A Chaotification model based on sine and cosecant functions for enhancing chaos

2021 ◽  
Author(s):  
Yuqing Li ◽  
Xing He ◽  
Dawen Xia
Keyword(s):  
Fixed Point ◽  
Lyapunov Exponent ◽  
Chaotic Maps ◽  
Dynamic Properties ◽  
Chaotic Map ◽  
Sample Entropy ◽  
One Dimensional ◽  
Model Based ◽  
Chaotic Region ◽  
Definition Of

Chaotic maps with higher chaotic complexity are urgently needed in many application scenarios. This paper proposes a chaotification model based on sine and cosecant functions (CMSC) to improve the dynamic properties of existing chaotic maps. CMSC can generate a new map with higher chaotic complexity by using the existing one-dimensional (1D) chaotic map as a seed map. To discuss the performance of CMSC, the chaos properties of CMSC are analyzed based on the mathematical definition of the Lyapunov exponent (LE). Then, three new maps are generated by applying three classical 1D chaotic maps to CMSC respectively, and the dynamic behaviors of the new maps are analyzed in terms of fixed point, bifurcation diagram, sample entropy (SE), etc. The results of the analysis demonstrate that the new maps have a larger chaotic region and excellent chaotic characteristics.

scholarly journals Research on Pseudorandom Number Generator Based on Several New Types of Piecewise Chaotic Maps

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hongyan Zang ◽  
Yue Yuan ◽  
Xinyuan Wei
Keyword(s):  
Theoretical Basis ◽  
Chaotic Maps ◽  
Dynamic Properties ◽  
Chaotic Map ◽  
Pseudorandom Number ◽  
Pseudorandom Number Generator ◽  
Number Generator ◽  
High Quality ◽  
One Dimensional ◽  
Construction Methods

This paper proposes three types of one-dimensional piecewise chaotic maps and two types of symmetrical piecewise chaotic maps and presents five theorems. Furthermore, some examples that satisfy the theorems are constructed, and an analysis and model of the dynamic properties are discussed. The construction methods proposed in this paper have a certain generality and provide a theoretical basis for constructing a new discrete chaotic system. In addition, this paper designs a pseudorandom number generator based on piecewise chaotic map and studies its application in cryptography. Performance evaluation shows that the generator can generate high quality random sequences efficiently.

scholarly journals A Novel S-Box Dynamic Design Based on Nonlinear-Transform of 1D Chaotic Maps

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1313
Author(s):  
Wenhao Yan ◽  
Qun Ding
Keyword(s):  
Chaotic Systems ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Logistic Map ◽  
Sample Entropy ◽  
One Dimension ◽  
Linear Combinations ◽  
Dynamic Design ◽  
Construction Methods ◽  
Low Dimensional

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.

Optimal Control of a Chaotic Map: Fixed Point Stabilization and Attractor Confinement

1997 ◽  
Vol 07 (02) ◽  
pp. 437-446 ◽  
Author(s):  
C. Piccardi ◽  
L. L. Ghezzi
Keyword(s):  
Optimal Control ◽  
Fixed Point ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Chaotic Attractor ◽  
Chaotic Map ◽  
Optimal Controller ◽  
Control Of Chaos ◽  
One Dimensional ◽  
Suppression Of Chaos

Optimal control is applied to a chaotic system. Reference is made to a well-known one-dimensional map. Firstly, attention is devoted to the stabilization of a fixed point. An optimal controller is obtained and compared with other controllers which are popular in the control of chaos. Secondly, allowance is made for uncertainty and emphasis is placed on the reduction rather than the suppression of chaos. The aim becomes that of confining a chaotic attractor within a prescribed region of the state space. A controller fulfilling this task is obtained as the solution of a min-max optimal control problem.

DESIGN OF PSEUDO-RANDOM BIT GENERATOR BASED ON CHAOTIC MAPS

2012 ◽  
Vol 26 (32) ◽  
pp. 1250208 ◽  
Author(s):  
XING-YUAN WANG ◽  
LEI YANG
Keyword(s):  
Cycle Length ◽  
Stream Cipher ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
The Other ◽  
One Dimensional ◽  
Random Bit Generator ◽  
Dynamical Properties ◽  
Finite States

In order to solve the problem of degradation of dynamical properties caused by finite states of computer, a new binary stream-cipher algorithm based on dual one-dimensional chaotic maps is proposed in this paper. In the process of generation, we employ a parameter of one chaotic map to perturb the other chaotic map's trajectory to lengthen the cycle-length of the other chaotic map's trajectory. In addition, we design a nonlinear principle to generate a pseudo-random chaotic bit sequence as key stream. Statistic proprieties show that the sequence is of high randomness.

scholarly journals A Simple Chaotic Map Model for Fractal Traffic Flows in High-speed Computer Networks (Extended and Renewed Version)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Computer Networks ◽  
Hurst Exponent ◽  
High Speed ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Traffic Flows ◽  
One Dimensional ◽  
Temporal Series ◽  
Proposed Model ◽  
Speed Computer

This paper presents an extension of the models used to generate fractal traffic flows in high-speed computer networks by means of the formulation of a model that considers the use of one-dimensional chaotic maps. Based on the disaggregation of the temporal series generated, a valid explanation of behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

scholarly journals A simple chaotic map model for fractal traffic generation in high-speed computer networks (Draft 2)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Hurst Exponent ◽  
High Speed ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Traffic Flows ◽  
One Dimensional ◽  
Temporal Series ◽  
Proposed Model ◽  
Traffic Generation ◽  
Speed Computer

An extension of the models used to generate fractal traffic flows is presented by means of the formulation of a model that considers the use of one-dimensional chaotic maps. Based on the disaggregation of the temporal series generated by the model, a valid explanation of behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

scholarly journals A Simple Chaotic Map Model for Fractal Traffic Flows in High-speed Computer Networks

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Computer Networks ◽  
Hurst Exponent ◽  
High Speed ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Traffic Flows ◽  
One Dimensional ◽  
Temporal Series ◽  
Proposed Model ◽  
Speed Computer

An extension of the models used to generate fractal traffic flows is presented by means of the formulation of a model that considers the use of one-dimensional chaotic maps. Based on the disaggregation of the temporal series generated by the model, a valid explanation of behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.<br>

scholarly journals A Simple Chaotic Map Model for Fractal Traffic Flows in High-speed Computer Networks

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Computer Networks ◽  
Hurst Exponent ◽  
High Speed ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Traffic Flows ◽  
One Dimensional ◽  
Temporal Series ◽  
Proposed Model ◽  
Speed Computer

An extension of the models used to generate fractal traffic flows is presented by means of the formulation of a model that considers the use of one-dimensional chaotic maps. Based on the disaggregation of the temporal series generated by the model, a valid explanation of behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.<br>

scholarly journals ENHANCED CHAOTIC IMAGE ENCRYPTION ALGORITHM BASED ON TRIGONOMETRIC FUNCTIONS

2013 ◽  
pp. 246-249
Author(s):  
M.K MOHSINA ◽  
ROBIN ABRAHAM
Keyword(s):  
Image Encryption ◽  
Chaotic Maps ◽  
Initial Conditions ◽  
Random Sequence ◽  
Chaotic Map ◽  
Secret Key ◽  
Home Office ◽  
One Dimensional ◽  
Extreme Sensitivity ◽  
Differential Attacks

The advent of wireless communications, both inside and outside the home-office environment has led to an Increased demand for effective encryption systems. The encryption of images is quite different from that of the texts due to the bulk data capacity and high redundancy of images. Traditional methods are difficult to handle the image encryption because of their small space of pseudo random sequence. At present, the chaotic maps have been widely used in image encryption for their extreme sensitivity to tiny changes of initial conditions. The chaos based algorithms have suggested a new and efficient way to deal with the problem of fast and highly secure image encryption. In this paper, we propose an algorithm in which two one-dimensional chaotic maps are used instead of a one-dimensional chaotic map. We also use an external secret key of 96-bits. Thereby it significantly increases the resistance to statistical and differential attacks. The results of experiment, statistical analysis, correlation coefficient analysis and key sensitivity tests show that the algorithm is of great security and practicability.

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