4D Hyperchaotic System Research Articles

High-security 3D CAP modulation scheme based on a pyramid constellation design for 7-core fiber.

This paper proposes a 3-dimensional (3D) carrier-less amplitude and phase modulation (CAP) based on a pyramid constellation design encryption scheme for 7-core fiber in passive optical network (PON). The chaos sequences generated by the 4D hyperchaotic system are applied to produce the masking factor, and the pyramid Rubik's cube rotation rules are used to flip and rotate the constellation points. To verify the performance of the proposed 3D CAP-PON system, 25.5Gb/s encrypted Pyraminx-3D-CAP-16 signal transmission over 2 km 7-core fiber is experimentally demonstrated. Compared with the traditional 3D-CAP-16 signal, the proposed Pyraminx-3D-CAP-16 signal achieves a sensitivity gain of 0.5 dB under the limit of hard decision forward error correction (HD-FEC) 3.8 × 10-3. Compared with the Pyraminx-3D-CAP-16 signal, the encrypted Pyraminx-3D-CAP-16 signal has little difference from that before encryption, which has a great application prospect in the physical layer security enhancement of the 3D-CAP-PON system.

Dynamic Analysis and FPGA Implementation of a New, Simple 5D Memristive Hyperchaotic Sprott-C System

In this paper, we first present a simple seven-term 4D hyperchaotic system based on the classical Sprott-C 3D chaotic system. This novel system is inspired by the simple 4D hyperchaotic system based on Sprott-B proposed by A. T. Sheet (2022). We discuss the phenomenon of premature divergence brought about by the improper choice of coupling parameters in that paper and describe the basic properties of the new system with phase diagrams, Lyapunov exponential spectra and bifurcation diagrams. Then, we find that the dynamical behaviors of the system suffer from the limitation of the control parameters and cannot represent the process of motion in detail. To improve the system, we expand the dimensionality and add the control parameters and memristors. A 5D memristive hyperchaotic system with hidden attractors is proposed, and the basic dynamical properties of the system, such as its dissipation, equilibrium point, stability, Lyapunov exponential spectra and bifurcation diagram, are analyzed. Finally, the hardware circuits of the 4D Sprott-C system and the 5D memristive hyperchaotic system were realized by a field programmable gate array (FPGA) and verified by an experiment. The experimental results are consistent with the numerical simulation results obtained in MATLAB, which demonstrates the feasibility and potential of the system.

Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis

In this article, a new nonlinear four-dimensional hyperchaotic model is presented. The dynamical aspects of the complex system are analyzed covering equilibrium points, linear stability, dissipation, bifurcations, Lyapunov exponent, phase portraits, Poincaré mapping, attractor projection, sensitivity and time series analysis. To analyze hidden attractors, the proposed system is investigated through nonlocal operator in Caputo sense. The existence of solution of the system in fractional sense is studied by fixed point theory. The stability of fractional order system is demonstrated via Matignon stability criteria. The fractional order system is numerically studied via newly developed numerical method which is based on Newton polynomial interpolation. The evolution of the attractors are depicted with different fractional orders. For few fractional orders, some hidden strange chaotic attractors are observed through graphs. Theoretical and numerical studies demonstrate that this model has complex dynamics with some stimulating physical characteristics. To verify and validate the results, we implement Field Programmable Analog Arrays (FPAA).

A New Simple 6D Hyperchaotic System with Hyperbolic Equilibrium and Its Electronic Circuit

This paper represents a sequential design of controlling from a 3D chaotic system to a simple 6D hyperchaotic system by adding three linear controllers via state feedback control and coupling strategies. The new 6D system has a unique non-hyperbolic equilibrium point with four positive Lyapunov exponents (LE). Moreover, some dynamic properties are analyzed which inclined equilibrium and their stability, dissipative, conservative, and multistability. In addition, the corresponding analog electronic circuit is designed and implemented to verify the new simple 6D hyperchaotic system. Finally, the NI Multisim simulation results observed from the digital oscilloscope are consistent with the mathematical simulation based on the Matlab R2021a.

A new 4D hyperchaotic system and its control

<abstract><p>This paper presents a new four-dimensional (4D) hyperchaotic system by introducing a linear controller to 3D chaotic Qi system. Based on theoretical analysis and numerical simulations, the dynamical behaviors of the new system are studied including dissipativity and invariance, equilibria and their stability, quasi-periodic orbits, chaotic and hyperchaotic attractors. In addition, the Hopf bifurcation at the zero equilibrium point and hyperchaos control of the system are investigated. The numerical simulations, including phase diagram, Lyapunov exponent spectrum, bifurcations and Poincaré maps are carried out in order to analyze and verify the complex phenomena of the 4D hyperchaotic system.</p></abstract>

Robust dual color images watermarking scheme with hyperchaotic encryption based on quaternion DFrAT and genetic algorithm

A robust dual color images watermarking algorithm is designed based on quaternion discrete fractional angular transform (QDFrAT) and genetic algorithm. To guarantee the watermark security, the original color watermark image is encrypted with a 4D hyperchaotic system. A pure quaternion matrix is acquired by performing the discrete wavelet transform (DWT), the block division and the discrete cosine transform on the original color cover image. The quaternion matrix is operated by the QDFrAT to improve the robustness and the security of the watermarking scheme with the optimal transform angle and the fractional order. Then the singular value matrix is obtained by the quaternion singular value decomposition (QSVD) to further enhance the scheme’s stability. The encryption watermark is also processed by DWT and QSVD. Afterward, the singular value matrix of the encryption watermark is embedded into the singular value matrix of the host image by the optimal scaling factor. Moreover, the values to balance imperceptibility and robustness are optimized with a genetic algorithm. It is shown that the proposed color image watermarking scheme performs well in imperceptibility, security, robustness and embedding capacity.

A New Image Encryption Scheme Based on 6D Hyperchaotic System and Random Signal Insertion

A New Image Encryption Scheme Based on 6D Hyperchaotic System and Random Signal Insertion

A hyperchaos generated from Rabinovich system

<abstract><p>In this paper, we present a 4D hyperchaotic Rabinovich system which obtained by adding a linear controller to 3D Rabinovich system. Based on theoretical analysis and numerical simulations, the rich dynamical phenomena such as boundedness, dissipativity and invariance, equilibria and their stability, chaos and hyperchaos are studied. In addition, the Hopf bifurcation at the zero equilibrium point of the 4D Rabinovich system is investigated. The numerical simulations, including phase diagrams, Lyapunov exponent spectrum, bifurcations, power spectrum and Poincaré maps, are carried out in order to analyze and verify the complex phenomena of the 4D Rabinovich system.</p></abstract>

A dynamic S-box generation based on a hybrid method of new chaotic system and DNA computing

S-box is one of the most significant structures used to construct encryption that is strong and resistant to attacks in encryption algorithms. The new 4D-hyper chaotic system and deoxyribonucleic acid (DNA) computing are used in this paper to provide a new dynamic S-box generating approach. The 4D generated numbers are processed to generate a hexadecimal number that will encode using the DNA coding method and using addition, subtraction, and exclusive-or operations to produce the final DNA string decoded to make the S-Box. The dynamic form of s-boxes is represented by a minor change in the initial conditions of the proposed chaotic method that will generate dynamic sequences of numbers. The proposed method enhances the security criteria of the block ciphers. The S-box testing criteria were done like strict avalanche, balanced, and bit independence criteria, in addition to differential approximation probability and linearity approximation probability, to test the security of the new S-Box. The results show that the new S-box has good security and is resistant to attacks.

Design and Analysis of a New Image Encryption Algorithm using Hyperchaotic System and Tent Map

Abstract: Users transfer millions of images every day in the era of information technology. Serious issues could arise if the information included in these photographs is open to unauthorised usage. There are numerous methods for protecting images. One of the most successful and well-known methods is digital image encryption. Confusion and diffusion are the two main phases of an encryption algorithm. This paper proposes a new image encryption technique that uses a hyperchaotic system and a tent chaotic map. With the help of random numbers produced by the 6D hyperchaotic system, the original image gets confused. A tent chaotic map is then used to create a key to diffuse the permuted image. Security analysis and time complexity are used to evaluate the suggested image encryption method's effectiveness. The security is tested using entropy, correlation coefficient, differential attacks, histograms, keyspace, sensitivity, noise, and data cut attacks. Additionally, the outcomes are compared using various encryption methods. The proposed method achieves a high level of security

Multiple attractors in a novel simple 4D hyperchaotic system with chaotic 2-torus and its circuit implementation

Multiple attractors in a novel simple 4D hyperchaotic system with chaotic 2-torus and its circuit implementation

Encrypted speech Biohashing authentication algorithm based on 4D hyperchaotic Bao system and feature fusion

Encrypted speech Biohashing authentication algorithm based on 4D hyperchaotic Bao system and feature fusion

On the Dynamics of New 4D and 6D Hyperchaotic Systems

One of the most interesting problems is the investigation of the boundaries of chaotic or hyperchaotic systems. In addition to estimating the Lyapunov and Hausdorff dimensions, it can be applied in chaos control and chaos synchronization. In this paper, by means of the analytical optimization, comparison principle, and generalized Lyapunov function theory, we find the ultimate bound set for a new six-dimensional hyperchaotic system and the globally exponentially attractive set for a new four-dimensional Lorenz- type hyperchaotic system. The novelty of this paper is that it not only shows the 4D hyperchaotic system is globally confined but also presents a collection of global trapping regions of this system. Furthermore, it demonstrates that the trajectories of the 4D hyperchaotic system move at an exponential rate from outside the trapping zone to its inside. Finally, some numerical simulations are shown to demonstrate the efficacy of the findings.

High randomness hyperchaos-based parameterizable TRNG: Design, FPGA implementation and exhaustive security analysis

Recently, chaotic systems have become a thrilling discipline for information security applications, particularly in designing entropy sources. This paper presents a novel technique to tame an optimized 4D hyperchaotic Lorenz system by building a reconfigurable high randomness and low-cost hardware true random number generator (HC-HTRNG). Moreover, the proposed architecture has been modeled using the fourth-order Runge–Kutta method (RK4) and the 32 bits (10Q22) fixed-point arithmetic representation. The adopted methodology consists of two crucial points. First, we proposed using both intermediate and final solutions of the RK4 method as a raw data source for our HTRNG. The provided raw data are used to generate random numbers with parameterizable sizes. This approach reduces the design latency from four clock cycles to only one cycle while increasing the generation speed and the entropy value. Second, the designed HC-HTRNG integrates a FIPS 140-2-based built-in self-security test module (BISSTM). The BISSTM is used as an environment failure protection and testing mechanism (EFPTM) to guarantee online and continuous control of the proposed HC-HTRNG’s reliability and availability. Furthermore, the proposed HC-HTRNG has been implemented on the Xilinx ML605 FPGA platform using an RTL design based on the VHDL description of the RK4 method. A panoply of online/offline investigations and experiments were carried out intensely, deeply, and thoroughly to analyze, evaluate and validate the robustness and security aspects of the proposed HTRNG regarding all the aspects related to embedded system security. Notably, the evaluations were conducted regarding of chaos validation, security analysis, statistical tests, design performances, and comparisons. The investigations and implementation findings validate that the proposed architecture can attain high performance in terms of maximum post place and route operating frequency (MPRF) and throughput while occupying low FPGA space. Furthermore, timing and power efficiencies result presents an excellent trade-off between design efficiency and high-performance achievement. To the best of our knowledge, the proposed HC-HTRNG is the only one in the literature whose investigation has been subjected to 25 analyses, including 17 related to security aspects. Moreover, among all TRNGs, our generator is the only one that successfully passed seven statistical test suites, as well as the hardest and the most complex.

Color image encryption and authentication using dynamic DNA encoding and hyper chaotic system

This paper takes a holistic approach to propose a comprehensive framework for color image encryption with some novel features. The framework is designed around a secure encryption and decryption scheme leveraging dynamic DNA encoding, hyperchaotic system and elliptic curve cryptography. The novel features being mutually authenticated key generation and exchange based on split share and digital signature for image authentication. A color image is encoded into a DNA sequence using randomly selected row-level encoding rules. A novel 4D-Hyperchaotic system is used to generate pseudo-random sequences to permutate image information at bit-level and block-level. The multidimensional Hyperchaotic system increases non-periodicity, ergodicity, and unpredictability than a simple chaotic system. An elliptic curve-based substitution system is employed to achieve computationally efficient encryption and authentication. Different subkeys have been employed to increase the key space and embed confusion and diffusion into the proposed scheme. Results and analysis show that the proposed framework is computationally efficient and robust to different types of attacks and cryptanalysis carried over the images

Image Encryption Using a Spectrally Efficient Halton Logistics Tent (HaLT) Map and DNA Encoding for Secured Image Communication.

With the advancement of technology worldwide, security is essential for online information and data. This research work proposes a novel image encryption method based on combined chaotic maps, Halton sequence, five-dimension (5D) Hyper-Chaotic System and Deoxyribonucleic Acid (DNA) encoding. Halton sequence is a known low-discrepancy sequence having uniform distribution in space for application in numerical methods. In the proposed work, we derived a new chaotic map (HaLT map) by combining chaotic maps and Halton sequence to scramble images for cryptography applications. First level scrambling was done by using the HaLT map along with a modified quantization unit. In addition, the scrambled image underwent inter- and intra-bit scrambling for enhanced security. Hash values of the original and scrambled image were used for initial conditions to generate a 5D hyper-chaotic map. Since a 5D chaotic map has complex dynamic behavior, it could be used to generate random sequences for image diffusion. Further, DNA level permutation and pixel diffusion was applied. Seven DNA operators, i.e., ADD, SUB, MUL, XOR, XNOR, Right-Shift and Left-Shift, were used for pixel diffusion. The simulation results showed that the proposed image encryption method was fast and provided better encryption compared to ‘state of the art’ techniques. Furthermore, it resisted various attacks.

Hidden and Coexisting Attractors in a Novel 4D Hyperchaotic System with No Equilibrium Point

The investigation of chaotic systems containing hidden and coexisting attractors has attracted extensive attention. This paper presents a four-dimensional (4D) novel hyperchaotic system, evolved by adding a linear state feedback controller to a 3D chaotic system with two stable node-focus points. The proposed system has no equilibrium point or two lines of equilibria, depending on the value of the constant term. Complex dynamical behaviors such as hidden chaotic and hyperchaotic attractors and five types of coexisting attractors of the simple 4D autonomous system are investigated and discussed, and are numerically verified by analyzing phase diagrams, Poincaré maps, the Lyapunov exponent spectrum, and its bifurcation diagram. The short unstable cycles in the hyperchaotic system are systematically explored via the variational method, and symbol codings of the cycles with four letters are realized based on the topological properties of the trajectory projection on the 2D phase space. The bifurcations of the cycles are explored through a homotopy evolution approach. Finally, the novel 4D system is implemented by an analog electronic circuit and is found to be consistent with the numerical simulation results.

Plaintext-related image encryption scheme based on chaos and game of life

To protect the security of image information in the process of storage or transmission, we propose an efficient image encryption method using chaos and game of life (GoL). First, a plaintext-related image scrambling method based on chaos and GoL is proposed to reduce the adjacent pixel correlation of the plain image. In this method, double scrambling is performed on the original image: the first scrambling matrix is constructed by logistic map and the rules of GoL; the second scrambling matrix is generated based on two-dimensional (2D) logistic map and magic square. The original image is scrambled by the above-mentioned scrambling matrices, which can efficiently reduce the strong adjacent pixel correlation, thus enhancing the image scrambling effect. Next, the 4D hyperchaotic system and GoL are employed to diffuse the scrambled image and get the cipher image. Additionally, the average pixel value of the original image is used to generate the initial values of the logistic map and 2D logistic map in scrambling process. Therefore, our encryption scheme is very sensitive to the plain image and can effectively resist the chosen-plaintext attack and known-plaintext attack. Finally, the experimental results and performance analyses show that the proposed encryption algorithm has the advantages of large key space and good scrambling effect, and it can effectively resist various typical attacks, so it can effectively protect the security of the image information.

A New 4D Hyperchaotic System with Dynamics Analysis, Synchronization, and Application to Image Encryption

In this paper, a new 4D hyperchaotic nonlinear dynamical system with two positive Lyapunov exponents is presented. Exhaustive dynamic analyses of the novel hyperchaotic model using several dynamical studies are described. The dynamics of the system considered are first investigated analytically and numerically to explore phenomena and the selection of hyperchaotic behavior utilized for designing image cryptosystem. Since the proposed hyperchaotic model has rich dynamics, it displays hidden attractors. It emerges from this dynamic the existence of a single unstable equilibrium point giving rise to self-excited attractors, hysteresis phenomenon, and hyperchaotic behavior strongly recommended for securing information by its character. Furthermore, the feasibility and synchronization of the proposed system are also presented by developing, respectively, Raspberry surveys and an adaptive synchronization approach of two identical hyperchaotic systems. By employing the hyperchaotic behavior of the 4D map, an image encryption scheme is proposed as well. It is one round of a pixel-based permutation and a bit-wise diffusion phase. The secret key of the 4D map is derived from the SHA-256 value of the input image. It acts as the signature of the input image. Hence, the secret key exhibits high sensitivity to single-bit alteration in the image, which makes the cryptosystem robust against chosen/known-plaintext attacks. Performance analyses prove that the proposed cryptosystem provides the best in terms of the performance/complexity trade-off, as compared to some recently published algorithms.

A 4D hyperchaotic Lorenz-type system: zero-Hopf bifurcation, ultimate bound estimation, and its variable-order fractional network

A 4D hyperchaotic Lorenz-type system: zero-Hopf bifurcation, ultimate bound estimation, and its variable-order fractional network