutation are performed on pixels, bits, and acid bases. The extensive experimental results on eight publicly available testing images demonstrate that the encryption algorithm can achieve state-of-the-art performance in terms of security and robustness when compared with some existing methods, showing that the FOHCLDNA is promising for image encryption.

Color image encryption scheme using coupled hyper chaotic system with multiple impulse injections

The paper proposes a color image encryption scheme based on coupled hyper chaotic Lorenz systems. The novelty is to randomly inject impulse signals into coupled Lorenz system during iterations to enhance the complexity of trajectory. Six state variables sequences are generated to encrypt the red, green and blue components by bitwise operations of exclusive or (XOR) and left or right cyclic shift. Six initial values and indeterminate multiple impulse signals can make the cryptosystem own larger variable key space to resist against exhaustive attack, even the attack from quantum computer. Simulation results show that the mean encryption speed is stable, which means the speed depends solely upon hardware equipment and algorithm. Statistical analysis demonstrates the high effectiveness of the proposed image encryption algorithm.

Different Generalized Synchronization Schemes Between Integer-Order and Fractional-Order Chaotic Systems with Different Dimensions

This paper addresses the problem of generalized synchronization (GS) between different dimensional integer-order and fractional-order chaotic systems. Based on the stability theory of linear continuous time dynamical systems, stability results of linear fractional order systems and nonlinear controllers, different criterions are derived to achieve generalized synchronization. The effectiveness of the proposed control schemes are verified by considering two examples: fractional-order chaotic Lorenz and hyperchaotic Lorenz systems and hyperchaotic Chen and fractional-order chaotic Chen systems.

Multiswitching Synchronization of Non-Identical Hyperchaotic Lorenz and Chen Systems

Multiswitching Synchronization of Non-Identical Hyperchaotic Lorenz and Chen Systems

A modified sliding mode approach for synchronization of fractional-order chaotic/hyperchaotic systems by using new self-structuring hierarchical type-2 fuzzy neural network

This paper presents a new adaptive sliding mode control approach for the synchronization of the uncertain fractional-order chaotic systems. A self-structuring hierarchical type-2 fuzzy neural network (SHT2FNN) is proposed for estimation of uncertainties. Also the switching control action in the conventional sliding mode scheme is replaced by combination type-2 fuzzy neural network (T2FNN) with hyperbolic tangent function. In SHT2FNN, the number of rules is determined by a proposed algorithm. Adaptation laws of all trainable parameters of T2FNN and the consequent parameters of SHT2FNN, are derived based on Lyapunov stability analysis. The simulation results on two kind systems: Genio-Tesi and Coullet System and fractional-order hyper-chaotic Lorenz system, confirm the efficacy of the proposed scheme in synchronization of the uncertain fractional-order hyperchaotic and fractional-order chaotic systems.The proposed controller is robust against the approximation error and external disturbance. The proposed self-structuring algorithm in this paper is simple and it can be applied in the high dimensional problems. Furthermore, the proposed algorithm can delete unimportant rules. Adjusting the structure of the T2FNN in the hierarchical form ensures that the estimation error is very small so it can be negligible. Furthermore, the proposed strategy guarantees the robustness of controller.

A security improved image encryption scheme based on chaotic Baker map and hyperchaotic Lorenz system

In recent years, chaos-based image cipher has been widely studied and a growing number of schemes based on permutation-diffusion architecture have been proposed. However, most of the existing schemes are based on low-dimensional chaotic systems and have the drawbacks of small key space and weak security. In this paper, we present a security improved image cipher which utilises chaotic Baker map and hyperchaotic Lorenz system for permutation and diffusion. Compared with ordinary chaotic systems, hyperchaotic systems, with more complex dynamical behaviours and number of system variables, offer greater potential for secure cryptosystem construction. In diffusion stage, a plain-image related key stream generation scheme is introduced, which further improves the security against known/chosen plaintext attack. Extensive security analysis has been performed on the proposed scheme, including the most important ones like key space analysis, key sensitivity analysis, differential analysis and various statistical analyses, which has demonstrated the satisfactory security of the proposed scheme.

Synchronisation of the hyperchaotic complex Lorenz system in a finite time

In this paper, we investigate the finite-time chaos synchronisation of hyperchaotic complex Lorenz systems. The sufficient conditions for achieving the finite-time synchronisation of two chaotic systems are derived based on the theory of finite-time stability of dynamical systems. In fact, we propose a simple adaptive control method for realising chaos synchronisation in a finite time. It is shown that the technique introduced here can be further applied to various finite-time synchronisations between dynamical systems. Simulation results show the effectiveness of the proposed method.