Phase space homogenization and dynamic characteristics of unimodal chaotic system

被引：0
|
作者：
Xu H. [1 ,2 ]
Tong X.-J. [1 ]
Zhang M. [1 ]
Liu Y. [1 ]
Wang Z. [1 ]
机构：
[1] School of Computer Science and Technology, Harbin Institute of Technology, Weihai, 264209, Shandong
[2] School of Rongcheng, Harbin University of Science and Technology, Rongcheng, 264300, Shandong
来源：
Kongzhi Lilun Yu Yingyong/Control Theory and Applications | 2019年 / 36卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Chaotic systems; Information entropy; Probability density; Unimodal mapping;
D O I：
10.7641/CTA.2018.80157
中图分类号：
学科分类号：
摘要：
The cryptosystem constructed by classical one-dimensional chaotic mapping has some shortcomings in terms of security such as short-period orbits, small key space and inhomogeneous distribution of phase space. In order to solve the security problem of classical one-dimensional chaotic ciphers, a novel one-dimensional unimodal chaotic system and its improved composite form were proposed. A universal homogenization algorithm was used to transform the chaotic sequence into an equal probability distribution and a probability density mathematical proof was given. The dynamics and random characteristic indicators such as ergodicity, Lyapunov exponents, phase space, bifurcations, information entropy and approximate entropy were calculated and analyzed for the improved unimodal chaotic system. Through comparison with related researches, it can be seen that the improved unimodal chaotic system has stable Lyapunov exponents, extended phase space, uniform probability density and higher approximate entropy. Theoretical derivation and numerical calculation demonstrate that this scheme can meet the security attributes of nonlinear components in cryptosystem. © 2019, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.
引用
收藏
页码：759 / 765
页数：6
相关论文
共 17 条
  • [1] Wang C., Ding Q., SM4 key scheme algorithm based on chaotic system, Acta Physica Sinica, 66, 2, (2017)
  • [2] Shen Z., Wu Y., Asymptotic stability of equilibrium points of uncertain unified chaotic systems, Control Theory & Applications, 33, 1, pp. 98-105, (2016)
  • [3] Wen H., Yu S., Lu J., Encryption algorithm based on Hadoop and non-degenerate high-dimensional discrete hyperchaotic system, Acta Physica Sinica, 66, 23, (2017)
  • [4] Li Z., Tang J., Chaotic synchronization with parameter perturbation and its secure communication scheme, Control Theory & Applications, 31, 5, pp. 592-600, (2014)
  • [5] Liu W., Wang Y., Wang Z., Synchronization for a class of discrete-time chaotic control systems under communication constraints, Control Theory & Applications, 31, 8, pp. 1128-1132, (2014)
  • [6] Zhang F., Chen R., Wang X., Et al., Dynamics of a new 5D hyperchaotic system of lorenz type, International Journal of Bifurcation and Chaos, 28, 3, (2018)
  • [7] Liu H., Wang X., Triple-image encryption scheme based on onetime key stream generated by chaos and plain images, Journal of Systems and Software, 86, 3, pp. 826-834, (2013)
  • [8] Liu Y., Tang S., Liu R., Et al., Secure and robust digital image watermarking scheme using logistic and RSA encryption, Expert Systems with Applications, 97, pp. 95-105, (2018)
  • [9] Parvaz R., Zarebnia M., A combination chaotic system and application in color image encryption, Optics and Laser Technology, 101, pp. 30-41, (2018)
  • [10] Zhou Y., Bao L., Chen C.L.P., A new 1D chaotic system for image encryption, Signal Processing, 97, 7, pp. 172-182, (2014)
12