Design and FPGA Implementation of New Multidimensional Chaotic Map for Secure Communication

2021 ◽  
pp. 2150280
Author(s):  
Belqassim Bouteghrine ◽  
Camel Tanougast ◽  
Said Sadoudi
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
Chaotic Behavior ◽  
Chaotic Map ◽  
Two Phase ◽  
Multiple Parameters ◽  
Random Keys ◽  
Field Programmable ◽  
Constrained Devices

Due to their structure and complexity, chaotic systems have been introduced in several domains such as electronic circuits, commerce domain, encryption and network security. In this paper, we propose a novel multidimensional chaotic system with multiple parameters and nonlinear terms. Then, a two-phase algorithm is presented for investigating the chaotic behavior using bifurcation and Lyapunov exponent (LE) theories. Finally, we illustrate the performances of our proposal by constructing three (03) chaotic maps (3-D, 4-D and 5-D) and implementing the 3-D map on Field-Programmable-Gate-Array (FPGA) boards to generate random keys for securing a client–server communication purpose. Based on the achieved results, the proposed scheme is considered an ideal candidate for numerous resource-constrained devices and internet of the things (IoT) applications.

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.

The Relationship Between Chaotic Maps and Some Chaotic Systems with Hidden Attractors

2016 ◽  
Vol 26 (13) ◽  
pp. 1650211 ◽  
Author(s):  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
S. Mohammad Reza Hashemi Golpayegani ◽  
Motahareh Moghtadaei ◽  
Sifeu Takougang Kingni
Keyword(s):  
Bifurcation Diagram ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Period Doubling ◽  
Hidden Attractors ◽  
Chaotic Flows ◽  
The Relationship

In this note, hidden attractors in chaotic maps are investigated. Although there are many new researches on hidden attractors in chaotic flows, no investigation has been done on hidden attractors in maps based on our knowledge. In addition, a new interesting chaotic map with a bifurcation diagram starting from any desired period and then continuing with period doubling is introduced in this paper.

scholarly journals A New Hyperchaotic Map for a Secure Communication Scheme with an Experimental Realization

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1881 ◽  
Author(s):  
Nadia M. G. Al-Saidi ◽  
Dhurgham Younus ◽  
Hayder Natiq ◽  
M. R. K. Ariffin ◽  
M. A. Asbullah ◽  
...  
Keyword(s):  
Secure Communication ◽  
Cross Correlation ◽  
Chaotic Systems ◽  
Complex Dynamics ◽  
Chaotic Map ◽  
High Sensitivity ◽  
Experimental Realization ◽  
Practical Applications ◽  
Communication Scheme ◽  
Different Chaotic Systems

Using different chaotic systems in secure communication, nonlinear control, and many other applications has revealed that these systems have several drawbacks in different aspects. This can cause unfavorable effects to chaos-based applications. Therefore, presenting a chaotic map with complex behaviors is considered important. In this paper, we introduce a new 2D chaotic map, namely, the 2D infinite-collapse-Sine model (2D-ICSM). Various metrics including Lyapunov exponents and bifurcation diagrams are used to demonstrate the complex dynamics and robust hyperchaotic behavior of the 2D-ICSM. Furthermore, the cross-correlation coefficient, phase space diagram, and Sample Entropy algorithm prove that the 2D-ICSM has a high sensitivity to initial values and parameters, extreme complexity performance, and a much larger hyperchaotic range than existing maps. To empirically verify the efficiency and simplicity of the 2D-ICSM in practical applications, we propose a symmetric secure communication system using the 2D-ICSM. Experimental results are presented to demonstrate the validity of the proposed system.

scholarly journals SYNCHRONIZATION INDUCED BY INTERMITTENT VERSUS PARTIAL DRIVES IN CHAOTIC SYSTEMS

2010 ◽  
Vol 20 (02) ◽  
pp. 323-330 ◽  
Author(s):  
O. ALVAREZ-LLAMOZA ◽  
M. G. COSENZA
Keyword(s):  
Chaotic Systems ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Chaotic Oscillators ◽  
Common Space ◽  
Two Systems ◽  
Common Drive ◽  
Average Information ◽  
Crucial Condition

We show that the synchronized states of two systems of identical chaotic maps subject to either, a common drive that acts with a probability p in time or to the same drive acting on a fraction p of the maps, are similar. The synchronization behavior of both systems can be inferred by considering the dynamics of a single chaotic map driven with a probability p. The synchronized states for these systems are characterized on their common space of parameters. Our results show that the presence of a common external drive for all times is not essential for reaching synchronization in a system of chaotic oscillators, nor is the simultaneous sharing of the drive by all the elements in the system. Rather, a crucial condition for achieving synchronization is the sharing of some minimal, average information by the elements in the system over long times.

scholarly journals FPAA Implementation of Chaotic Modulation Based on Nahrain Map

2019 ◽  
Vol 1 (3) ◽  
pp. 17-30
Author(s):  
Hamsa A. Abdullah ◽  
Hikmat N. Abdullah
Keyword(s):  
Real Time ◽  
Chaotic System ◽  
Hardware Implementation ◽  
Chaotic Systems ◽  
Chaotic Map ◽  
Multiuser Transmission ◽  
Modulation And Demodulation ◽  
Security Applications ◽  
Field Programmable ◽  
Simulation Results

Due to characteristic of chaotic systems in terms of nonlinearity, sensitivity to initial values, and non-periodicity, they are used in many applications like security and multiuser transmission. Nahrain chaotic map is an example of such systems that are recently proposed with excellent features for the use in multimedia security applications. Although the implementation of chaotic systems is easy using low costanalogue ICs, this approach does not provide the flexibility that the reconfigurable analogue devices have in design possibilities such as reducing the complexity of design, real-time modification, software control and adjustment within the system. This paper presents a description of data modulation and demodulation based on Nahrain chaotic system and there hardware implementation using field programmable analogue array (FPAA) device. AN231E04 dpASP board is used as a target device for the implementation. The simulation results of system closely matched the programmable hardware testing results.

scholarly journals GENERATION OF VALUES FROM DISCRETE PROBABILITY DISTRIBUTIONS WITH THE USE OF CHAOTIC MAPS

2020 ◽  
pp. 49-54
Author(s):  
Marcin Lawnik ◽  
Arkadiusz Banasik ◽  
Adrian Kapczyński
Keyword(s):  
Chaotic Maps ◽  
Chaotic Behavior ◽  
Probability Distributions ◽  
Discrete Dynamical System ◽  
Chaotic Map ◽  
Random Variables ◽  
Discrete Distribution ◽  
Random Variable ◽  
Discrete Probability ◽  
Discrete Probability Distributions

The values of random variables are commonly used in the field of artificial intelligence. The literature shows plenty of methods, which allows us to generate them, for example, inverse cumulative density function method. Some of the ways are based on chaotic projection. The chaotic methods of generating random variables are concerned with mainly continuous random variables. This article presents the method of generating values from discrete probability distributions with the use of properly constructed piece-wise linear chaotic map. This method is based on a properly constructed discrete dynamical system with chaotic behavior. Successive probability values cover the unit interval and the corresponding random variable values are assigned to the determined subintervals. In the next step, a piece-wise linear map on the subintervals is constructed. In the course of iterations of the chaotic map, consecutive values from a given discrete distribution are derived. The method is presented on the example of Bernoulli distribution. Furthermore, an analysis of the discussed example is conducted and shows that the presented method is the fastest of all analyzed methods.

Chaotic Map Construction from Common Nonlinearities and Microcontroller Implementations

2016 ◽  
Vol 26 (07) ◽  
pp. 1650121 ◽  
Author(s):  
Günyaz Ablay
Keyword(s):  
Chaotic Systems ◽  
Pulse Width Modulation ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Experimental Studies ◽  
Cross Coupling ◽  
Electrical Machines ◽  
High Dimensional ◽  
Map Construction ◽  
Arduino Microcontroller

This work presents novel discrete-time chaotic systems with some known physical system nonlinearities. Dynamic behaviors of the models are examined with numerical methods and Arduino microcontroller-based experimental studies. Many new chaotic maps are generated in the form of [Formula: see text] and high-dimensional chaotic systems are obtained by weak coupling or cross-coupling the same or different chaotic maps. An application of the chaotic maps is realized with Arduino for chaotic pulse width modulation to drive electrical machines. It is expected that the new chaotic maps and their microcontroller implementations will facilitate practical chaos-based applications in different fields.

RADIAL BASIS FUNCTION NETWORKS AS CHAOTIC GENERATORS FOR SECURE COMMUNICATION SYSTEMS

1999 ◽  
Vol 09 (01) ◽  
pp. 221-232 ◽  
Author(s):  
S. PAPADIMITRIOU ◽  
A. BEZERIANOS ◽  
T. BOUNTIS
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
Training Data ◽  
Radial Basis Function Networks ◽  
Rbf Networks ◽  
Radial Basis

This paper improves upon a new class of discrete chaotic systems (i.e. chaotic maps) recently introduced for effective information encryption. The nonlinearity and adaptability of these systems are achieved by designing proper radial basis function networks. The potential for automatic synchronization, the lack of periodicity and the extremely large parameter spaces of these chaotic maps offer robust transmission security. The Radial Basis Function (RBF) networks offer a large number of parameters (i.e. the centers and spreads of the RBF kernels and the weights of the linear layer) while at the same time as universal approximators they have the flexibility to implement any function. The RBF networks can learn the dynamics of chaotic systems (maps or flows) and mimic them accurately by using many more parameters than the original dynamical recurrence. Since the parameter space size increases exponentially with respect to the number of parameters, the RBF based systems greatly outperform previous designs in terms of encryption security. Moreover, the learning of the dynamics from data generated by chaotic systems guarantees the chaoticity of the dynamics of the RBF networks and offers a convenient method of implementing any desirable chaotic dynamics. Since each sequence of training data gives rise to a distinct RBF configuration, theoretically there exists an infinity of possible configurations.

scholarly journals A Class of Quadratic Polynomial Chaotic Maps and Their Fixed Points Analysis

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 658 ◽  
Author(s):  
Chuanfu Wang ◽  
Qun Ding
Keyword(s):  
Fixed Points ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Chaotic Maps ◽  
Quadratic Polynomial ◽  
Chaotic Attractors ◽  
Pseudorandom Sequence ◽  
Practical Applications ◽  
Polynomial Maps ◽  
Existence And Stability

When chaotic systems are used in different practical applications, such as chaotic secure communication and chaotic pseudorandom sequence generators, a large number of chaotic systems are strongly required. However, for a lack of a systematic construction theory, the construction of chaotic systems mainly depends on the exhaustive search of systematic parameters or initial values, especially for a class of dynamical systems with hidden chaotic attractors. In this paper, a class of quadratic polynomial chaotic maps is studied, and a general method for constructing quadratic polynomial chaotic maps is proposed. The proposed polynomial chaotic maps satisfy the Li–Yorke definition of chaos. This method can accurately control the amplitude of chaotic time series. Through the existence and stability analysis of fixed points, we proved that such class quadratic polynomial maps cannot have hidden chaotic attractors.

scholarly journals Energy Conservation, Singular Orbits, and FPGA Implementation of Two New Hamiltonian Chaotic Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Enzeng Dong ◽  
Guanghan Liu ◽  
Zenghui Wang ◽  
Zengqiang Chen
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Dynamical Evolution ◽  
Casimir Energy ◽  
Chaotic Attractors ◽  
Chaotic Flows ◽  
Field Programmable ◽  
Singular Orbits ◽  
Nist Tests

Since the conservative chaotic system (CCS) has no general attractors, conservative chaotic flows are more suitable for the chaos-based secure communication than the chaotic attractors. In this paper, two Hamiltonian conservative chaotic systems (HCCSs) are constructed based on the 4D Euler equations and a proposed construction method. These two new systems are investigated by equilibrium points, dynamical evolution map, Hamilton energy, and Casimir energy. They look similar, but it is found that one can be explained using Casimir power and another cannot be explained in terms of the mechanism of chaos. Furthermore, a pseudorandom signal generator is developed based on these proposed systems, which are tested based on NIST tests and implemented by using the field programmable gate array (FPGA) technique.

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