广义二维多项式混沌映射及其在信息传输中的应用

doi:10.11959/j.issn.1000-436x.2022168

通信学报 ›› 2022, Vol. 43 ›› Issue (9): 80-89.doi: 10.11959/j.issn.1000-436x.2022168

广义二维多项式混沌映射及其在信息传输中的应用

闫文浩¹, 姜子敬¹, 黄欣¹, 朱淑娟², 丁群¹

¹ 黑龙江大学电子工程学院，黑龙江哈尔滨 150080
² 澳大利亚佛林德斯大学科学与工程学院，通斯利 SA 5042

修回日期:2022-08-25 出版日期:2022-09-25 发布日期:2022-09-01
作者简介:闫文浩（1995- ），男，陕西渭南人，黑龙江大学博士生，主要研究方向为混沌映射动力学分析、混沌同步及混沌信息传输
姜子敬（1994- ），男，黑龙江哈尔滨人，黑龙江大学博士生，主要研究方向为网络信息安全及硬件加密侧信道分析
黄欣（1992- ），女，黑龙江哈尔滨人，黑龙江大学博士生，主要研究方向为图像加密及网络信息安全
朱淑娟（1965– ），女，博士，澳大利亚佛林德大学科学与工程学院研究员，主要研究方向为智能计算、数据挖掘、数字水印及信息隐藏
丁群（1957- ），女，黑龙江哈尔滨人，博士，黑龙江大学教授、博士生导师，主要研究方向为混沌加密算法与系统集成、混沌信息传输和网络信息安全等
基金资助:
国家自然科学基金资助项目(61471158);黑龙江省自然科学基金优秀青年基金资助项目(YQ2020F012)

Generalized 2D polynomial chaotic map and its application in information transmission

Wenhao YAN¹, Zijing JIANG¹, Xin HUANG¹, Shujuan ZHU², Qun DING¹

¹ College of Electronic Engineering, Heilongjiang University, Harbin 150080, China
² College of Science and Engineering, Flinders University, Tonsley SA 5042, Australia

Revised:2022-08-25 Online:2022-09-25 Published:2022-09-01
Supported by:
The National Natural Science Foundation of China(61471158);The Natural Science Foundation of Heilongjiang Province for Distinguished Young Scholars(YQ2020F012)

摘要/Abstract

摘要：

现有混沌映射在工程应用中存在许多缺陷，如混沌参数范围不连续、弱混沌、混沌序列输出不均匀和动力学退化等。基于此，提出了一种广义二维多项式混沌映射，通过设定不同控制参数和多项式最高次数，得到一系列特定 Lyapunov 指数的二维多项式混沌映射。为避免该映射第二个状态方程的输出塌陷为一个固定值，引入了一个不随时间变化的随机扰动变量。然后，通过具体的数值实例验证了该映射的有效性，动力分析表明该映射具有复杂的动力学行为。最后，将该映射应用于信息传输技术，相较于其他混沌映射，该映射可以取得更小的误码率，表明该混沌映射更适用于混沌信息传输。

关键词: Lyapunov指数, 动力学退化, 混沌映射, 信息传输

Abstract:

Existing chaotic systems have many defects in engineering applications, such as discontinuous chaotic parameter range, weak chaos, uneven output of chaotic sequences and dynamic degradation.Therefore, a generalized 2D polynomial chaotic mapping model was proposed.By setting different control parameters and the highest degree of polynomial, a series of 2D robust chaotic maps with specific Lyapunov exponent could be obtained.In order to avoid the output of the second state equation collapsing to a fixed value, a random disturbance variable which did not change with time was introduced.Finally, a numerical example was given to verify the effectiveness of the proposed model, and the dynamic analysis showed that the mapping has complex dynamic behavior.Finally, the system was applied to information transmission technology.Compared with other chaotic maps, the system can achieve lower bit error rate, which indicates that the chaotic map is more suitable for chaotic information transmission.

Key words: Lyapunov exponent, dynamic degradation, chaotic map, secure communication

中图分类号:

TN918

闫文浩, 姜子敬, 黄欣, 朱淑娟, 丁群. 广义二维多项式混沌映射及其在信息传输中的应用[J]. 通信学报, 2022, 43(9): 80-89.

Wenhao YAN, Zijing JIANG, Xin HUANG, Shujuan ZHU, Qun DING. Generalized 2D polynomial chaotic map and its application in information transmission[J]. Journal on Communications, 2022, 43(9): 80-89.

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映射	初始值(x₀,y₀)	参数(a,b)	CD
Hénon映射	(0.4,0.3)	(1.4,0.3)	1.359 9
2D-SLM	(0.4,0.3)	(1,3)	1.546 2
LSMCL	(0.4,0.3)	(0.75 3)	1.491 4
本文映射	(0.4,0.3)	(49,49)	1.990 8

测试序号	测试项目	P值		结果
测试序号	测试项目	x序列	y序列	结果
1	频率	0.554 320	0.326 810	通过
2	组内频数	0.834 570	0.577 802	通过
3	游程	0.547 600	0.197 506	通过
4	组内最长游程	0.801 265	0.792 351	通过
5	二元矩阵秩	0.972 745	0.267 811	通过
6	离散傅里叶变换	0.035 687	0.948 721	通过
7	非重叠模板匹配	0.235 874	0.478 512	通过
8	重叠模板匹配	0.497 832	0.089 451	通过
9	通用统计	0.935 647	0.058 974	通过
10	线性复杂度	0.798 145	0.278 945	通过
11	串行	0.754 612	0.845 971	通过
12	近似熵	0.616 784	0.089 451	通过
13	累积和	0.168 745	0.944 513	通过
14	随机偏离	0.654 123	0.087 945	通过
15	随机偏离变量	0.565 209	0.058 799	通过

广义二维多项式混沌映射及其在信息传输中的应用

Generalized 2D polynomial chaotic map and its application in information transmission

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