A new hyperchaotic map and its application for image encryption

  • Hayder NatiqEmail author
  • N. M. G. Al-Saidi
  • M. R. M. Said
  • Adem Kilicman
Regular Article
Part of the following topical collections:
  1. Focus Point on Systems and Security: Advanced Methods with Chaos and Complexity


Based on the one-dimensional Sine map and the two-dimensional Hénon map, a new two-dimensional Sine-Hénon alteration model (2D-SHAM) is hereby proposed. Basic dynamic characteristics of 2D-SHAM are studied through the following aspects: equilibria, Jacobin eigenvalues, trajectory, bifurcation diagram, Lyapunov exponents and sensitivity dependence test. The complexity of 2D-SHAM is investigated using Sample Entropy algorithm. Simulation results show that 2D-SHAM is overall hyperchaotic with the high complexity, and high sensitivity to its initial values and control parameters. To investigate its performance in terms of security, a new 2D-SHAM-based image encryption algorithm (SHAM-IEA) is also proposed. In this algorithm, the essential requirements of confusion and diffusion are accomplished, and the stochastic 2D-SHAM is used to enhance the security of encrypted image. The stochastic 2D-SHAM generates random values, hence SHAM-IEA can produce different encrypted images even with the same secret key. Experimental results and security analysis show that SHAM-IEA has strong capability to withstand statistical analysis, differential attack, chosen-plaintext and chosen-ciphertext attacks.


  1. 1.
    Suchindran S. Maniccam, Nikolaos G. Bourbakis, Pattern Recogn. 37, 725 (2004)CrossRefGoogle Scholar
  2. 2.
    Rong-Jian Chen, Shi-Jinn Horng, Signal Process. Image Commun. 25, 413 (2010)CrossRefGoogle Scholar
  3. 3.
    Gaurav Bhatnagar, Q.M. Jonathan Wu, Balasubramanian Raman, Inf. Sci. 223, 297 (2013)CrossRefGoogle Scholar
  4. 4.
    Li Li, Ahmed A. Abd El-Latif, Xiamu Niu, Signal Process. 92, 1069 (2012)CrossRefGoogle Scholar
  5. 5.
    Xingyuan Wang, Dapeng Luan, Commun. Nonlinear Sci. Numer. Simul. 18, 3075 (2013)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Zhongyun Hua, Yicong Zhou, Inf. Sci. 396, 97 (2017)CrossRefGoogle Scholar
  7. 7.
    Zhongyun Hua, Shuang Yi, Yicong Zhou, Signal Process. 144, 134 (2018)CrossRefGoogle Scholar
  8. 8.
    Jiri Fridrich, Int. J. Bifurc. Chaos 8, 1259 (1998)CrossRefGoogle Scholar
  9. 9.
    Toshiki Habutsu, Yoshifumi Nishio, Iwao Sasase, Shinsaku Mori, A secret key cryptosystem by iterating a chaotic map, in Eurocrypt 1991: Advances in Cryptology, edited by D.W. Davies, Lecture Notes in Computer Science, Vol. 547 (Springer, Berlin, Heidelberg, 1991) pp. 127--140Google Scholar
  10. 10.
    Santo Banerjee, A. Roy Chowdhury, Commun. Nonlinear Sci. Numer. Simul. 14, 2248 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    Santo Banerjee, D. Ghosh, A. Ray, A. Roy Chowdhury, EPL 81, 20006 (2007)CrossRefGoogle Scholar
  12. 12.
    Santo Banerjee, D. Ghosh, A. Roy Chowdhury, Phys. Scr. 78, 015010 (2008)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Yue Wu, Gelan Yang, Huixia Jin, Joseph P. Noonan, J. Electron. Imaging 21, 013014 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    Qiang Zhang, Ling Guo, Xiaopeng Wei, Math. Comput. Model. 52, 2028 (2010)CrossRefGoogle Scholar
  15. 15.
    Hongjun Liu, Abdurahman Kadir, Signal Process. 113, 104 (2015)CrossRefGoogle Scholar
  16. 16.
    Zhongyun, Hua, Yicong Zhou, Chi-Man Pun, C.L. Philip Chen, Inf. Sci. 297, 80 (2015)CrossRefGoogle Scholar
  17. 17.
    David Arroyo, Rhouma Rhouma, Gonzalo Alvarez, Shujun Li, Veronica Fernandez, Chaos 18, 033112 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    Wu Xiaofu, Sun Songgeng, IEEE Trans. Signal Process. 47, 1424 (1999)CrossRefGoogle Scholar
  19. 19.
    Dibakar Ghosh, Santo Banerjee, Phys. Rev. E 78, 056211 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    Shaobo He, Kehui Sun, Santo Banerjee, Eur. Phys. J. Plus 131, 254 (2016)CrossRefGoogle Scholar
  21. 21.
    Yixin Xu, Kehui Sun, Shaobo He, Limin Zhang, Eur. Phys. J. Plus 131, 186 (2016)CrossRefGoogle Scholar
  22. 22.
    T.S. Dang, S.K. Palit, S. Mukherjee, T.M. Hoang, S. Banerjee, Eur. Phys. J. ST 225, 159 (2016)CrossRefGoogle Scholar
  23. 23.
    S. Mukherjee, S.K. Palit, S. Banerjee, M.R.K. Ariffin, L. Rondoni, D.K. Bhattacharya, Physica A 439, 93 (2015)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    S. Banerjee, S.K. Palit, S. Mukherjee, M.R.K. Ariffin, L. Rondoni, Chaos 26, 033105 (2016)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    Peter Grassberger, Itamar Procaccia, Phys. Rev. A 28, 2591 (1983)CrossRefGoogle Scholar
  26. 26.
    Steven M. Pincus, Proc. Natl. Acad. Sci. 88, 2297 (1991)ADSCrossRefGoogle Scholar
  27. 27.
    Joshua S. Richman, J. Randall Moorman, Am. J. Physiol. 278, H2039 (2000)Google Scholar
  28. 28.
    M. Costa, C.K. Peng, A.L. Goldberger, J.M. Hausdorff, Physica A 330, 53 (2003)ADSCrossRefGoogle Scholar
  29. 29.
    B. Fadlallah, B. Chen, A. Keil, J. Prncipe, Phys. Rev. E 87, 022911 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    C. Liu, K. Li, L. Zhao, F. Liu, D. Zheng, C. Liu, S. Liu, Comput. Biol. Med. 43, 100 (2013)ADSCrossRefGoogle Scholar
  31. 31.
    Michel Hénon, A two-dimensional mapping with a strange attractor, in The Theory of Chaotic Attractors (Springer, New York, 1976) pp. 94--102Google Scholar
  32. 32.
    F. Hubertus, Firdaus E. Udwadia, Wlodek Proskurowski, Physica D 101, 1 (1997)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    F. Kaffashi, R. Foglyano, C.G. Wilson, K.A. Loparo, Physica D 237, 3069 (2008)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Gonzalo Alvarez, Shujun Li, Int. J. Bifurc. Chaos 16, 2129 (2006)CrossRefGoogle Scholar
  35. 35.
    Xingyuan Wang, Qian Wang, Nonlinear Dyn. 75, 567 (2014)CrossRefGoogle Scholar
  36. 36.
    Lu Xu, Zhi Li, Jian Li, Wei Hua, Opt. Lasers Eng. 78, 17 (2016)CrossRefGoogle Scholar
  37. 37.
    Xingyuan Wang, Lintao Liu, Yingqian Zhang, Opt. Lasers Eng. 66, 10 (2015)CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Mathematical ResearchUniversiti Putra MalaysiaSerdangMalaysia
  2. 2.Malaysia-Italy Centre of Excellence for Mathematical ScienceUniversiti Putra MalaysiaSerdangMalaysia
  3. 3.Department of MathematicsUniversiti Putra MalaysiaSerdangMalaysia
  4. 4.The Branch of Applied Mathematics, Applied Science DepartmentUniversity of TechnologyBaghdadIraq

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