scholarly journals ON THE DYNAMICAL DEGRADATION OF DIGITAL PIECEWISE LINEAR CHAOTIC MAPS

2005 ◽  
Vol 15 (10) ◽  
pp. 3119-3151 ◽  
Author(s):  
SHUJUN LI ◽  
GUANRONG CHEN ◽  
XUANQIN MOU

When chaotic systems are realized with finite precisions in digital computers, their dynamical properties are often found to be entirely different from the original versions in the continuous setting. In the literature, there does not seem to be much work on quantitative analysis of such degradation of digitized chaos and how to reduce its negative influence on chaos-based digital systems. Focusing on 1D piecewise linear chaotic maps (PWLCM), this paper reports some findings on a new series of dynamical indicators, which can quantitatively reflect the degradation effects on a digital PWLCM realized with a fixed-point finite precision. On top of that, the paper introduces a new method for studying digital chaos from an algorithmic point of view. In addition, the theoretical results obtained in this paper should be very helpful for the consideration of reducing negative influence of dynamical degradation in real design of various digital chaotic systems. As typical examples, the proposed dynamical indicators are applied to the performance comparison of different remedies for improving dynamical degradation, cryptanalysis of digital chaotic ciphers based on 1D PWLCM, and design of chaotic pseudo-random number generators with desired characteristics.

2018 ◽  
Vol 29 (08) ◽  
pp. 1850074 ◽  
Author(s):  
Jin Zhong ◽  
Dong Jiang ◽  
Qi-Guo Huang ◽  
Yang Cao

Chaotic cryptography has been extensively investigated over the past three decades, especially in the field of digital chaotic cryptography. In this paper, we propose a new digital chaotic stream cipher based on double piecewise linear chaotic maps. It initially takes four real numbers as the key, periodically updates the chaotic maps, and efficiently outputs the bit strings. Theoretical analysis shows that our protocol achieves higher anti-cryptanalysis capacities, effectively alleviates the dynamical degradation problem, and thus reaches higher security. Statistical evaluation demonstrates that our protocol can generate bit strings with outstanding statistical properties. In addition, we apply our protocol to image encryption and decryption. Experimental results verify the conclusions of the statistical evaluation, and prove the strong sensitivity of the protocol to the key.


2019 ◽  
Vol 29 (08) ◽  
pp. 1930023 ◽  
Author(s):  
Chunlei Fan ◽  
Qun Ding ◽  
Chi K. Tse

The performance of digital chaotic systems in secure communications and cryptographic applications is significantly degraded due to the limited precision of digital computational devices that are used to implement digital chaotic systems. However, regardless of the initial value, the digital chaotic map employed in these applications converges to several periodic orbits. Thus, a periodic orbit search algorithm (POSA) can be designed to accurately locate fixed points and limit cycles. In addition, an effective method based on stochastic jumps of chaotic orbits is proposed to counteract the performance degradation of digital chaos. Numerical simulations were performed to assess the effectiveness and feasibility of the proposed method in terms of autocorrelation, phase space inspection, approximate entropy and periodicity analysis. Furthermore, comparison with other existing methods is presented to show the competitiveness of the proposed scheme. Finally, a pseudorandom bit generator (PRBG), with desirable statistical properties, is constructed for chaos cryptography and other applications.


2015 ◽  
Vol 26 (02) ◽  
pp. 1550022 ◽  
Author(s):  
Yashuang Deng ◽  
Hanping Hu ◽  
Lingfeng Liu

The dynamical properties will degrade when chaotic systems are implemented in digital computers with finite precisions, and such degradation often has serious negative influence on some digital chaos-based systems. Degradation reduction for a class of digital chaotic systems is investigated in this paper. A varying parameter control method is proposed based on the state feedback control technology at first. Then two chaotic maps are applied to verify its validity. Finally, a novel pseudorandom number generator is constructed, which can pass all the tests of NIST SP800-22 at both level-one and level-two approaches and also most of the tests of TestU01. Moreover, it performs better than some existing pseudorandom number generators. Thus, it has acceptable quality of randomness and can be used for cryptography and other applications.


Author(s):  
R. A. Orekhov ◽  

There is a common point of view in Egyptology that Memphis was a state capital since the earliest times and that its protecting gods were Ptah and his spouse Sekhmet. Arguing this concept, the author tries to find the reason why a pyramid city of Pepi I — Mennefer — became a core of the future capital. The main conclusion is following: Constructing his pyramid complex, Pepi I probably included into it a cult center of Habes where Bastet and Imhotep, a high priest of Ra, were worshiped. Imhotep, a companion of the king Djoser, was known as a priest and charmer who tamed the fiery forces of Sirius associated with Bastet, after which the great drought was over. To commemorate this, New Year celebration and the first sun calendar were established. Imhotep’s tomb became an important cult place, where ceremonies important for surviving of the Egyptian state were conducted. In the second half of the Old Kingdom period the Nile started to flood much less, which led to the decline of agriculture. Thus, the role of the cult center of Habes and Imhotep grew greatly. By including Habes, Pepi protected the dominion of his pyramid city from negative influence of Bastet and decreased flooding. The fact that Mennefer was a successor of the aforementioned cult center determined its capital functions in future.


2018 ◽  
Vol 3 (5) ◽  
pp. 39
Author(s):  
Yéssica Elizabeth Barreto Macías ◽  
Colón Avellán Velásquez

El actual trabajo afronta una de las problemáticas más apremiantes de los actuales momentos como es el alto índice de dispendio de drogas en las Instituciones Educativas, que afectan considerablemente a la sociedad ecuatoriana. Su objetivo es analizar los lineamientos que permitan mejorar la orientación familiar, y desarrollar relaciones interpersonales apropiadas que fomenten la unión familiar, practicar principios, fomentar valores morales, y que los jóvenes aprendan a decir “no” ante una eventual propuesta de consumir compuestos prohibidos, que lo único que se consigue es materializarse en un estado no idóneo ante la comunidad, considerar que las consecuencias para la salud son devastadoras, personas que a temprana edad padecen de enfermedades que en muchas ocasiones son gravísimas, causando malestar no solamente propio sino a la familia. Puedo mencionar como aporte de este artículo; y en base a resultados establecidos que resulta primordial e importante mantener la asistencia de un profesional especializado en psicología, diálogos científicos y motivadores, conjuntamente con atención médica provocarán en la persona afectada la erradicación del consumo de drogas. Constan muchos factores que causan gran influencia negativa en las familias, partiendo de que actualmente el mundo vive la tendencia del consumismo lo que influye en sobremanera que exista menos dialogo en el hogar, la aparición de la tecnología es otra de las situaciones adversas. Los profesionales encargados de brindar orientación familiar deben considerar siempre, que el comportamiento del ser humano debe ser comprendido desde el punto de vista de su forma de pensar, solo así se desarrollara una cultura que permita a las familias tomar las decisiones acertadas al momento de formar a sus hijos, lo que en un futuro se evidenciará como seres útiles a la sociedad. PALABRAS CLAVE: Consumo de drogas; orientación familiar; valores morales.  FAMILY COUNSELING, FOR THE PREVENTION OF DRUG USE IN THIRDYEAR HIGH SCHOOL STUDENTS  ABSTRACT  The current work addresses one of the most pressing issues of current times such as the high rate of drug use in educational institutions, which greatly affect Ecuadorian society. Its objective is to analyze the guidelines for improving family orientation, and develop appropriate interpersonal relationships that promote family unity, value the principles, and that young people learn to say "no" to a possible proposal to use prohibited drugs, that the only thing that is achieved is to materialize in an unsuitable state before the community, to consider that the consequences for health are devastating, people who at an early age suffer from diseases that in many occasions are very serious, causing discomfort not only their own but also the family. I can mention as contribution of this article; and based on established results that it is essential and important to maintain the assistance of a professional specialized in psychology, scientific and motivational dialogues, together with medical care, will cause the affected person to eradicate drug use. There are many factors that cause great negative influence on families, based on the fact that the world currently lives the trend of consumerism which greatly influences that there is less dialogue at home, the emergence of technology is another of the adverse situations. The professionals responsible for providing family counseling should always consider that the behavior of the human being should be understood from the point of view of their way of thinking, only in this way will a culture be developed that allows families to make the right decisions when forming to their children, which in the future will be evident as useful beings to society. KEYWORDS: drug use; family orientation; moral values.


2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.


Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1313
Author(s):  
Wenhao Yan ◽  
Qun Ding

In this paper, a method to enhance the dynamic characteristics of one-dimension (1D) chaotic maps is first presented. Linear combinations and nonlinear transform based on existing chaotic systems (LNECS) are introduced. Then, a numerical chaotic map (LCLS), based on Logistic map and Sine map, is given. Through the analysis of a bifurcation diagram, Lyapunov exponent (LE), and Sample entropy (SE), we can see that CLS has overcome the shortcomings of a low-dimensional chaotic system and can be used in the field of cryptology. In addition, the construction of eight functions is designed to obtain an S-box. Finally, five security criteria of the S-box are shown, which indicate the S-box based on the proposed in this paper has strong encryption characteristics. The research of this paper is helpful for the development of cryptography study such as dynamic construction methods based on chaotic systems.


2019 ◽  
Vol 29 (08) ◽  
pp. 1950112 ◽  
Author(s):  
Erivelton G. Nepomuceno ◽  
Priscila F. S. Guedes ◽  
Alípio M. Barbosa ◽  
Matjaž Perc ◽  
Robert Repnik

Soft computing strategies are drawing widespread interest in engineering and science fields, particularly so because of their capacity to reason and learn in a domain of inherent uncertainty, approximation, and unpredictability. However, soft computing research devoted to finite precision effects in chaotic system simulations is still in a nascent stage, and there are ample opportunities for new discoveries. In this paper, we consider the error that is due to finite precision in the simulation of chaotic systems. We present a generalized version of the lower bound error using an arbitrary number of natural interval extensions. The lower bound error has been used to simulate a chaotic system with lower and upper bounds. The width of this interval does not diverge, which is an advantage compared to other techniques. We illustrate our approach on three systems, namely the logistic map, the Singer map and the Chua circuit. Moreover, we validate the method by calculating the largest Lyapunov exponent.


1997 ◽  
Vol 07 (07) ◽  
pp. 1617-1634 ◽  
Author(s):  
G. Millerioux ◽  
C. Mira

Recently, it was demonstrated that two chaotic dynamical systems can synchronize each other, leading to interesting applications as secure communications. We propose in this paper a special class of dynamical systems, noninvertible discrete piecewise linear, emphasizing on interesting advantages they present compared with continuous and differentiable nonlinear ones. The generic aspect of such systems, the simplicity of numerical implementation, and the robustness to mismatch of technological parameters make them good candidates. The classical concept of controllability in the control theory is presented and used in order to choose and predict the number of appropriate variables to be transmitted for synchronization. A necessary and sufficient condition of chaotic synchronization is established without computing numerical quantities, introducing a state affinity structure of chaotic systems which provides an a priori establishment of synchronization.


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