中国物理B ›› 2022, Vol. 31 ›› Issue (8): 80508-080508.doi: 10.1088/1674-1056/ac6335

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Exponential sine chaotification model for enhancing chaos and its hardware implementation

Rui Wang(王蕊)1, Meng-Yang Li(李孟洋)3, and Hai-Jun Luo(罗海军)1,2,†   

  1. 1 College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China;
    2 National Center for Applied Mathematics in Chongqing, Chongqing 401331, China;
    3 The University of Chicago, Chicago 60637, United States of America
  • 收稿日期:2021-12-14 修回日期:2022-02-11 接受日期:2022-04-01 出版日期:2022-07-18 发布日期:2022-07-27
  • 通讯作者: Hai-Jun Luo E-mail:luohaijun@cqnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 51507023), Chongqing Municipal Natural Science Foundation (Grant No. cstc2020jcyjmsxmX0726), and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJZD-K202100506).

Exponential sine chaotification model for enhancing chaos and its hardware implementation

Rui Wang(王蕊)1, Meng-Yang Li(李孟洋)3, and Hai-Jun Luo(罗海军)1,2,†   

  1. 1 College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China;
    2 National Center for Applied Mathematics in Chongqing, Chongqing 401331, China;
    3 The University of Chicago, Chicago 60637, United States of America
  • Received:2021-12-14 Revised:2022-02-11 Accepted:2022-04-01 Online:2022-07-18 Published:2022-07-27
  • Contact: Hai-Jun Luo E-mail:luohaijun@cqnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 51507023), Chongqing Municipal Natural Science Foundation (Grant No. cstc2020jcyjmsxmX0726), and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJZD-K202100506).

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摘要： Chaotic systems have been intensively studied for their roles in many applications, such as cryptography, secure communications, nonlinear controls, etc. However, the limited complexity of existing chaotic systems weakens chaos-based practical applications. Designing chaotic maps with high complexity is attractive. This paper proposes the exponential sine chaotification model (ESCM), a method of using the exponential sine function as a nonlinear transform model, to enhance the complexity of chaotic maps. To verify the performance of the ESCM, we firstly demonstrated it through theoretical analysis. Then, to exhibit the high efficiency and usability of ESCM, we applied ESCM to one-dimensional (1D) and multi-dimensional (MD) chaotic systems. The effects were examined by the Lyapunov exponent and it was found that enhanced chaotic maps have much more complicated dynamic behaviors compared to their originals. To validate the simplicity of ESCM in hardware implementation, we simulated three enhanced chaotic maps using a digital signal processor (DSP). To explore the ESCM in practical application, we applied ESCM to image encryption. The results verified that the ESCM can make previous chaos maps competitive for usage in image encryption.

关键词: chaotic system, nonlinear system, image encryption, hardware implementation

Abstract: Chaotic systems have been intensively studied for their roles in many applications, such as cryptography, secure communications, nonlinear controls, etc. However, the limited complexity of existing chaotic systems weakens chaos-based practical applications. Designing chaotic maps with high complexity is attractive. This paper proposes the exponential sine chaotification model (ESCM), a method of using the exponential sine function as a nonlinear transform model, to enhance the complexity of chaotic maps. To verify the performance of the ESCM, we firstly demonstrated it through theoretical analysis. Then, to exhibit the high efficiency and usability of ESCM, we applied ESCM to one-dimensional (1D) and multi-dimensional (MD) chaotic systems. The effects were examined by the Lyapunov exponent and it was found that enhanced chaotic maps have much more complicated dynamic behaviors compared to their originals. To validate the simplicity of ESCM in hardware implementation, we simulated three enhanced chaotic maps using a digital signal processor (DSP). To explore the ESCM in practical application, we applied ESCM to image encryption. The results verified that the ESCM can make previous chaos maps competitive for usage in image encryption.

Key words: chaotic system, nonlinear system, image encryption, hardware implementation

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Jn (High-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)