scholarly journals CCII and FPGA Realization: A Multistable Modified Fourth-Order Autonomous Chua’s Chaotic System with Coexisting Multiple Attractors

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Fei Yu ◽  
Hui Shen ◽  
Li Liu ◽  
Zinan Zhang ◽  
Yuanyuan Huang ◽  
...  
Keyword(s):  
Limit Cycle ◽  
Chaotic System ◽  
Fourth Order ◽  
Secure Communication ◽  
Random Number Generator ◽  
Cycle Period ◽  
Chaotic Oscillator ◽  
Current Conveyors ◽  
Multiple Attractors ◽  
Operation Speed

In this paper, a multistable modified fourth-order autonomous Chua’s chaotic system is investigated. In addition to the dynamic characteristics of the third-order Chua’s chaotic system itself, what interests us is that this modified fourth-order autonomous Chua’s chaotic system has five different types of coexisting attractors: double-scroll, single band chaotic attractor, period-4 limit cycle, period-2 limit cycle, and period-1 limit cycle. Then, an inductorless modified fourth-order autonomous Chua’s chaotic circuit is proposed. The active elements as well as the synthetic inductor employed in this circuit are designed using second-generation current conveyors (CCIIs). The reason for using CCIIs is that they have high conversion rate and operation speed, which enable the circuit to work at a higher frequency range. The Multisim simulations confirm the theoretical estimates of the performance of the proposed circuit. Finally, using RK-4 numerical algorithm of VHDL 32-bit IQ-Math floating-point number format, the inductorless modified fourth-order autonomous Chua’s chaotic system is implemented on FPGA for the development of embedded engineering applications based on chaos. The system is simulated and synthesized on Virtex-6 FPGA chip. The maximum operating frequency of modified Chua’s chaotic oscillator based on FPGA is 180.180 MHz. This study demonstrates that the hardware-based multistable modified fourth-order autonomous Chua’s chaotic system is a very good source of entropy and can be applied to various embedded systems based on chaos, including secure communication, cryptography, and random number generator.

scholarly journals Chaos-Based Application of a Novel Multistable 5D Memristive Hyperchaotic System with Coexisting Multiple Attractors

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19 ◽  
Author(s):  
Fei Yu ◽  
Li Liu ◽  
Shuai Qian ◽  
Lixiang Li ◽  
Yuanyuan Huang ◽  
...  
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Random Number Generator ◽  
Phase Portraits ◽  
Hyperchaotic System ◽  
The Novel ◽  
Multiple Attractors ◽  
Period 2 ◽  
Different Types ◽  
System Designs

Novel memristive hyperchaotic system designs and their engineering applications have received considerable critical attention. In this paper, a novel multistable 5D memristive hyperchaotic system and its application are introduced. The interesting aspect of this chaotic system is that it has different types of coexisting attractors, chaos, hyperchaos, periods, and limit cycles. First, a novel 5D memristive hyperchaotic system is proposed by introducing a flux-controlled memristor with quadratic nonlinearity into an existing 4D four-wing chaotic system as a feedback term. Then, the phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy are used to analyze the basic dynamics of the 5D memristive hyperchaotic system. For a specific set of parameters, we find an unusual metastability, which shows the transition from chaotic to periodic (period-2 and period-3) dynamics. Moreover, its circuit implementation is also proposed. By using the chaoticity of the novel hyperchaotic system, we have developed a random number generator (RNG) for practical image encryption applications. Furthermore, security analyses are carried out with the RNG and image encryption designs.

scholarly journals Circuit Implementation, Synchronization of Multistability, and Image Encryption of a Four-Wing Memristive Chaotic System

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Guangya Peng ◽  
Fuhong Min ◽  
Enrong Wang
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Secure Communication ◽  
Secret Key ◽  
Multiple Attractors ◽  
Dynamical Behaviors ◽  
Key Space ◽  
Control Scheme ◽  
Memristive System ◽  
Coexistence Of Multiple Attractors

The four-wing memristive chaotic system used in synchronization is applied to secure communication which can increase the difficulty of deciphering effectively and enhance the security of information. In this paper, a novel four-wing memristive chaotic system with an active cubic flux-controlled memristor is proposed based on a Lorenz-like circuit. Dynamical behaviors of the memristive system are illustrated in terms of Lyapunov exponents, bifurcation diagrams, coexistence Poincaré maps, coexistence phase diagrams, and attraction basins. Besides, the modular equivalent circuit of four-wing memristive system is designed and the corresponding results are observed to verify its accuracy and rationality. A nonlinear synchronization controller with exponential function is devised to realize synchronization of the coexistence of multiple attractors, and the synchronization control scheme is applied to image encryption to improve secret key space. More interestingly, considering different influence of multistability on encryption, the appropriate key is achieved to enhance the antideciphering ability.

scholarly journals A Torus-Chaotic System and Its Pseudorandom Properties

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Jizhao Liu ◽  
Xiangzi Zhang ◽  
Qingchun Zhao ◽  
Jing Lian ◽  
Fangjun Huang ◽  
...  
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Cyber Security ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Random Number ◽  
Current Knowledge ◽  
Random Number Generator ◽  
Qr Code ◽  
Security Systems

Exploring and investigating new chaotic systems is a popular topic in nonlinear science. Although numerous chaotic systems have been introduced in the literature, few of them focus on torus-chaotic system. The aim of our short work is to widen the current knowledge of torus chaos. In this paper, a new torus-chaotic system is proposed, which has one positive Lyapunov exponent, two zero Lyapunov exponents, and two negative Lyapunov exponents. The dynamic behavior is investigated by Lyapunov exponents, bifurcations, and stability. The analysis shows that this system has an interesting route leading to chaos. Furthermore, the pseudorandom properties of output sequence are well studied and a random number generator algorithm is proposed, which has the potential of being used in several cyber security systems such as the verification code, secure QR code, and some secure communication protocols.

scholarly journals Multistability Analysis, Coexisting Multiple Attractors, and FPGA Implementation of Yu–Wang Four-Wing Chaotic System

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Fei Yu ◽  
Li Liu ◽  
Hui Shen ◽  
Zinan Zhang ◽  
Yuanyuan Huang ◽  
...  
Keyword(s):  
Chaotic System ◽  
Basin Of Attraction ◽  
Fpga Implementation ◽  
Chaotic Oscillator ◽  
Stable Node ◽  
Multiple Attractors ◽  
Standard Format ◽  
Offset Boosting ◽  
The Stability ◽  
Lyapunov Exponent Spectrum

In this paper, we further study the dynamic characteristics of the Yu–Wang chaotic system obtained by Yu and Wang in 2012. The system can show a four-wing chaotic attractor in any direction, including all 3D spaces and 2D planes. For this reason, our interest is focused on multistability generation and chaotic FPGA implementation. The stability analysis, bifurcation diagram, basin of attraction, and Lyapunov exponent spectrum are given as the methods to analyze the dynamic behavior of this system. The analyses show that each system parameter has different coexistence phenomena including coexisting chaotic, coexisting stable node, and coexisting limit cycle. Some remarkable features of the system are that it can generate transient one-wing chaos, transient two-wing chaos, and offset boosting. These phenomena have not been found in previous studies of the Yu–Wang chaotic system, so they are worth sharing. Then, the RK4 algorithm of the Verilog 32-bit floating-point standard format is used to realize the autonomous multistable 4D Yu–Wang chaotic system on FPGA, so that it can be applied in embedded engineering based on chaos. Experiments show that the maximum operating frequency of the Yu–Wang chaotic oscillator designed based on FPGA is 161.212 MHz.

scholarly journals Efficient design of chaos based 4 bit true random number generator on FPGA

2018 ◽  
Vol 7 (3) ◽  
pp. 1783
Author(s):  
Ramji Gupta ◽  
Alpana Pandey ◽  
R. K.Baghel
Keyword(s):  
Secure Communication ◽  
High Speed ◽  
Random Number ◽  
Random Number Generator ◽  
Fpga Implementation ◽  
Experimental Result ◽  
Chaotic Oscillator ◽  
Number Generator ◽  
Efficient Design ◽  
True Random Number Generator

True random number generator is a basic building block of any modern secure communication and cryptography system. FPGA implementation of any system has a flexible architecture and low-cost test cycle. In this paper, we present an FPGA implementation of a high speed true random number generator based on chaos oscillator which gives optimize ratio of bit rate to area. The proposed generator is faster and more compact than the existing chaotic oscillator based TRNGs. The Experimental result shows that the proposed TRNG gives 1439 Mbps with optimizing the use of LUTs and registers. It is verified that the generator passes all the NIST SP 800-22 tests. The proposed TRNG is implemented in two FPGA families Nexus 4 (Artix 7) DDR XC7A100TCSG-1 and Basys 3 XC7A35T1CPG236C (Artix 7) using Xilinx Vivado v.2017.3 design suite. 

Research about Secure Communication Based on Fourth-Order Hyper-Chaotic System

2014 ◽  
Vol 543-547 ◽  
pp. 2535-2538
Author(s):  
Chun Yan Nie ◽  
Hua Tian ◽  
Hai Xin Sun
Keyword(s):  
Chaotic System ◽  
Fourth Order ◽  
Secure Communication ◽  
Pseudorandom Sequences ◽  
New Thought ◽  
Key Space ◽  
Encryption And Decryption ◽  
Encryption Schemes ◽  
Chaotic Secure Communication ◽  
Synchronization Theory

In this paper, we propose a new secure communication synchronization system which exploits the combination of the fourth-order hyper-chaotic system and the synchronization theory. We study the fast encryption and decryption methods of the images and the performance analysis of the secure communication based on the hyper-chaotic system. The simulation results show that the proposed hyper-chaotic secure communication generates the unpredicted pseudorandom sequences which have greater complexity and better randomness characteristics comparing to the traditional chaotic encryption schemes. Furthermore, it has larger key space and higher safety performance. Since the proposed system provides a new thought for the synchronization problems of the hyper-chaotic system, it is regarded as a potential scheme for resisting the popular attack means.

Analysis, circuit implementation and applications of a novel chaotic system

Circuit World ◽  
2017 ◽  
Vol 43 (3) ◽  
pp. 118-130 ◽  
Author(s):  
Li Xiong ◽  
Zhenlai Liu ◽  
Xinguo Zhang
Keyword(s):  
Chaotic System ◽  
Fourth Order ◽  
Secure Communication ◽  
Phase Portraits ◽  
The Novel ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Third Order ◽  
Content Type ◽  
Chaotic Secure Communication

Purpose Lack of optimization and improvement on experimental circuits precludes comprehensive statements. It is a deficiency of the existing chaotic circuit technology. One of the aims of this paper is to solve the above mentioned problems. Another purpose of this paper is to construct a 10 + 4-type chaotic secure communication circuit based on the proposed third-order 4 + 2-type circuit which can output chaotic phase portraits with high accuracy and high stability. Design/methodology/approach In Section 2 of this paper, a novel third-order 4 + 2 chaotic circuit is constructed and a new third-order Lorenz-like chaotic system is proposed based on the 4 + 2 circuit. Then some simulations are presented to verify that the proposed system is chaotic by using Multisim software. In Section 3, a fourth-order chaotic circuit is proposed on the basis of the third-order 4 + 2 chaotic circuit. In Section 4, the circuit design method of this paper is applied to chaotic synchronization and secure communication. A new 10 + 4-type chaotic secure communication circuit is proposed based on the novel third-order 4 + 2 circuit. In Section 5, the proposed third-order 4 + 2 chaotic circuit and the fourth-order chaotic circuit are implemented in an analog electronic circuit. The analog circuit implementation results match the Multisim results. Findings The simulation results show that the proposed fourth-order chaotic circuit can output six phase portraits, and it can output a stable fourth-order double-vortex chaotic signal. A new 10 + 4-type chaotic secure communication circuit is proposed based on the novel third-order 4 + 2 circuit. The scheme has the advantages of clear thinking, efficient and high practicability. The experimental results show that the precision is improved by 2-3 orders of magnitude. Signal-to-noise ratio meets the requirements of engineering design. It provides certain theoretical and technical bases for the realization of a large-scale integrated circuit with a memristor. The proposed circuit design method can also be used in other chaotic systems. Originality/value In this paper, a novel third-order 4 + 2 chaotic circuit is constructed and a new chaotic system is proposed on the basis of the 4 + 2 chaotic circuit for the first time. Some simulations are presented to verify its chaotic characteristics by Multisim. Then the novel third-order 4 + 2 chaotic circuit is applied to construct a fourth-order chaotic circuit. Simulation results verify the existence of the new fourth-order chaotic system. Moreover, a new 10 + 4-type chaotic secure communication circuit is proposed based on chaotic synchronization of the novel third-order 4 + 2 circuit. To illustrate the effectiveness of the proposed scheme, the intensity limit and stability of the transmitted signal, the characteristic of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. Finally, the proposed third-order 4 + 2 chaotic circuit and the fourth-order chaotic circuit are implemented through an analog electronic circuit, which are characterized by their high accuracy and good robustness. The analog circuit implementation results match the Multisim results.

COMMUNICATION BETWEEN SYNCHRONIZED RANDOM NUMBER GENERATORS

2004 ◽  
Vol 14 (11) ◽  
pp. 3995-4008 ◽  
Author(s):  
WEIGUANG YAO ◽  
PEI YU ◽  
CHRISTOPHER ESSEX
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Random Number ◽  
Lorenz System ◽  
Random Number Generator ◽  
Number Generator ◽  
Random Number Generators ◽  
The Lorenz System ◽  
Chaotic Carrier

In most published chaos-based communication schemes, the system's parameters used as a key could be intelligently estimated by a cracker based on the fact that information about the key is contained in the chaotic carrier. In this paper, we will show that the least significant digits (LSDs) of a signal from a chaotic system can be so highly random that the system can be used as a random number generator. Secure communication could be built between the synchronized generators nonetheless. The Lorenz system is used as an illustration.

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