4D Hyperchaotic System Research Articles

Image encryption based on 5D hyperchaotic system using hybrid random matrix transform

Image encryption based on 5D hyperchaotic system using hybrid random matrix transform

Modelling, bifurcation analysis and multistability of a new 4D hyperchaotic system with no balance point, its master-slave synchronisation and MultiSim circuit simulation

This research manuscript focuses on the modelling, bifurcation analysis and multistability of a new four-dimensional hyperchaotic system with no balance point. The proposed hyper chaos system has four quadratic nonlinear terms and three parameters. We perform a detailed bifurcation analysis of the hyper chaos system and illustrate that it has coexisting hyperchaotic attractors. The proposed system has no balance point, and it is equipped with hidden attractors. Using integral sliding mode control, we derive control results for the global hyper chaos synchronisation of a pair of hyper chaos systems and MATLAB plots are shown as illustrations. Finally, circuit simulations of the new 4D hyperchaotic system with no balance point are carried out using MultiSim.

Dynamics of a New Multistable 4D Hyperchaotic Lorenz System and Its Applications

Using an effective nonlinear feedback controller, a novel 4D hyperchaotic Lorenz system is built. Dynamical analyses show that it has interesting properties. Using some well-known analysis tools like Lyapunov spectrum, bifurcation analysis, chaos diagram, and phase space trajectories, it is found that several bifurcations enable the hyperchaotic dynamics to occur in the introduced model. Also, many windows of heterogeneous multistability are found in the parameter space (i.e. coexistence of a pair of chaotic attractors, coexistence of a periodic and a chaotic attractor). Besides, DSP implementation is successfully used to support the results of the theoretical prediction. Finally, a judicious image encryption algorithm based on the hyperchaotic Lorenz system is proposed with detailed analysis. The effectiveness of the proposed approach is confirmed via several security analyses, which yields a secure image encryption application.

Hyperchaos and MD5 Based Efficient Color Image Cipher

While designing and developing encryption algorithms for text and images, the main focus has remained on security. This has led to insufficient attention on the improvement of encryption efficiency, enhancement of hyperchaotic sequence randomness, and dynamic DNA-based S-box. In this regard, a new symmetric block cipher scheme has been proposed. It uses dynamic DNA-based S-box connected with MD5 and a hyperchaotic system to produce confusion and diffusion for encrypting color images. Our proposed scheme supports various size color images. It generates three DNA based S-boxes for substitution namely DNA_1_s-box, DNA_2_s-box and DNA_3_s-box, each of size . Next, the 4D hyperchaotic system followed by MD5 is employed in a novel way to enhance security. The three DNA-based S-boxes are generated from real DNA sequences taken from National Center for Biotechnology Information (NCBI) databases and are dependent on the mean intensity value of an input image, thus effectively introducing content-based confusion. Finally, Conservative Site-Specific Recombination (CSSR) is applied on the output DNA received from DNA based S-boxes. The experimental results indicate that the proposed encryption scheme is more secure, robust, and computationally efficient than some of the recently published similar works. Being computational efficient, our proposed scheme is feasible on many emergent resource-constrained platforms.

Modelling, bifurcation analysis and multistability of a new 4D hyperchaotic system with no balance point, its master-slave synchronisation and MultiSim circuit simulation

Modelling, bifurcation analysis and multistability of a new 4D hyperchaotic system with no balance point, its master-slave synchronisation and MultiSim circuit simulation

A Color Image Encryption Scheme Combining Hyperchaos and Genetic Codes

In consideration of the reduced chaotic range and susceptibility of a single chaotic map, we exploit the 4D-hyperchaotic system for creating three S-boxes i.e., red, green and blue S-boxes and a logistic map to transform a plain image into DNA strands. Afterwards, a logistic map based fake image is also generated which is also mapped to deoxyribonucleic acid (DNA) strands. Then DNA operations based on logistic map sequence are performed among the DNA strands and the resultant strands are decoded. The decoded strands are substituted by three substitution-boxes (s-boxes) to create an encrypted image. In this research, a cryptanalysis driven design approach is used to prove the security of a proposed encryption scheme. The proposed scheme operates on numerous image dimensions N <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> M and different image file sizes and formats. Experimental results and analysis are completed for visual analysis, key space, key sensitivity, energy analysis, homogeneity analysis, contrast analysis, entropy analysis, histogram analysis, correlation analysis, chosen-plaintext attacks, number of pixels change rate (NPCR), universal average changing intensity (UACI), mean absolute error, robustness against noises and occlusion attacks and encryption efficiency analysis. The visual as well as numerical simulations demonstrate that the proposed algorithm is safe and reliable.

Analysis and Stability Control of a Novel 5D Hyperchaotic System

In this paper, a novel Five-Dimensional (5D) autonomous hyperchaotic system is presented, and the characteristics of the 5D system are given in brief. For stability control of the 5D hyperchaotic system, a linear feedback controller and its simplification are designed via the Lyapunov stability theory, so that the 5D system is no longer hyperchaotic but globally asymptotically converges to the equilibrium point at the origin. The numerical simulation results are given to illustrate the feasibility and effectiveness of the method.

A Class of New Correlative and Switchable Hyperchaotic Systems and Their Switch-Synchronization

A new population of correlative and switchable 4D hyperchaotic systems and their switch-synchronization are investigated. First, the switched system with the self-contained subsystems which show some symmetry are constructed. The Lyapunov exponent spectrums and Lyapunov dimensions are displayed to indicate the existence of hyperchaos, and the complex dynamical properties are discussed. Second, its real circuit implement is exhibited for application, and the switching with the flexible and diverse operation assembled can be accomplished randomly by using system selector. Third, nonlinear control strategies are presented to ensure the synchronization stability of the switched system. Simulations are displayed to verify the effectiveness of the control.

A New 4D Hyperchaotic System and Its Analog and Digital Implementation

This work presents a new four-dimensional autonomous hyperchaotic system based on Méndez-Arellano-Cruz-Martínez (MACM) 3D chaotic system. Analytical and numerical studies of the dynamic properties are conducted for the new hyperchaotic system (NHS) in its continuous version (CV), where the Lyapunov exponents are calculated. The CV of the NHS is simulated and implemented using operational amplifiers (OAs), whereas the Discretized Version (DV) is simulated and implemented in real-time. Besides, a novel study of the algorithm performance of the proposed DV of NHS is conducted with the digital-electronic implementation of the floating-point versus Q1.15 fixed-point format by using the Digital Signal Processor (DSP) engine of a 16-bit dsPIC microcontroller and two external dual digital to analog converters (DACs) in an embedded system (ES).

Synchronization and Chaos Control Using a Single Controller of Five Dimensional Autonomous Homopolar Disc Dynamo

The electronic implementation, synchronization, and control of hyperchaos in a five-dimensional (5D) autonomous homopolar disc dynamo are investigated in this paper. The hyperchaotic behavior is found numerically using phase portraits and time series in 5D autonomous homopolar disc dynamo is ascertained on Orcad-PSpice software. The synchronization of the unidirectional coupled 5D hyperchaotic system is also studied by using the feedback control method. Finally, hyperchaos found in 5D autonomous homopolar disc dynamo is suppressed thanks to the designed single feedback. Numerical simulations and electronic implementation reveal the effectiveness of the single proposed control.

Secure image encryption scheme using 4D-Hyperchaotic systems based reconfigurable pseudo-random number generator and S-Box

This paper introduces the design of a hardware efficient reconfigurable pseudorandom number generator (PRNG) using two different feedback controllers based four-dimensional (4D) hyperchaotic systems i.e. Hyperchaotic-1 and -2 to provide confidentiality for digital images. The parameter's value of these two hyperchaotic systems is set to be a specific value to get the benefits i.e. all the multiplications (except a few multiplications) are performed using hardwired shifting operations rather than the binary multiplications, which doesn't utilize any hardware resource. The ordinary differential equations (ODEs) of these two systems have been exploited to build a generic architecture that fits in a single architecture. The proposed architecture provides an opportunity to switch between two different 4D hyperchaotic systems depending on the required behavior. To ensure the security strength, that can be also used in the encryption process in which encrypt the input data up to two times successively, each time using a different PRNG configuration. The proposed reconfigurable PRNG has been designed using Verilog HDL, synthesized on the Xilinx tool using the Virtex-5 (XC5VLX50T) and Zynq (XC7Z045) FPGA, its analysis has been done using Matlab tool. It has been found that the proposed architecture of PRNG has the best hardware performance and good statistical properties as it passes all fifteen NIST statistical benchmark tests while it can operate at 79.101-MHz or 1898.424-Mbps and utilize only 0.036 %, 0.23 %, and 1.77 % from the Zynq (XC7Z045) FPGA's slice registers, slice LUTs, and DSP blocks respectively. Utilizing these PRNGs, we design two 16 × 16 substitution boxes (S-boxes). The proposed S-boxes fulfill the following criteria: Bijective, Balanced, Non-linearity, Dynamic Distance, Strict Avalanche Criterion (SAC) and BIC non-linearity criterion. To demonstrate these PRNGs and S-boxes, a new three different scheme of image encryption algorithms have been developed: a) Encryption using S-box-1, b) Encryption using S-box-2 and, c) Two times encryption using S-box-1 and S-box-2. To demonstrate that the proposed cryptosystem is highly secure, we perform the security analysis (in terms of the correlation coefficient, key space, NPCR, UACI, information entropy and image encryption quantitatively in terms of (MSE, PSNR and SSIM)).

Correction to: Pseudorandom number generator based on a 5D hyperchaotic four-wing memristive system and its FPGA implementation

Correction to: Pseudorandom number generator based on a 5D hyperchaotic four-wing memristive system and its FPGA implementation

Pseudorandom number generator based on a 5D hyperchaotic four-wing memristive system and its FPGA implementation

Pseudorandom number generator based on a 5D hyperchaotic four-wing memristive system and its FPGA implementation

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

PurposeThe purpose of this paper is to develop new four-dimensional (4D) hyperchaotic system by adding another state variable and linear controller to three-dimensional T chaotic dynamical systems. Its dynamical analyses, circuit experiment, control and synchronization applications are presented.Design/methodology/approachA new 4D hyperchaotic attractor is achieved through a simulation, circuit experiment and mathematical analysis by obtaining the Lyapunov exponent spectrum, equilibrium, bifurcation, Poincaré maps and power spectrum. Moreover, hardware experimental measurements are performed and obtained results well validate the numerical simulations. Also, the passive control method is presented to make the new 4D hyperchaotic system stable at the zero equilibrium and synchronize the two identical new 4D hyperchaotic system with different initial conditions.FindingsThe passive controllers can stabilize the new 4D chaotic system around equilibrium point and provide the synchronization of new 4D chaotic systems with different initial conditions. The findings from Matlab simulations, circuit design simulations in computer and physical circuit experiment are consistent with each other in terms of comparison.Originality/valueThe 4D hyperchaotic system is presented, and dynamical analysis and numerical simulation of the new hyperchaotic system were firstly carried out. The circuit of new 4D hyperchaotic system is realized, and control and synchronization applications are performed.

An adjustable visual image cryptosystem based on 6D hyperchaotic system and compressive sensing

In this paper, an efficient and adjustable visual image encryption scheme is proposed by combining a 6D hyperchaotic system, compressive sensing, and Bezier curve embedding. First, the plain image is sparse by discrete wavelet transform (DWT). Then, the sparse image is encrypted and compressed through game-of-life (GOL) hybrid scrambling and compressive sensing into a cipher image. Next, Bezier curve embedding is utilized to embed the cipher image into the carrier image in wavelet domain. After these operations, the final visually meaningful steganographic image is generated. Additionally, the frequency-domain information of the plain image is used to generate the initial values of the 6D hyperchaotic system in scrambling process, which makes the proposed encryption scheme able to effectively resist the chosen-plaintext attacks (CPA) and the known-plaintext attacks (KPA). Moreover, our scheme exhibits excellent adjustable performance compared with existing related schemes. Ultimately, simulation results and comprehensive performance analyses demonstrate that the scheme proposed in this paper has high decryption quality, visual security, robustness, and operating efficiency.

Robust large image steganography using LSB algorithm and 5D hyper-chaotic system

This paper contains a robust hiding system proposed to hide and reconstruct efficiently a large size secret image based on merging encrypting and hiding. This approach deals with a video utilized as a cover of frames to hide the blocks of large image inside it. Frames are selected according to 5D hyperchaotic algorithms and consequently change value of the pixel in the original image depends on it. Secret image will divide into many blocks and hide each block in one frame selected by 5D chaotic. This method will support and enhance the techniques of information security with less time and morecapacity of transmission. The results obtained are analyzed under criteria including: Peak signal to noise ratio, Mean square error, key space and sensitivity, correlation coefficient and capacity of hiding. The results demonstrate both of the secret color image and cover video, where retaining its explicitness and properties after reconstruction in the receiver. However, the results prove stability and reliability of the proposed system under several conditions and can avoid attacks.

Hyper-Chaotic Color Image Encryption Based on Transformed Zigzag Diffusion and RNA Operation.

With increasing utilization of digital multimedia and the Internet, protection on this digital information from cracks has become a hot topic in the communication field. As a path for protecting digital visual information, image encryption plays a crucial role in modern society. In this paper, a novel six-dimensional (6D) hyper-chaotic encryption scheme with three-dimensional (3D) transformed Zigzag diffusion and RNA operation (HCZRNA) is proposed for color images. For this HCZRNA scheme, four phases are included. First, three pseudo-random matrices are generated from the 6D hyper-chaotic system. Second, plaintext color image would be permuted by using the first pseudo-random matrix to convert to an initial cipher image. Third, the initial cipher image is placed on cube for 3D transformed Zigzag diffusion using the second pseudo-random matrix. Finally, the diffused image is converted to RNA codons array and updated through RNA codons tables, which are generated by codons and the third pseudo-random matrix. After four phases, a cipher image is obtained, and the experimental results show that HCZRNA has high resistance against well-known attacks and it is superior to other schemes.

Adaptive Control and Multi-variables Projective Synchronization of Hyperchaotic Finance System

This paper introduces a new hyperchaotic finance system and show that it is a self-excited hyperchaotic attractor with the coexistence of double attractor with difference initial conditions for the same set of parameter values. Nonlinear feedback control function u i (t), (i= 1,2,3,4) via adaptive control laws are design for the control and synchronization of the 4D-hyperchaotic finance system with the multiple values of the economics scaling factor αi , (i = 1,2,3,4), a special case of projective synchronization. The proposed schemes are able to stabilize as well as globally synchronize the two identical finance systems evolving from different initial conditions with uncertain parameter for the different values of α i (i = 1,2,3,4) . The analytical results were verified through numerical simulation.

Robust Secure Color Image Watermarking Using 4D Hyperchaotic System, DWT, HbD, and SVD Based on Improved FOA Algorithm

In the recent past, a different set of algorithms for watermarking and securing the color images have been developed by using transformation, decomposition, and optimization techniques for watermark embedding and extraction. In this paper, we propose an optimized and robust watermarking algorithm coupled with a 4D hyperchaotic system, and its performance is analyzed by extending and differentiating the existing work. Our contribution in the presented work is watermarking and securing the color images by an optimized algorithm that uses transformation technique such as Discrete Wavelet Transformation (DWT) and decomposition techniques such as Hessenberg decomposition (HbD) and singular value decomposition (SVD) coupled with the 4D hyperchaotic system, while the optimization is carried out by improved evolution fruit fly optimization algorithm (IEFOA). The experimental results based on different types of attacks (filter attacks, noise attacks, cropping attack, JPEG compression, motion blur, sharpening, and rotation), key sensitivity, normalized correlation, peak signal-to-noise ratio, and structural similarity index measure are done for measuring the algorithm’s performance regarding invisibility and robustness. The experimental results show that the proposed scheme has excellent invisibility and keeps a good trade-off between invisibility and robustness. The experiment results show that the proposed approach outperforms the previous approaches.

Stability analysis and modified projective synchronization of fractional-order hyperchaotic dynamical systems using nonlinear controllers

This paper deals with the modified projective synchronization between two fractional-order four-dimensional (4D) hyperchaotic systems. Based on the Lyapunov stability theory, a new controller for the synchronization of two fractional-order hyperchaotic systems is developed. The stability analysis of the error dynamics system is performed by the fractional-order Lyapunov direct method alongwith Routh–Hurwitz stability criterion. Numerical simulations are presented to demonstrate the validity and verify the effectiveness of the proposed synchronization scheme.