Controllable grid multi-scroll chaotic system family and its hardware circuit implementation

doi:10.11772/j.issn.1001-9081.2022020193

Journal of Computer Applications ›› 2023, Vol. 43 ›› Issue (3): 956-961.DOI: 10.11772/j.issn.1001-9081.2022020193

• Frontier and comprehensive applications • Previous Articles

Controllable grid multi-scroll chaotic system family and its hardware circuit implementation

Yingjie MA, Jing XIAO(), Geng ZHAO, Ping ZENG, Yatao YANG

Department of Electronic and Communication Engineering，Beijing Electronic Science and Technology Institute，Beijing 100070，China

Received:2022-02-22 Revised:2022-05-20 Accepted:2022-05-23 Online:2022-08-16 Published:2023-03-10
Contact: Jing XIAO
About author:MA Yingjie， born in 1979， Ph. D.， associate professor. Her research interests include chaotic secure communication， unmanned aerial vehicle security.
ZHAO Geng， born in 1964， Ph. D.， professor. His research interests include chaotic cryptography.
ZENG Ping， born in 1969， Ph. D.， professor. Her research interests include communication and network security， internet of things security.
YANG Yatao， born in 1978， Ph. D.， professor. His research interests include cryptographic algorithms and protocols.
Supported by:
National Natural Science Foundation of China(61772047);Beijing University "High, Precision and Top Notch" Discipline Construction Project(3201017)

可控网格多涡卷混沌系统族及其硬件电路实现

马英杰, 肖靖(), 赵耿, 曾萍, 杨亚涛

北京电子科技学院电子与通信工程系，北京 100070

通讯作者: 肖靖
作者简介:马英杰（1979—），女，吉林通化人，副教授，博士，主要研究方向：混沌保密通信、无人机安全
肖靖（1998—），男，湖南长沙人，硕士研究生，主要研究方向：混沌保密通信、无人机航迹规划
赵耿（1964—），男，四川长溪人，教授，博士，主要研究方向：混沌密码
曾萍（1969—），女，河南驻马店人，教授，博士，主要研究方向：通信与网络安全、物联网安全
杨亚涛（1978—），男，河南平顶山人，教授，博士，主要研究方向：密码算法与协议。
基金资助:
国家自然科学基金资助项目(61772047);北京高校“高精尖”学科建设项目(3201017)

Abstract

Abstract:

In order to strengthen anti-interference and anti-interception performance of chaotic system in communication link， and improve complexity of chaotic system behavior， based on typical Chua’s circuit and step function， a new type of grid multi-scroll chaotic system family with controllable quantity was constructed. First， two sets of step functions were used as nonlinear controllers of the system， which respectively controlled the numbers of the odd and even columns and the arranging rows for the grid multi-scroll chaotic attractors， and kept the scrolls and bonds in chaotic attractors being interleaved with each other. As a result， the arbitrary number of odd and even columns for the grid multi-scroll were realized. Then， the dynamic properties of system such as equilibrium point， Lyapunov exponent and attractor were theoretically analyzed and numerically simulated. Finally， the hardware experiment results of up to 4 rows and 12 columns of grid multi-scroll were given by Field Programmable Gate Array （FPGA）. Hardware and software experimental results are in full agreement with theoretical analysis results， which furtherly proves the proposed system’s physical realizability.

Key words: grid multi-scroll, step function, Chua’s circuit, chaotic attractor, Field Programmable Gate Array (FPGA)

摘要：

为加强混沌系统在通信链路的抗干扰和抗截获等性能，提高混沌系统性态的复杂度，基于典型蔡氏电路和阶梯函数，构造了一类数量可控的新型网格多涡卷混沌系统族。首先利用两组阶梯函数作为系统的非线性控制器，分别控制网格多涡卷混沌吸引子的奇偶列数和排列行数，并保持混沌吸引子中涡卷与键带的相互间置，以实现网格多涡卷的任意奇偶列数；然后对系统的平衡点、李雅普诺夫指数和吸引子等动力学特性进行理论分析和数值仿真实现；最后通过现场可编程门阵列（FPGA）给出最多4行12列网格多涡卷的硬件实验结果。软硬件实验结果和理论分析结果完全一致，进一步验证了所提系统的物理可实现性。

关键词: 网格多涡卷, 阶梯函数, 蔡氏电路, 混沌吸引子, 现场可编程门阵列

CLC Number:

TP391.9

Yingjie MA, Jing XIAO, Geng ZHAO, Ping ZENG, Yatao YANG. Controllable grid multi-scroll chaotic system family and its hardware circuit implementation[J]. Journal of Computer Applications, 2023, 43(3): 956-961.

马英杰, 肖靖, 赵耿, 曾萍, 杨亚涛. 可控网格多涡卷混沌系统族及其硬件电路实现[J]. 《计算机应用》唯一官方网站, 2023, 43(3): 956-961.

Figures/Tables 10

Fig.1 Structure of Chua’s chaotic circuit

Fig.2 Roots of 4×12 scroll chaotic system equilibrium points

Fig.3 Roots of 4×11 scroll chaotic system equilibrium points

Fig.4 Lyapunov exponent spectrum of system

Fig. 5 X-Y phase diagram of grid multi-scroll chaotic system

Fig.6 Overall system architecture

Fig.7 System RTL view

Tab.1 Chaotic system resource occupancy

资源名称	资源占用	资源总量	占用比例/%
LUT	18 588	53 200	34.94
FF	4 883	106 400	4.59
DSP	12	220	5.45
IO	48	125	38.40

Fig. 8 Experiment results of chaotic system hardware

Fig.9 Analysis diagram of system dynamics characteristics

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Controllable grid multi-scroll chaotic system family and its hardware circuit implementation

可控网格多涡卷混沌系统族及其硬件电路实现

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