Search Results (186)

Most existing low-dimensional chaotic maps suffer from a limited dynamical complexity and dynamic degradation, which restrict their effectiveness in image encryption. To address this issue, a novel three-dimensional chaotic map (3D-TCM) was constructed to improve dynamical complexity and stability, and its superiority was verified through a dynamical analysis. Based on these advantages, a plaintext-related image encryption scheme was designed by combining bit-level permutation and S-box-based diffusion. The experimental results show that the proposed scheme achieved high information entropy, a low pixel correlation, and desirable NPCR and UACI values, and successfully passed NIST SP800-22 statistical tests, demonstrating a strong resistance to differential attacks and overall robustness. Full article

This paper introduces a novel memristor-based hyperchaotic system in which the integer-order derivatives are replaced by a variable-order fractal-fractional operator. The dynamical properties of the system, including equilibrium points, Lyapunov exponents, bifurcation diagrams with respect to the variable orders, and the Kaplan–Yorke dimension, are analyzed. A synchronization scheme based on active control is designed for the master–slave configuration, and global Mittag–Leffler stability of the error dynamics is established using a suitable variable-order Lyapunov function. The synchronized states are then applied to an image encryption algorithm. Numerical simulations, security analyses, and NIST randomness tests demonstrate the effectiveness and enhanced performance of the proposed framework compared to existing fixed-order and classical fractional-order methods. Full article

Reservoir computing (RC) is an efficient framework for processing time-series data. This work investigates the synchronization of two independently trained reservoir computers that, after training, operate without external input from the chaotic system and interact solely through symmetric linear coupling. This approach addresses a gap in existing reservoir computing-based synchronization studies, which predominantly rely on master–slave or system-driven configurations. In this work, we first build and train two reservoir computing models based on 3D nonlinear chaotic maps and hyperchaotic systems and then introduce a symmetric linear coupling mechanism between them. This study demonstrates that reservoir computing can accurately reproduce the short-term dynamics of chaotic systems and provides insight into the interactions between learned dynamical models, while also helping us understand how complex systems connect and operate collectively. We use this systematic approach to establish a framework for understanding how two trained reservoir computers interact under varying coupling strengths, enabling a detailed investigation of their synchronization behavior. To demonstrate the adaptability of the proposed framework to diverse dynamical behaviors, we systematically investigated three discrete chaotic and hyperchaotic systems: (1) discrete 3D sinusoidal map with discrete Lorenz attractor, (2) 3D sinusoidal map with conjoined Lorenz twin attractor, and (3) 3D quadratic hyperchaotic map. For performance evaluation, we trained coupled RCs and computed the synchronization error for different coupling strengths. We also present phase portraits and time-series plots of the attractors and RCs, along with the synchronization error as a function of the coupling strength, thereby demonstrating the possibility of synchronization of two linearly coupled RCs, which are independently trained on discrete, three-dimensional chaotic and hyperchaotic systems. Full article

This paper proposes a novel four-dimensional strongly dissipative nonlinearly coupled hyperchaotic system, investigates its dynamical characteristics, and demonstrates its applicability through Deoxyribonucleic Acid (DNA)-encoded RGB image encryption. First, a four-dimensional nonlinearly coupled hyperchaotic system with strong dissipativity is constructed. Nonlinear dynamics analysis methods, including phase trajectory diagrams, Lyapunov exponent spectra, and bifurcation diagrams, are employed to thoroughly reveal the system’s complex dynamical evolution mechanisms. The analysis indicates that the system not only possesses a wide range of chaotic parameters but also exhibits rich phenomena of multiple coexisting attractors, demonstrating a high degree of multistability. This characteristic offers potential advantages for image encryption, as it increases the diversity of dynamical behaviors and enhances sensitivity to initial conditions. The physical realizability of the chaotic behavior is further verified through an analog circuit implementation. Consequently, the system supports the design of encryption algorithms with larger key spaces, stronger resistance to phase space reconstruction, and improved pseudo-randomness, making it particularly suitable for applications with extremely high security requirements. Subsequently, leveraging the highly random chaotic sequences generated by this system, combined with various DNA coding rules and operations, the RGB image components are scrambled and diffused for encryption. Security analysis demonstrates that the algorithm effectively passes examinations across multiple dimensions, including histogram analysis, information entropy, adjacent pixel correlation, Number of Pixel Change Rate (NPCR), Unified Average Changing Intensity (UACI), and The Peak Signal-to-noise Ratio (PSNR). It achieves favorable encryption results, significantly enhances image resistance against attacks, and provides a reliable technical solution for the secure transmission of remote sensing and military images. Full article

To address the high redundancy and weak security inherent in satellite image transmission, this paper proposes an image encryption algorithm founded on a novel five-dimensional fractional-order cosine memristive Hopfield neural network (5D-FOCMHNN). The constructed hyperchaotic system exhibits long-term memory and multistability, capable of generating reconfigurable multi-scroll attractors. A multivariate bit-level scrambling strategy effectively disrupts pixel correlations using neuron state sequences. Furthermore, the system’s chaotic output dynamically governs DNA encoding rules, while a bidirectional diffusion mechanism ensures strong randomization and resistance to differential attacks. Comprehensive experiments demonstrate that the 5D-FOCMHNN-based scheme provides a key space of $2^{256}$, has an information entropy approaching the ideal value of 8, and exhibits robust resilience against cropping, noise, and statistical cryptanalysis, thereby providing a highly secure solution for satellite image transmission. Full article

Secure compressive sensing (SCS) mostly benefits scenes such as IoT with finite computer resources, the fields of spaceflight and medicine, etc. Recently, research on SCS has aroused widespread interest. Nevertheless, existing work on embedding security of CS usually requires an extra cryptographic routine applied to the measurement vectors. In this paper, we proposed an SCS scheme boosted by the hyper-chaotic system, which outperforms state-of-the-art methods and endows the SCS with a high level of inherent security. Encryption and sampling processing are accomplished simultaneously in our scheme, i.e., security is achieved when sampling with a measurement matrix, which is generated by an initial-value (secret key)-driven discrete hyper-chaotic (HC) system. Moreover, the application of the HC matrix decreases both the computing and bandwidth consumption costs of secret key streams transmission compared with traditional CS-based encryption methods. Experimentally, the HC-based matrix demonstrates excellent reconstruction performance, achieving an average SSIM of 0.91 and PSNR of 29.09 dB on the Set5 dataset at a sampling ratio of 0.5, outperforming conventional matrices such as Bernoulli and Hadamard. Security analysis confirms that the system exhibits asymptotic spherical secrecy and high key sensitivity—a deviation of ${10}^{-16}$ in the initial value results in complete decryption failure. Furthermore, the scheme shows strong robustness against additive Gaussian white noise and cropping attacks, maintaining a PSNR above 15 dB even under 50% cropping. Compared to existing methods, the proposed approach reduces bandwidth consumption by transmitting only the HC initial parameters rather than the entire measurement matrix. These results demonstrate that the HC-driven SCS framework provides inherent security, high reconstruction fidelity, and practical efficiency, making it suitable for secure sensing in constrained environments. Full article

In this work, the polarity balance of a novel two-dimensional hyperchaotic map is considered, and thus the corresponding manifold of conditional symmetry is coined. The unique map has a simple structure but provides direct 2-D offset boosting, which brings the possibility for the construction of conditional symmetry by introducing an absolute value function. The corresponding evolution of the discrete sequences from the system is verified by the circuit implementation based on the microcontroller of CH32V307. The pseudorandom data from the map increases its adaptability for applications in information security. The hyperchaotic sequence-injected Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Sparrow Search Algorithm (SSA) show their improved performance in the optimization algorithm. Robot path planning experiments confirm that all three algorithms exhibit superior convergence performance, global search capability, and path smoothness compared with the original algorithms. Full article

In this paper, a generalized synchronization (GS) framework for identical hyperchaotic systems is presented. The main objective is to achieve generalized synchronization with guaranteed global stability and effective convergence, which remains a key challenge in synchronization-based secure communication systems. The proposed controller is systematically derived to ensure global asymptotic convergence of the synchronization errors for arbitrary initial conditions and distinct scaling factors. This formulation unifies complete, anti-, and generalized synchronization within a single control structure. To demonstrate the applicability of the proposed method, it is integrated into an image encryption algorithm, where the hyperchaotic trajectories of the drive system generate highly random permutation and diffusion sequences. Simulation results verify that the designed controller achieves effective generalized synchronization and that the encrypted images exhibit uniform histograms and low pixel correlation, indicating strong security and resistance to statistical attacks. Full article

This paper investigates the dynamical properties of the fractional-order Arneodo system using a Grünwald–Letnikov-based numerical discretization. Fractional-order operators introduce memory and hereditary effects, enabling a more realistic description than classical integer-order models. The local stability of equilibrium points is examined through eigenvalue analysis of the Jacobian matrix, along with dissipativity conditions and the emergence of complex attractors. A comprehensive dynamical investigation is presented through phase portraits, time series, Lyapunov exponents, and bifurcation diagrams for varying fractional orders. Numerical findings demonstrate the emergence of new chaotic and hyperchaotic attractors. The results confirm that the fractional order strongly influences the system’s stability, sensitivity, and complexity. Our results confirm the relevance of fractional-order modeling in applications, such as secure communication, random number generation, and complex system analysis. Full article

Amid growing threats of image data leakage and misuse, image encryption has become a critical safeguard for protecting visual information. However, many recent image encryption algorithms remain constrained by trade-offs between security, efficiency, and practicability. To address these challenges, this paper first proposes a novel two-dimensional variable fractional-order coupled quadratic hyperchaotic map (2D-VFCQHM), which incorporates a state-dependent dynamic memory effect, wherein the fractional-order is adaptively determined at each iteration by the mean of the system’s current state. This mechanism substantially enhances the complexity and unpredictability of the underlying chaotic dynamics. Building upon the superior hyperchaotic properties of the 2D-VFCQHM, we further develop a high-performance image encryption algorithm that integrates a novel fusion strategy within a dynamic vector-level diffusion-scrambling framework (IEA-VMFD). Comprehensive security analyses and experimental results demonstrate that the proposed algorithm achieves robust cryptographic performance, including a key space of $2^{298}$, inter-pixel correlation coefficients below 0.0018, ciphertext entropy greater than 7.999, and near-ideal plaintext sensitivity. Crucially, the algorithm attains an encryption speed of up to 126.2963 Mbps. The exceptional balance between security strength and computational efficiency underscores the practical viability of our algorithm, rendering it well-suited for modern applications such as telemedicine, instant messaging, and cloud computing. Full article

Images, as carriers of rich information, are generated, stored, and transmitted in various forms across diverse scenarios. It has become an important issue in the field of information security today to encrypt images to ensure information security. To address this issue, this paper proposes a Pixel-Level and DNA-Level Image Encryption Method Based on a Five-Dimensional Hyperchaotic System, named PD5H. The proposed method combines a five-dimensional chaotic system, a novel pixel-block internal diffusion method, and a new flow diffusion method integrating Pixel-Level and DNA-Level encryption, hereinafter referred to as ‘joint diffusion’. The improved 5D chaotic system can generate highly complex and unpredictable chaotic sequences. The intra-block diffusion process utilizes the internal information of the image to perform preliminary diffusion and reduce pixel correlation. The joint diffusion process can effectively employ various encryption methods to encrypt images with different step sizes at the bit level. PD5H has a large key space, extremely low image correlation, a uniform ciphertext pixel distribution, an excellent ciphertext entropy value (>7.999), and strong resistance to differential attacks. It also demonstrates strong resistance to data loss. The security analysis confirms that PD5H demonstrates excellent performance in color image encryption and can effectively resist various common attacks. Full article

To address the limitations of traditional image encryption algorithms in key optimization and encryption quality assessment, in this paper we propose a framework for image encryption based on surrogate-assisted differential evolution. First, we construct a novel fitness function based on pixel correlation, which quantitatively evaluates and optimizes encryption quality by minimizing the pixel correlation coefficient. Second, we propose an adaptive hierarchical surrogate-assisted differential evolution algorithm (HSADE-IQUA), which combines global and local phases. In the global optimization phase, HSADE-IQUA significantly improves the convergence speed and solution quality in constrained optimization through adaptive parameter control. In the local optimization phase, the population size is dynamically adjusted using the exponential moving average (EMA), achieving a balance between exploration and exploitation. The performance of HSADE-IQUA has been validated on a commonly used expensive optimization benchmark suite, achieving excellent experimental results. Third, a Chen hyperchaotic-DNA coding fusion encryption framework optimized by HSADE-IQUA (HSADE-IQUA-DNA) was constructed and tested on standard computer vision images, labeled datasets, and remote sensing images, proving that HSADE-IQUA-DNA can significantly reduce pixel correlation, effectively resist exhaustive attacks, noise attacks, and shearing attacks, and accurately recover the original image. Compared with traditional chaotic image encryption, HSADE-IQUA-DNA not only has a bottleneck in parameter optimization but also alleviates the single-key issue, further improving encryption security. Full article

This study applies reinforcement learning to search parameter regimes that yield chaotic dynamics across six systems: the Logistic map, the Hénon map, the Lorenz system, Chua’s circuit, the Lorenz–Haken model, and a custom 5D hyperchaotic design. The largest Lyapunov exponent (LLE) is used as a scalar reward to guide exploration toward regions with high sensitivity to initial conditions. Under matched evaluation budgets, the approach reduces redundant simulations relative to grid scans and accelerates discovery of parameter sets with large positive LLE. Experiments report learning curves, parameter heatmaps, and representative phase portraits that are consistent with Lyapunov-based assessments. Q-learning typically reaches high-reward regions earlier, whereas SARSA shows smoother improvements over iterations. Several evaluated systems possess equation-level symmetry—most notably sign-reversal invariance in the Lorenz system and Chua’s circuit models and a coordinate-wise sign pattern in the Lorenz–Haken equations—which manifests as mirror attractors and paired high-reward regions; one representative is reported for each symmetric pair. Overall, Lyapunov-guided reinforcement learning serves as a practical complement to grid and random search for chaos identification in both discrete maps and continuous flows, and transfers with minimal changes to higher-dimensional settings. The framework provides an efficient method for identifying high-complexity parameters for applications in chaos-based cryptography and for assessing stability boundaries in engineering design. Full article

The dynamic confrontation between medical image-encryption technology and cryptanalysis enhances the security of sensitive healthcare information. Recently, Lai et al. proposed a color medical image-encryption scheme (LG-IES) based on a 2D Logistic-Gaussian hyperchaotic map (Applied Mathematics and Computation, 2023). This paper identifies that the LG-IES suffers from vulnerabilities stemming from the existence of equivalent keys and the linear solvability of the diffusion equation, enabling successful attacks through crafted chosen-plaintext attacks and known-plaintext attacks. For an $M\times N$ image, a system of linear equations with rank r can be constructed, resulting in a reduction of the key space from $2^{32\times M\times N}$ to $2^{32\times (M\times N-r)}$. To address these security flaws, the improved ILG-IES integrates the SHA-3 Edge-Pixel Filling Algorithm (SHA-3-EPFA), which includes plaintext-related SHA-3 hashing for parameter generation, a chaos-driven 3 × 3 × 3 Unit Rubik’s Cube rotation to achieve cross-channel fusion, and edge-pixel filling rules for diffusion encryption. ILG-IES outperforms LG-IES in attack resistance (resists CPA/KPA/differential attacks) while maintaining comparable security indicators (e.g., NPCR 99.6%, UACI 33.5%) to reference schemes. In future work, SHA-3-EPFA can be embedded as an independent module into most permutation-diffusion-based image-encryption systems, offering new perspectives for securing sensitive color images. Full article

The aim of this article is to introduce the distributed-order hyperchaotic detuned (DOHD) laser model. Its dissipative dynamics, invariance, and fixed points (FPs) and their stability are investigated. Numerical solutions of the DOHD laser model are computed using the modified Predictor–Corrector approach. Its viscoelasticity is described by the so-called DO derivative, allowing for the study of different technical systems and materials, and the model is found to have a whole circle of FPs as a hyperchaotic attractor. We discuss the coexistence of more attractors under various initial conditions and the same sets of parameters for our model (multistability). We also introduce the notion of dual combination synchronization (DCS), using four integer-order drive models and two DO response models. A theorem is stated and proved to obtain an analytical control function that ensures DCS for our models. Numerical simulations are presented to support these analytical results. Regarding the use of the well–known Caputo derivative, the results are very similar to those of DO, except when the Caputo order, $0<\sigma \le 1$, is very close to 1, where the dynamics shows a “spiralling behavior” towards a fixed point. In all other cases, both Caputo and DO exhibit a very similar behavior. Full article