4D Hyperchaotic System Research Articles

A new family of 5D, 6D, 7D and 8D hyperchaotic systems from the 4D hyperchaotic Vaidyanathan system, the dynamic analysis of the 8D hyperchaotic system with six positive Lyapunov exponents and an application to secure communication design

This work reports a new family of 5D, 6D, 7D and 8D hyperchaotic systems derived successively from the 4D hyperchaotic Vaidyanathan system (2018). The new 8D hyperchaotic system possesses six positive Lyapunov exponents. We discuss the dynamic properties of the new 8D hyperchaos system, describe its self-synchronisation and provide an application in secure communication. Anequivalent electronic circuit of the 8D hyperchaos is implemented using Multisim software to validate the physical feasibility of the system. As an application to secure communications, a new hyperchaotic transmission scheme is developed based on the drive-response synchronisation method and using all the 8D hyperchaos signals generated by the proposed system. With its six positive Lyapunov exponents, the proposed 8D hyperchaos system generates high complex behaviour. Thus, the new 8D hyperchaos system can be deployed in many engineering applications such as cryptosystems and secure communication.

一个有任意给定数目平衡点的四维超混沌系统

一个有任意给定数目平衡点的四维超混沌系统

An Encrypted Speech Retrieval Method Based on Deep Perceptual Hashing and CNN-BiLSTM

Since convolutional neural network (CNN) can only extract local features, and long short-term memory (LSTM) neural network model has a large number of learning calculations, a long processing time and an obvious degree of information loss as the length of speech increases. Utilizing the characteristics of autonomous feature extraction in deep learning, CNN and bidirectional long short-term memory (BiLSTM) network are combined to present an encrypted speech retrieval method based on deep perceptual hashing and CNN-BiLSTM. Firstly, the proposed method extracts the Log-Mel Spectrogram/MFCC features of the original speech and enters the CNN and BiLSTM networks in turn for model training. Secondly, we use the trained fusion network model to learn the deep perceptual feature and generate deep perceptual hashing sequences. Finally, the normalized Hamming distance algorithm is used for matching retrieval. In order to protect the speech security in the cloud, a speech encryption algorithm based on a 4D hyperchaotic system is proposed. The experimental results show that the proposed method has good discrimination, robustness, recall and precision compared with the existing methods, and it has good retrieval efficiency and retrieval accuracy for longer speech. Meanwhile, the proposed speech encryption algorithm has a high key space to resist exhaustive attacks.

A new family of 5D, 6D, 7D and 8D hyperchaotic systems from the 4D hyperchaotic Vaidyanathan system, the dynamic analysis of the 8D hyperchaotic system with six positive Lyapunov exponents and an application to secure communication design

A new family of 5D, 6D, 7D and 8D hyperchaotic systems from the 4D hyperchaotic Vaidyanathan system, the dynamic analysis of the 8D hyperchaotic system with six positive Lyapunov exponents and an application to secure communication design

A Tweak-Cube Color Image Encryption Scheme Jointly Manipulated by Chaos and Hyper-Chaos

This paper proposes a novel tweak-cube color image encryption scheme jointly manipulated by chaos and hyper-chaos. One-dimensional (1D) chaotic maps are effortless to operate, but the key space is relatively small. The hyperchaotic system has complex dynamics properties, which are capable of compensating for the defects of 1D chaotic maps. Thus, we first raise an improved 1D chaotic map with an increased key space. Then, we associate it with a four-dimensional (4D) hyperchaotic system to generate the key streams and further rotate and shift the rows and columns of each component of Red (R), Green (G), and Blue (B) for the color image. The permuting mode is to disturb the original position of the pixels by mimicking the way of twisting the Rubik’s cube. Moreover, the key stream updated by the plain images is also utilized for diffusion and scramble at the bit level. As a consequence, our cryptosystem enhances the security without at the expense of increasing time cost.

Dynamics of a new hyperchaotic system and multistability

In this paper, a new 4D hyperchaotic system is proposed. By boosting a trigonometric function into a single variable, the system produces different multistable regions. Bifurcation diagrams and cross-section of basins can quantify the presence of coexisting attractors. Furthermore, a nonlinear controller is implemented, which can shift the coexisting attractor in the negative region in the phase space and merge it to the positive region, for a threshold value of the control parameter. It has also been noticed that complexity increases with the addition of the nonlinear controller, when the coexisting attractors shift to the positive region in the phase space.

PAPR and security in OFDM-PON via optimum block dividing with dynamic key and 2D-LASM.

An approach for peak-to-average-power ratio (PAPR) reduction and security improvement in an orthogonal frequency division multiplexing passive optical network (OFDM-PON) is proposed by using optimum block dividing with 2-dimensional logistic adjusted sine map (2D-LASM) and dynamic key assignment technique. One frame of OFDM signal can be regarded as a symbol matrix. All the divisors of length and width of matrix can be calculated out, and each divisor of length and width can be arbitrarily combined to divide the matrix into blocks. A 4D hyperchaotic system is applied to generate a cipher book for 2D-LASM. And we assign different dynamic key groups from the cipher book for 2D-LASM to encrypt different block dividing situations. Different encrypted divisor blocks can obtain different values of PAPR. The optimum dividing situation is obtained by calculating out the minimum value of PAPR (VPAPR). The values of optimum encryption signal (VPAPR-op), the original signal (VPAPR-or) and the optimization ratio (η) are gradually equal to 146, 269 and 1.82, respectively, with the number of quadrature amplitude modulation (QAM) symbols in each subcarrier increasing. Simulating 1000 sets of 120×200 QAM symbols, the distribution of η approximately meets the Rayleigh distribution and its central distribution is around 1.7. The processing time decreases with the number of QAM symbols increasing in each block. The performance of PAPR reduction is more than 3 dB between the secure optimum signal and the original signal. In addition, the hyper-threading technique with two algorithms is applied to improve the performance of the encryption method. They promote the processing time by 38.6% and 50%, respectively. Finally, a 22.06 Gb/s optimum encryption OFDM signal transmits through a back-to-back (BTB) system and a 25-km standard single mode fiber (SSMF). These experimental results verify that the proposed approach is a promising candidate for solving both of PAPR reduction and security improvement in access network systems.

Multistability and bifurcations in a 5D segmented disc dynamo with a curve of equilibria

Multistability, i.e., coexisting attractors, is one of the most exciting phenomena in dynamical systems. This paper presents a new category of coexisting hidden attractor: five-dimensional (5D) systems with a curve of equilibria. Based on the segmented disc dynamo, a new 5D hyperchaotic system is proposed. The paper studies not only coexisting self-excited attractors but also coexisting hidden attractors in the new system with four types of equilibria: a curve of equilibria, a line equilibrium, a stable equilibrium, and no equilibria. Furthermore, the paper proves that the degenerate Hopf and pitchfork bifurcations occur in the system. Numerical simulations demonstrate the emergence of the two bifurcations.

An iris biometric protection scheme using 4D hyperchaotic system and modified equal modulus decomposition in hybrid multi resolution wavelet domain

In this paper, a hybrid iris biometric protection scheme using 4D hyperchaotic system by means of coherent superposition and modified equal modulus decomposition in hybrid multi-resolution wavelet domain is proposed. The 4D hyperchaotic framework is employed for producing the permutation keystream for pixel swap-over mechanism. The hybrid multi-resolution is produced by means of Kronecker product of Walsh transform and fractional Fourier transform of different orders. Fractional orders of the hybrid multiresolution wavelet along with the parameters and initial conditions of the 4D hyperchaotic framework, later fill in as additional keys, thus enhancing the key space of the proposed mechanism. The proposed scheme has nonlinear characteristics and has high robustness against brute-force attack attributable to its enormous key-space. Numerical simulations have been carried out on grayscale images to prove the authenticity and efficacy of the proposed cryptosystem. The functioning of the proposed cryptosystem is investigated against various attacks including special attack. Outcomes display that the proposed iris template protection scheme not only has higher robustness against noise attack but is also unassailable to the iterative transform-based attacks.

Complex dynamics from a novel memristive 6D hyperchaotic autonomous system

A simple 5D hyperchaotic system recently introduced in the literature is modified by using a charge-controlled memristor model and striking behaviors are uncovered. The resulting system is a 6D hyperchaotic system, which generates hidden attractors with the unusual feature of having plan and line equilibrium under different parameter conditions. Its dynamical behaviors are characterized through bifurcation diagrams, Lyapunov exponents, phase portraits, Poincare sections and time series. Rich nonlinear dynamics such as limit cycles, quasi-periodicity, chaos, hyperchaos, bursting and hidden extreme multistability are found for appropriate sets of parameter values. The high complexity of the system is confirmed by its Kaplan–yorke dimension (greater than five). Additionally, an electronic circuit is designed to implement the novel system and PSpice simulation results are in good accordance with the numerical investigations. To the best of our knowledge, this system is the first with higher order presenting all those phenomena.

Image Encryption Based on Pixel-Level Diffusion with Dynamic Filtering and DNA-Level Permutation with 3D Latin Cubes.

Image encryption is one of the essential tasks in image security. In this paper, we propose a novel approach that integrates a hyperchaotic system, pixel-level Dynamic Filtering, DNA computing, and operations on 3D Latin Cubes, namely DFDLC, for image encryption. Specifically, the approach consists of five stages: (1) a newly proposed 5D hyperchaotic system with two positive Lyapunov exponents is applied to generate a pseudorandom sequence; (2) for each pixel in an image, a filtering operation with different templates called dynamic filtering is conducted to diffuse the image; (3) DNA encoding is applied to the diffused image and then the DNA-level image is transformed into several 3D DNA-level cubes; (4) Latin cube is operated on each DNA-level cube; and (5) all the DNA cubes are integrated and decoded to a 2D cipher image. Extensive experiments are conducted on public testing images, and the results show that the proposed DFDLC can achieve state-of-the-art results in terms of several evaluation criteria.

A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability

Abstract This paper presents a 6D autonomous system, obtained by introducing a flux-controlled memristor model into an existing 5D hyperchaotic autonomous system. The dynamics of the novel system are investigated in terms of equilibrium points, bifurcation diagrams, Lyapunov exponent spectra, phase portraits, time series and attraction basins. Moreover, its circuit implementation is also proposed. The system is hyperchaotic under a line or a plan of equilibria. Other attractive dynamics observed are: hidden extreme multistability, transient chaos, bursting and offset boosting phenomenon. Interestingly, for a particular set of parameters, an unusual metastability showing transition from chaotic to periodic bursting dynamics is found. Dynamical systems capable of producing the above complexity are not common in the literature; thus, this novel memristive 6D hyperchaotic autonomous system deserves particular attention. PSpice based simulations are in good agreement with numerical computations. To the best of our knowledge, this system is the first with higher order presenting all those phenomena.

Fractional-order 4D hyperchaotic memristive system and application in color image encryption

In this paper, some properties of the fractional-order four-dimensional (4D) hyperchaotic memristive system are analyzed by the phase diagram, Lyapunov exponent spectrum and bifurcation diagram according to the Adomian decomposition method. Based on the chaotic system, a color image encryption scheme is proposed through combining the DNA sequence operation. The algorithm simulation results and security feature analysis show that the encryption scheme has good encryption effect and high safety performance, which provides an experimental basis and theoretical guidance for the safe transmission of image information.

Ultimate boundary estimation and topological horseshoe analysis on a parallel 4D hyperchaotic system with any number of attractors and its multi-scroll

This paper constructs a new four-dimensional autonomous hyperchaotic system with complex dynamic behaviors, and its boundary is estimated based on the proposed method and the optimization idea. Inspired by the “parallel universe theory,” a trigonometric function is used to do coordinate transformation of the original new system to generate any number of attractors. Simulation results show that there are infinite equilibriums in the transformed system. Compared with the original new system, the transformed system is more sensitive to the initial values. Based on the estimated boundary of the original system, the boundary of transformed system could be obtained. To verify the existence of chaos of the transformed system, the topology horseshoe of the system is investigated. The positive topological entropy of the transformed system verifies the existence of hyperchaos. Furthermore, selecting proper parameter values, the transformed system shows a multi-scroll attractor. Applying multi-variable trigonometric transformation can also induce any number of attractors and multi-scroll phenomenon in multi-dimension, which is an interesting phenomenon.

Analysis and FPGA Realization of a Novel 5D Hyperchaotic Four‐Wing Memristive System, Active Control Synchronization, and Secure Communication Application

By introducing a flux‐controlled memristor with quadratic nonlinearity into a 4D hyperchaotic system as a feedback term, a novel 5D hyperchaotic four‐wing memristive system (HFWMS) is derived in this paper. The HFWMS with multiline equilibrium and three positive Lyapunov exponents presented very complex dynamic characteristics, such as the existence of chaos, hyperchaos, limit cycles, and periods. The dynamic characteristics of the HFWMS are analyzed by using equilibria, phase portraits, poincare map, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy. Of particular interest is that this novel system can generate two‐wing hyperchaotic attractor under appropriate parameters and initial conditions. Moreover, the FPGA realization of the novel 5D HFWMS is reported, which prove that the system has complex dynamic behavior. Finally, synchronization of the 5D hyperchaotic system with different structures by active control and a secure signal masking application of the HFWMS are implemented based on numerical simulations and FPGA. This research demonstrates that the hardware‐based design of the 5D HFWMS can be applied to various chaos‐based embedded system applications including random number generation, cryptography, and secure communication.

Coexisting hidden attractors in a 5D segmented disc dynamo with three types of equilibria

Little seems to be known about coexisting hidden attractors in hyperchaotic systems with three types of equilibria. Based on the segmented disc dynamo, this paper proposes a new 5D hyperchaotic system which possesses the properties. This new system can generate hidden hyperchaos and chaos when initial conditions vary, as well as self-excited chaotic and hyperchaotic attractors when parameters vary. Furthermore, the paper proves that the Hopf bifurcation and pitchfork bifurcation occur in the system. Numerical simulations demonstrate the emergence of the two bifurcations. The MATLAB simulation results are further confirmed and validated by circuit implementation using NI Multisim.

A Novel Plaintext-Related Image Encryption Algorithm Based on Stochastic Signal Insertion and Block Swapping

Image encryption is an important method for protecting private data during communication. This paper proposes a novel hyperchaotic image encryption algorithm based on stochastic signal insertion and block permutation. First, the 5D hyperchaotic system is applied to generate pseudorandom number sequences. The SHA-256 hash function and secret keys are used to produce the initial values of the cryptosystem. The hash values can effectively enhance the sensitivity to plain image. To enlarge the key space and change orbit of cryptosystem, some stochastic signals are inserted during iteration. The plain image is equally divided into two parts. An X-coordinate, a Y-coordinate and a control table are established with produced pseudonumber sequences. The pixel is swapped with another pixel in the current block or another block depending on the control table. Cyclic shift is performed during the diffusion process. Performance and security analyses are executed to verify the effect of the proposed scheme. It is clear that the proposed scheme has a large key space and is highly sensitive to plain image and secret keys. Moreover, the cryptosystem has low computation complexity and can resist correlation analysis, entropy analysis, statistical attack, differential attack, noise and data loss attacks.

一个新五维超混沌系统的分析与电路设计

一个新五维超混沌系统的分析与电路设计

Optical asymmetric watermarking using 4D hyperchaotic system and modified equal modulus decomposition in hybrid multi resolution wavelet domain

In this paper, an asymmetric optical watermarking scheme using 4D hyperchaotic system with coherent superposition and modified equal modulus decomposition in hybrid multi-resolution wavelet domain is proposed. The 4D hyperchaotic system is used for generating permutation keystream for a pixel-swapping mechanism. The hybrid multi-resolution is generated using both the fractional Fourier transform of multiple orders and Walsh transform. The 4D hyperchaotic system’s parameters and initial conditions along with the multiple fractional orders of the fractional Fourier transform increase the key-space and hence provide additional strength to the watermarking mechanism. The designed watermarking scheme is non-linear in nature and resists brute-force attack due to its large key-space. Computer-based simulations have been performed on grayscale images to verify the validity and performance of the scheme against various attacks including special attack. Results show that the proposed watermarking scheme not only offers high resistance to occlusion and noise attacks but is also invulnerable to the special attack.

A new 5D hyperchaotic system with stable equilibrium point, transient chaotic behaviour and its fractional-order form

Hidden attractors with the family of stable equilibrium points in higher-dimensional systems are more interesting and difficult discover compared to other families of hidden attractors. In this paper, a new 5D hyperchaotic system is reported. The proposed system has only one stable equilibrium point. Hence, the new system belongs to the category of hidden attractors. Although some lower-dimensional chaotic systems with stable equilibrium points are available in the literature, but very few hyperchaotic systems with stable equilibrium points are reported. The new system is simple considering the number of terms, compared with the existing similar type of systems. The proposed system exhibits multistability and transient chaotic behaviour. The fractional-order counterpart of the proposed system is analysed using Adams–Bashforth–Moulton algorithm and the chaotic nature is validated by bifurcation diagram. The simulation results confirm the claims made in the paper.