Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application

The definition of fractional calculus is introduced into a 3D multi-attribute chaotic system in this paper. The fractional multi-attribute chaotic system (FMACS) numerical solution is obtained based on the Adomian decomposition method (ADM). The balance points and dynamical behaviors of self-excited and hidden attractors in FMACS are compared and analyzed through the Lyapunov spectrum, bifurcation model, and complexity. It is worth noting that some hidden coexistence attractors with different shapes are affected by the order. Besides, a novel chaotic system without equilibrium points is constructed, in which the nonlinear function term in FMACS is replaced with a rare nonlinear function e x . Meanwhile, its degradation phenomenon and state transition phenomenon are analyzed in detail. Finally, the digital circuit of the system is realized on the DSP board. The research result shows that FMACS has richer dynamical behaviors and higher complexity. This research provides a theoretical basis and guidance for the application of fractional chaotic systems.

A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation

Recently, a lot of research has been done in chaotic cryptography field using different kinds of chaotic systems, like chaotic maps, which are being considered as one of the secure and efficient methods to protect confidential information. This article highlights that the main cryptography requirements demand that the new embedded cryptosystems have to be more efficient and secure, it means that they must be faster and offer greater security. For instance, the new cryptosystems require to be compatible with the new telecommunication protocols and, in addition, to be efficient in energy consumption. In this manner, this article introduces a process to improve the randomness of five chaotic maps that are implemented on a PIC-microcontroller. The improved chaotic maps are tested to encrypt digital images in a wireless communication scheme, particularly on a machine-to-machine (M2M) link, via ZigBee channels. We show that function mod 255 improves the randomness of the pseudo-random number generators (PRNG), which is verified performing NIST SP 800-22 statistical tests, histograms, phase-plane analysis, entropy, correlation of adjacent pixels, differential attacks, and using digital images of size 256 × 256 and 512 × 512 pixels. A comparative analysis is presented versus related works that also use chaotic encryption and classic algorithms, such as: AES, DES, 3DES and IDEA. The security analysis confirms that the proposed process to improve the randomness of chaotic maps, is appropriate to implement an encryption scheme that is secure and robust against several known attacks and other statistical tests. Finally, it was experimentally verified that this chaotic encryption scheme can be used in practical applications such as M2M and Internet of things (IoT).

Randomness improvement of chaotic maps for image encryption in a wireless communication scheme using PIC-microcontroller via Zigbee channels

Abstract : The emerging discipline known as \"chaos theory\" is a relatively new field of study with a diverse range of applications (i.e., economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for \"chaos\" as it applies to general dynamical systems. Various approaches range from topological methods of a qualitative description; to physical notions of randomness, information, and entropy in ergodic theory; to the development of computational definitions and algorithms designed to obtain quantitative information. This thesis develops some of the current definitions and discusses several quantitative measures of chaos. It is intended to stimulate the interest of undergraduate and graduate students and is accessible to those with a knowledge of advanced calculus and ordinary differential equations. In covering chaos for continuous systems, it serves as a complement to the work done by Philip Beaver, which details chaotic dynamics for discrete systems.

Introduction of chaotic dynamical systems

Smart cameras and image sensors are widely used in industrial processes, from the designing to the quality checking of the final product. Images generated by these sensors are at continuous risk of disclosure and privacy breach in the industrial Internet of Things (IIoT). Traditional solutions to secure sensitive data fade in IIoT environments because of the involvement of third parties. Blockchain technology is the modern-day solution for trust issues and eliminating or minimizing the role of the third party. In the context of the IIoT, we propose a permissioned private blockchain-based solution to secure the image while encrypting it. In this scheme, the cryptographic pixel values of an image are stored on the blockchain, ensuring the privacy and security of the image data. Based on the number of pixels change rate (NPCR), the unified averaged changed intensity (UACI), and information entropy analysis, we evaluate the strength of proposed image encryption algorithm ciphers with respect to differential attacks. We obtained entropy values near to an ideal value of 8, which is considered to be safe from brute force attack. Encrypted results show that the proposed scheme is highly effective for data leakage prevention and security.

https://www.mdpi.com/1099-4300/22/2/175/pdf

A Blockchain-Based Secure Image Encryption Scheme for the Industrial Internet of Things.

Based on the one-dimensional Sine map and the two-dimensional Henon map, a new two-dimensional Sine-Henon alteration model (2D-SHAM) is hereby proposed. Basic dynamic characteristics of 2D-SHAM are studied through the following aspects: equilibria, Jacobin eigenvalues, trajectory, bifurcation diagram, Lyapunov exponents and sensitivity dependence test. The complexity of 2D-SHAM is investigated using Sample Entropy algorithm. Simulation results show that 2D-SHAM is overall hyperchaotic with the high complexity, and high sensitivity to its initial values and control parameters. To investigate its performance in terms of security, a new 2D-SHAM-based image encryption algorithm (SHAM-IEA) is also proposed. In this algorithm, the essential requirements of confusion and diffusion are accomplished, and the stochastic 2D-SHAM is used to enhance the security of encrypted image. The stochastic 2D-SHAM generates random values, hence SHAM-IEA can produce different encrypted images even with the same secret key. Experimental results and security analysis show that SHAM-IEA has strong capability to withstand statistical analysis, differential attack, chosen-plaintext and chosen-ciphertext attacks.

A new hyperchaotic map and its application for image encryption

In this paper, a new 3D chaotic system with trigonometric function term as a nonlinear controller is proposed. Depending on the nonlinear controller and the value of the parameters, the proposed system exhibits self-excited attractor with an unstable equilibrium, and hidden attractor with no equilibrium or a stable equilibrium. In addition, the unusual and striking dynamic behavior of the coexistence of self-excited chaotic with periodic attractors, two self-excited chaotic attractors with periodic attractor, three periodic attractors, hidden chaotic with point attractors, two hidden chaotic attractors, and four hidden chaotic attractors are explored by selecting appropriate initial values. Consequently, the proposed system has high sensitivity to its initial values and parameters, hence it can be applied in chaos-based cryptographic applications. Thus, the non-periodicity of coexisting attractors of the system is investigated through Lyapunov exponents and Sample Entropy. To demonstrate the performance of the system in real applications, we construct a pseudo-random number generator (PRNG) based on the hidden attractor case. The randomness test results show that the generated PRNG pass all the statistical tests.

Self-excited and hidden attractors in a novel chaotic system with complicated multistability

Derived from Lorenz-Haken equations, this paper presents a new 4D chaotic laser system with three equilibria and only two quadratic nonlinearities. Dynamics analysis, including stability of symmetric equilibria and the existence of coexisting multiple Hopf bifurcations on these equilibria, are investigated, and the complex coexisting behaviors of two and three attractors of stable point and chaotic are numerically revealed. Moreover, a conducted research on the complexity of the laser system reveals that the complexity of the system time series can locate and determine the parameters and initial values that show coexisting attractors. To investigate how much a chaotic system with multistability behavior is suitable for cryptographic applications, we generate a pseudo-random number generator (PRNG) based on the complexity results of the laser system. The randomness test results show that the generated PRNG from the multistability regions fail to pass most of the statistical tests.

https://www.mdpi.com/1099-4300/21/1/34/pdf

Dynamics and Complexity of a New 4D Chaotic Laser System

Due to the rapid development of the fifth-generation (5G) applications, and increased demand for even faster communication networks, we expected to witness the birth of a new 6G technology within the next ten years. Many references suggested that the 6G wireless network standard may arrive around 2030. Therefore, this paper presents a critical analysis of 5G wireless networks’, significant technological limitations and reviews the anticipated challenges of the 6G communication networks. In this work, we have considered the applications of three of the highly demanding domains, namely: energy, Internet-of-Things (IoT) and machine learning. To this end, we present our vision on how the 6G communication networks should look like to support the applications of these domains. This work presents a thorough review of 370 papers on the application of energy, IoT and machine learning in 5G and 6G from three major libraries: Web of Science, ACM Digital Library, and IEEE Explore. The main contribution of this work is to provide a more comprehensive perspective, challenges, requirements, and context for potential work in the 6G communication standard.

From 5G to 6G Technology: Meets Energy, Internet-of-Things and Machine Learning: A Survey

In this paper, we investigate the dynamical behavior in an M-dimensional nonlinear hyperchaotic model (M-NHM), where the occurrence of multistability can be observed. Four types of coexisting attractors including single limit cycle, cluster of limit cycles, single hyperchaotic attractor, and cluster of hyperchaotic attractors can be found, which are unusual behaviors in discrete chaotic systems. Furthermore, the coexistence of asymmetric and symmetric properties can be distinguished for a given set of parameters. In the endeavor of chaotification, this work introduces a simple controller on the M-NHM, which can add one more loop in each iteration, to overcome the chaos degradation in the multistability regions.

Hayder Natiq

Papers

A new hyperchaotic map and its application for image encryption

Self-excited and hidden attractors in a novel chaotic system with complicated multistability

Dynamics and Complexity of a New 4D Chaotic Laser System

From 5G to 6G Technology: Meets Energy, Internet-of-Things and Machine Learning: A Survey

Can hyperchaotic maps with high complexity produce multistability