Search Results (9)

To address the growing threat of quantum computing to classical cryptographic primitives, this study introduces NTRU-MCF, a novel lattice-based signature scheme that integrates multidimensional lattice structures with fractional-order chaotic systems. By extending the NTRU framework to multidimensional polynomial rings, NTRU-MCF exponentially expands the private key search space, achieving a key space size $\ge 2^{256}$ for dimensions $m\ge 2$ and rendering brute-force attacks infeasible. By incorporating fractional-order chaotic masks generated via a hyperchaotic Lü system, the scheme introduces nonlinear randomness and robust resistance to physical attacks. Fractional-order chaotic masks, generated via a hyperchaotic Lü system validated through NIST SP 800-22 randomness tests, replace conventional pseudorandom number generators (PRNGs). The sensitivity to initial conditions ensures cryptographic unpredictability, while the use of a fractional-order L hyperchaotic system—instead of conventional pseudorandom number generators (PRNGs)—leverages multiple Lyapunov exponents and initial value sensitivity to embed physically unclonable properties into key generation, effectively mitigating side-channel analysis. Theoretical analysis shows that NTRU-MCF’s security reduces to the Ring Learning with Errors (RLWE) problem, offering superior quantum resistance compared to existing NTRU variants. While its computational and storage complexity suits high-security applications like military and financial systems, it is less suitable for resource-constrained devices. NTRU-MCF provides robust quantum resistance and side-channel defense, advancing PQC for classical computing environments. Full article

This paper proposes a novel, practical, predefined-time control theory for chaotic system synchronization under external disturbances and modeling uncertainties. Based on this theory, a robust sliding mode surface is designed to minimize chattering on a sliding surface, enhancing system stability. Additionally, a norm-based adaptive control strategy is developed to dynamically adjust control gains, ensuring system convergence to the equilibrium point within the predefined time. Theoretical analysis guarantees predefined-time stability using a Lyapunov framework. Numerical simulations on the Chen and multi-wing chaotic Lu systems demonstrate the proposed method’s superior convergence speed, precision, and robustness, highlighting its applicability to complex systems. Full article

Along with the recent advancements in video streaming, concerns over the security of transferred data have increased. Thus, the development of fast and reliable image encryption methodologies has become an emerging research area in the field of communications. In this paper, a systolic array-based image encryption architecture is proposed. Systolic arrays are used to apply the convolution operation, and a Lü–Chen chaotic oscillator is used to obtain a convolutional filter. To decrease resource consumption, a method to fuse confusion and diffusion processes by using systolic arrays is also proposed in this paper. The results show that the proposed method is highly secure against some differential and statistical attacks. It is also shown that the proposed method has a high speed of encryption compared to other methods. Full article

It is well known that multiplication inside a computer does not follow the associative property because of roundoff effects. It is possible to use this fact to generate other different chaotic instances of chaotic maps or oscillators when a multiplication of three terms appears. Chaos is very sensitive to small changes in the initial conditions and amplifies these small rounding effects. We use this condition to build different chaotic instances, which give different results, of the Lü oscillator and the 2D map, and we show one application to create new instances of a pseudo random number generator using the 2D map. Both chaotic systems are simulated in software and in hardware within an FPGA where another 144 different 2D map instances and 81 different Lü oscillators can be created. To best of our knowledge, it is the first paper that analyze the construction of new chaotic entities by using the roundoff effects. Full article

The presence of uncertainty and disturbance can lead to asymmetric control of nonlinear systems, and this asymmetric control can lead to a decrease in the productivity of the engineered system. In order to improve the control speed of the improved nonlinear system, complete synchronization and partial anti-synchronization of complex Lü chaotic systems with uncertainty and disturbance are investigated in the present paper. First, a new UDE-based dynamic feedback control method is proposed for the complete synchronization problem of the system. The method unites the dynamic gain feedback control method and the uncertainty and perturbation estimator (UDE) control method, where the dynamic gain feedback controller is used to achieve asymptotic stability of the nominal system and the UDE controller is used to handle a given controlled system with uncertainty and disturbance. Second, for the partial desynchronization problem of this system, a new UDE-based linear-like feedback control method is proposed, which consists of two controllers: a linear-like feedback controller used to achieve the asymptotic stabilization of the nominal system and the other UDE controller is designed to handle the given controlled system with uncertainty and disturbance. Finally, numerical simulations are performed to verify the correctness and stability of the theoretical results. Full article

Recently, with the rapid development of biomedical information, establishing secure communication and appropriate security services has become necessary to ensure a secure information exchange process. Therefore, to protect the privacy and confidentiality of personal data, in this study, we use a chaotic system, Lü system of the Lorenz-like system, to generate chaotic signals and apply them to encrypt the biomedical information. In addition, with one of the states of the chaotic system, we design a simple proportional-derivative (PD) controller to synchronize the master-slave chaotic systems for decrypting the biomedical information. Then, we encrypt the biomedical information, electrocardiography (ECG) and electromyography (EMG), measured about 30 s to 60 s to get tens of thousands of data from the subjects at the transmitting side (master) and send them to the receiving side (slave). After the receiving side receives the encrypted information, it decrypts them with the PD controller and then obtains the 1 mV to 2 mV biomedical signals. Thus, the security of the biomedical information can be ensured and realized. Full article

Although complex Lü systems have been considered in many studies, application of the self-time-delay synchronization (STDS) of complex Lü systems in secure speech communications does not appear to have been covered in much of the literature. Therefore, it is meaningful to study the STDS of complex Lü systems and its application in secure speech communication. First, a complex Lü system with double time-delay is introduced and its chaotic characteristics are analyzed. Second, a synchronization controller is designed to achieve STDS. Third, the improved STDS controller is used to design a speech communication scheme based on a complex Lü system. Finally, the effectiveness of the controller and communication scheme are verified by simulation. Full article

In this paper, we apply the differential Galoisian approach to investigate the meromorphic non-integrability of a class of 3D equations in mathematical physics, including Nosé–Hoover equations, the Lü system, the Rikitake-like system and Rucklidge equations, which are well known in the fields of molecular dynamics, chaotic theory and fluid mechanics, respectively. Our main results show that all these considered systems are, in fact, non-integrable in nearly all parameters. Full article

In this paper, we demonstrate that anti-synchronization (AS) phenomena of chaotic systems with different dimensions can coexist in the finite-time with under the effect of both unknown model uncertainty and external disturbance. Based on the finite-time stability theory and using the master-slave system AS scheme, a generalized approach for the finite-time AS is proposed that guarantee the global stability of the closed-loop for reduced order and increased order AS in the finite time. Numerical simulation results further verify the robustness and effectiveness of the proposed finite-time reduced order and increased order AS schemes. Full article