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一个新多涡卷混沌系统的设计及在图像加密中的应用

摆玉龙 杨阳 唐丽红

摆玉龙, 杨阳, 唐丽红. 一个新多涡卷混沌系统的设计及在图像加密中的应用[J]. 电子与信息学报, 2021, 43(2): 436-444. doi: 10.11999/JEIT191002
引用本文: 摆玉龙, 杨阳, 唐丽红. 一个新多涡卷混沌系统的设计及在图像加密中的应用[J]. 电子与信息学报, 2021, 43(2): 436-444. doi: 10.11999/JEIT191002
Yulong BAI, Yang YANG, Lihong TANG. Design of a Multi-scroll Chaotic System and its Application to Image Encryption[J]. Journal of Electronics & Information Technology, 2021, 43(2): 436-444. doi: 10.11999/JEIT191002
Citation: Yulong BAI, Yang YANG, Lihong TANG. Design of a Multi-scroll Chaotic System and its Application to Image Encryption[J]. Journal of Electronics & Information Technology, 2021, 43(2): 436-444. doi: 10.11999/JEIT191002

一个新多涡卷混沌系统的设计及在图像加密中的应用

doi: 10.11999/JEIT191002
基金项目: 国家自然科学基金(41861047, 41461078),西北师范大学青年教师科研能力提升计划(NWNU-LKQN-17-6)
详细信息
    作者简介:

    摆玉龙:男,1973年生,教授,博士生导师,研究方向为控制理论与应用

    杨阳:女,1995年生,硕士生,研究方向为混沌系统

    唐丽红:女,1995年生,硕士生,研究方向为时间序列与风速预测

    通讯作者:

    杨阳 2442361622@qq.com

  • 中图分类号: TN918.4

Design of a Multi-scroll Chaotic System and its Application to Image Encryption

Funds: The National Natural Science Foundation of China (41861047, 41461078), The Northwest Normal University Young Teachers' Scientific Research Capability Upgrading Program (NWNU-LKQN-17-6)
  • 摘要:

    该文提出一种三涡卷混沌系统,首先对系统的李雅普诺夫指数、分岔图、Poincare截面图、功率谱图及平衡点稳定性等动力学特性进行了理论分析和数值仿真,结果表明该系统具有良好的动力学特性和丰富的拓扑吸引子。基于电路仿真软件Multisim研制了实验仿真电路, 该电路结构简单、易于实际制作,且仿真实验与理论分析结论十分吻合,证实了提出的混沌系统电路在物理上是可以实现的,从而验证了该混沌系统的混沌产生能力。最后结合DNA算法设计了一种彩色图像加密算法,利用新系统混沌序列对图像进行加密,重点分析了加密直方图、相邻像素相关性。结果表明,新系统对混沌密钥及明文都非常敏感,密钥空间较大,提出的混沌系统应用于图像加密具有较高的安全性能。

  • 图  1  三涡卷混沌系统的相图

    图  2  参数$\delta $变化时的Lyapunov指数谱

    图  3  z变量随参数$\delta $变化时的分岔图

    图  4  系统式(1)的Poincare截面图

    图  5  系统的功率谱图

    图  6  电路原理图

    图  7  电路实验吸引子相图

    图  8  图像加密算法框架图

    图  9  图像加密效果

    图  10  水平方向R通道相邻像素分布

    图  11  加密后完整相邻像素分布

    12  图像像素分布直方图

    表  1  相邻像素在不同方向上的相关系数

    方法水平相关性垂直相关性对角相关性
    原始Lena图像0.97120.97820.9547
    文献[13]0.00610.01530.0031
    文献[14]0.01020.02140.0061
    文献[15]0.00270.01520.0071
    文献[16]0.01510.00110.0403
    文献[17]–0.0034–0.00600.0063
    文献[18]0.00290.00410.0019
    本文算法0.00060.0013–0.0011
    下载: 导出CSV

    表  2  RGB三个通道的信息熵

    方法信息熵
    原始Lena图像6.9951
    文献[13]7.9964
    文献[14]7.9979
    文献[18]7.9983
    文献[19]7.9978
    文献[20]7.9968
    本文算法7.9995
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-12-16
  • 修回日期:  2020-08-29
  • 网络出版日期:  2020-12-07
  • 刊出日期:  2021-02-23

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