Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

On the Term Set's Semantics for Pairwise Comparisons in Fuzzy Linguistic Preference Models

The main objective of this paper is the definition of a membership function assignment procedure based on inherent features of linguistic terms to determine their semantics when they are used for preference modelling. For this purpose, we consider what linguists say about concepts such as language complementarity, the influence of context, or the effects of the use of hedges (modifiers) on adverbs meaning. As a result, specificity, entropy and position in the universe of discourse of the functions assigned to each linguistic term are mainly determined by the intrinsic meaning of the hedges concerned. We uphold that the meaning of weakening hedges is linguistically non-inclusive because their semantics are subordinated to the proximity to the indifference meaning, whereas reinforcement hedges are linguistically inclusive. Consequently, the membership function assignment rules are different: fuzzy relational calculus and the horizon shifting model derived from the Alternative Set Theory are used to handle weakening and reinforcement hedges, respectively. The proposed elicitation method provides for the term set semantics, non-uniform distributions of non-symmetrical triangular fuzzy numbers, depending on the number of terms used and the character of the hedges involved. (This article belongs to the section "Information Theory, Probability and Statistics").

Chaos-enhanced multi-objective tunicate swarm algorithm for economic-emission load dispatch problem

Climate change and environmental protection have a significant impact on thermal plants. So, the main principles of combined economic-emission dispatch (CEED) problem are indeed to reduce greenhouse gas emissions and fuel costs. Many approaches have demonstrated their efficacy in addressing CEED problem. However, designing a robust algorithm capable of achieving the Pareto optimal solutions under its multimodality and non-convexity natures caused by valve ripple effects is a true challenge. In this paper, chaos-enhanced multi-objective tunicate swarm algorithm (CMOTSA) for CEED problem. To promote the exploration and exploitation abilities of the basic tunicate swarm algorithm (TSA), an exponential strategy based on chaotic logistic map (ESCL) is incorporated. Based on ESCL in CMOTSA, it can improve the possibility of diversification feature to search different areas within the solution space, and then, gradually with the progress of iterative process it converts to emphasize the intensification ability. The efficacy of CMOTSA is approved by applying it to some of multi-objective benchmarking functions which have different Pareto front characteristics including convex, discrete, and non-convex. The inverted generational distance (IGD) and generational distance (GD) are employed to assess the robustness and the good quality of CMOTSA against some successful algorithms. Additionally, the computational time is evaluated, the CMOTSA consumes less time for most functions. The CMOTSA is applied to one of the practical engineering problems such as combined economic and emission dispatch (CEED) with including the valve ripples. By using three different systems (IEEE 30-bus with 6 generators system, 10 units system and IEEE 118-bus with 14 generating units), the methodology validation is made. It can be stated for the large-scale case of 118-bus systems that the results of the CMOTSA are equal to 8741.3 $/h for the minimum cost and 2747.6 ton/h for the minimum emission which are very viable to others. It can be pointed out that the cropped results of the proposed CMOTSA based methodology as an efficient tool for CEED is proven.

A Novel Discrete-Time Chaos-Function-Based Random-Number Generator: Design and Variability Analysis

This paper presents a novel discrete-time (DT) chaotic map-based random-number generator (RNG), namely the Siponi map, which is a modification of the Logistic map. The Logistic map is usually applied to cryptosystems, mainly for the purposes of generating random numbers. In addition to being easy to implement, it has a better security level than other nonlinear functions. However, it can only process positive real-number inputs. Our proposed map is a deterministic function that can process positive and negative real values. We explored the map comprehensively and investigated its characteristics and parameters. We calculated the optimum parameter values using empirical and theoretical mathematical models to yield the maximum randomness of a sequence of bits. The limit variation of the maximum parameter value was determined based on a practical information measure. Empirical verification was performed for the Siponi map to generate bit sequences unrelated to the previous bit with high entropy values, and we found the extractor function threshold value to be 0.5, while the parameter control was −2 or 2. Using our proposed map, a simple RNG without post-processing passed DieHard statistical tests and all the tests on the NIST SP 800-22. Finally, we have implemented a Siponi map-based RNG on the FPGA board and demonstrated that the sources used are LUT = 4086, DSP = 62, and register = 2206.

Critical Analysis of Hypothesis Tests in Federal Information Processing Standard (140-2)

This work presents an analysis of the existing dependencies between the tests of the FIPS 140-2 battery. Two main analytical approaches are utilized, the first being a study of correlations through the Pearson’s correlation coefficient that detects linear dependencies, and the second one being a novel application of the mutual information measure that allows detecting possible non-linear relationships. In order to carry out this study, the FIPS 140-2 battery is reimplemented to allow the user to obtain p-values and statistics that are essential for more rigorous end-user analysis of random number generators (RNG).

An Optical Image Encryption Method Using Hopfield Neural Network

In this paper, aiming to solve the problem of vital information security as well as neural network application in optical encryption system, we propose an optical image encryption method by using the Hopfield neural network. The algorithm uses a fuzzy single neuronal dynamic system and a chaotic Hopfield neural network for chaotic sequence generation and then obtains chaotic random phase masks. Initially, the original images are decomposed into sub-signals through wavelet packet transform, and the sub-signals are divided into two layers by adaptive classification after scrambling. The double random-phase encoding in 4f system and Fresnel domain is implemented on two layers, respectively. The sub-signals are performed with different conversions according to their standard deviation to assure that the local information’s security is guaranteed. Meanwhile, the parameters such as wavelength and diffraction distance are considered as additional keys, which can enhance the overall security. Then, inverse wavelet packet transform is applied to reconstruct the image, and a second scrambling is implemented. In order to handle and manage the parameters used in the scheme, the public key cryptosystem is applied. Finally, experiments and security analysis are presented to demonstrate the feasibility and robustness of the proposed scheme.

Chaos in the Real World: Recent Applications to Communications, Computing, Distributed Sensing, Robotic Motion, Bio-Impedance Modelling and Encryption Systems

Most of the papers published so far in literature have focused on the theoretical phenomena underlying the formation of chaos, rather than on the investigation of potential applications of chaos to the real world. This paper aims to bridge the gap between chaos theory and chaos applications by presenting a survey of very recent applications of chaos. In particular, the manuscript covers the last three years by describing different applications of chaos as reported in the literature published during the years 2018 to 2020, including the matter related to the symmetry properties of chaotic systems. The topics covered herein include applications of chaos to communications, to distributed sensing, to robotic motion, to bio-impedance modelling, to hardware implementation of encryption systems, to computing and to random number generation.

Single Neuronal Dynamical System in Self-Feedbacked Hopfield Networks and Its Application in Image Encryption

Image encryption is a confidential strategy to keep the information in digital images from being leaked. Due to excellent chaotic dynamic behavior, self-feedbacked Hopfield networks have been used to design image ciphers. However, Self-feedbacked Hopfield networks have complex structures, large computational amount and fixed parameters; these properties limit the application of them. In this paper, a single neuronal dynamical system in self-feedbacked Hopfield network is unveiled. The discrete form of single neuronal dynamical system is derived from a self-feedbacked Hopfield network. Chaotic performance evaluation indicates that the system has good complexity, high sensitivity, and a large chaotic parameter range. The system is also incorporated into a framework to improve its chaotic performance. The result shows the system is well adapted to this type of framework, which means that there is a lot of room for improvement in the system. To investigate its applications in image encryption, an image encryption scheme is then designed. Simulation results and security analysis indicate that the proposed scheme is highly resistant to various attacks and competitive with some exiting schemes.

Multi-scroll hidden attractor in memristive HR neuron model under electromagnetic radiation and its applications

This paper aims to propose a novel no-equilibrium Hindmarsh-Rose (HR) neuron model with memristive electromagnetic radiation effect. Compared with other memristor-based HR neuron models, the uniqueness of this memristive HR neuron model is that it can generate multi-scroll hidden attractors with sophisticated topological structures and the parity of the scrolls can be controlled conveniently with changing the internal parameters of the memristor. In particular, the number of scrolls of the multi-scroll hidden attractors is also associated with the intensity of external electromagnetic radiation stimuli. The complex dynamics is numerically studied through phase portraits, bifurcation diagrams, Lyapunov exponents, and a two-parameter diagram. Furthermore, hardware circuit experiments are carried out to demonstrate theoretical analyses and numerical simulations. From the perspective of engineering application, a pseudo-random number generator is designed. Besides, an image encryption application and security analysis are also performed. The obtained results show that the memristive HR neuron model possesses excellent randomness and high security, which is suitable for chaos-based real-world applications.

Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors II

According to the pioneering work of Leonov and Kuznetsov [...].

Coexisting Infinite Orbits in an Area-Preserving Lozi Map

Extreme multistability with coexisting infinite orbits has been reported in many continuous memristor-based dynamical circuits and systems, but rarely in discrete dynamical systems. This paper reports the finding of initial values-related coexisting infinite orbits in an area-preserving Lozi map under specific parameter settings. We use the bifurcation diagram and phase orbit diagram to disclose the coexisting infinite orbits that include period, quasi-period and chaos with different types and topologies, and we employ the spectral entropy and sample entropy to depict the initial values-related complexity. Finally, a microprocessor-based hardware platform is developed to acquire four sets of four-channel voltage sequences by switching the initial values. The results show that the area-preserving Lozi map displays coexisting infinite orbits with complicated complexity distributions, which heavily rely on its initial values.