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.

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.

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 An Investigation into the Performance of Particle Swarm Optimization with Various Chaotic Maps

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Akugbe Martins Arasomwan ◽  
Aderemi Oluyinka Adewumi
Keyword(s):  
Particle Swarm Optimization ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Logistic Map ◽  
Particle Swarm ◽  
Test Problems ◽  
Swarm Optimization ◽  
Inertia Weight ◽  
Mathematical Problems ◽  
Logistic Chaotic Map

This paper experimentally investigates the effect of nine chaotic maps on the performance of two Particle Swarm Optimization (PSO) variants, namely, Random Inertia Weight PSO (RIW-PSO) and Linear Decreasing Inertia Weight PSO (LDIW-PSO) algorithms. The applications of logistic chaotic map by researchers to these variants have led to Chaotic Random Inertia Weight PSO (CRIW-PSO) and Chaotic Linear Decreasing Inertia Weight PSO (CDIW-PSO) with improved optimizing capability due to better global search mobility. However, there are many other chaotic maps in literature which could perhaps enhance the performances of RIW-PSO and LDIW-PSO more than logistic map. Some benchmark mathematical problems well-studied in literature were used to verify the performances of RIW-PSO and LDIW-PSO variants using the nine chaotic maps in comparison with logistic chaotic map. Results show that the performances of these two variants were improved more by many of the chaotic maps than by logistic map in many of the test problems. The best performance, in terms of function evaluations, was obtained by the two variants using Intermittency chaotic map. Results in this paper provide a platform for informative decision making when selecting chaotic maps to be used in the inertia weight formula of LDIW-PSO and RIW-PSO.

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 Speech encryption by multiple chaotic map with fast fourier transform

2020 ◽  
Vol 10 (6) ◽  
pp. 5658
Author(s):  
Yahia Alemami ◽  
Mohamad Afendee Mohamed ◽  
Saleh Atiewi ◽  
Mustafa Mamat
Keyword(s):  
Social Communication ◽  
Data Security ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Logistic Map ◽  
The Other ◽  
Mathematical Structures ◽  
Multiple Encryption ◽  
Encryption Algorithms ◽  
Speech Encryption

There are various ways of social communication including writing (WhatsApp, Messenger, Facebook, Twitter, Skype, etc), calling (mobile phone) and voice recording (record your voice and then send it to the other party), but there are ways to eavesdropping the calls and voice messages, One way to solve this problem is via cryptographic approach. Chaos cryptography build on top of nonlinear dynamics chaotic system has gained some footstep in data security. It provides an alternative to conventional cryptography built on top of mathematical structures. This research focuses on the protection of speech recording by encrypting it with multiple encryption algorithms, including chaotic maps (Logistic Map and Sine Maps).

scholarly journals A Nonlinearly Modulated Logistic Map With Delay for Image Encryption

Electronics ◽  
2018 ◽  
Vol 7 (11) ◽  
pp. 326 ◽  
Author(s):  
Shouliang Li ◽  
Benshun Yin ◽  
Weikang Ding ◽  
Tongfeng Zhang ◽  
Yide Ma
Keyword(s):  
Lyapunov Exponents ◽  
Image Encryption ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Logistic Map ◽  
Delay Model ◽  
Test Results ◽  
Bit Plane ◽  
Differential Attacks ◽  
Image Encryption Algorithm

Considering that a majority of the traditional one-dimensional discrete chaotic maps have disadvantages including a relatively narrow chaotic range, smaller Lyapunov exponents, and excessive periodic windows, a new nonlinearly modulated Logistic map with delay model (NMLD) is proposed. Accordingly, a chaotic map called a first-order Feigenbaum-Logistic NMLD (FL-NMLD) is proposed. Simulation results demonstrate that FL-NMLD has a considerably wider chaotic range, larger Lyapunov exponents, and superior ergodicity compared with existing chaotic maps. Based on FL-NMLD, we propose a new image encryption algorithm that joins the pixel plane and bit-plane shuffle (JPB). The simulation and test results confirm that JPB has higher security than simple pixel-plane encryption and is faster than simple bit-plane encryption. Moreover, it can resist the majority of attacks including statistical and differential attacks.

scholarly journals The Design and FPGA-Based Implementation of a Stream Cipher Based on a Secure Chaotic Generator

2021 ◽  
Vol 11 (2) ◽  
pp. 625
Author(s):  
Fethi Dridi ◽  
Safwan El Assad ◽  
Wajih El Hadj Youssef ◽  
Mohsen Machhout ◽  
René Lozi
Keyword(s):  
Stream Cipher ◽  
Chaotic Maps ◽  
Statistical Tests ◽  
Chaotic Map ◽  
Logistic Map ◽  
Tent Map ◽  
First Order ◽  
Recursive Filters ◽  
Weakly Coupled ◽  
Chebyshev Map

In this study, with an FPGA-board using VHDL, we designed a secure chaos-based stream cipher (SCbSC), and we evaluated its hardware implementation performance in terms of computational complexity and its security. The fundamental element of the system is the proposed secure pseudo-chaotic number generator (SPCNG). The architecture of the proposed SPCNG includes three first-order recursive filters, each containing a discrete chaotic map and a mixing technique using an internal pseudo-random number (PRN). The three discrete chaotic maps, namely, the 3D Chebyshev map (3D Ch), the 1D logistic map (L), and the 1D skew-tent map (S), are weakly coupled by a predefined coupling matrix M. The mixing technique combined with the weak coupling technique of the three chaotic maps allows preserving the system against side-channel attacks (SCAs). The proposed system was implemented on a Xilinx XC7Z020 PYNQ-Z2 FPGA platform. Logic resources, throughput, and cryptanalytic and statistical tests showed a good tradeoff between efficiency and security. Thus, the proposed SCbSC can be used as a secure stream cipher.

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 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.

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.

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