Multimedia Tools and Applications

, Volume 78, Issue 12, pp 15997–16010 | Cite as

Construction of a new 2D Chebyshev-Sine map and its application to color image encryption

  • Hongjun LiuEmail author
  • Fengtong Wen
  • Abdurahman Kadir


A new 2D Chebyshev-Sine map with natural evaluation is proposed and its dynamical behavior is analyzed. To investigate its application in information security, a color image encryption algorithm is designed. One-time initial condition expressed as ordered quaternion is extracted from colored non Gaussian noise before each encryption process. The algorithm can achieve desired effect after two rounds by exclusive or (XOR) operation with avalanche effect. Simulation results demonstrated that the speed is fast, so the algorithm is suitable for image encryption over the Cloud.


2D Chebyshev-Sine map One-time keys Avalanche effect 



This research is supported by the National Natural Science Foundation of China (No: 61662073, 61363082), the Natural Science Foundation of Shandong Province (No: ZR2018LF006).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.


  1. 1.
    Abdallah E, Ben AH, Prabir B (2007) MPEG video watermarking using tensor singular value decomposition. //International Conference Image Analysis and Recognition. Springer, Berlin, HeidelbergGoogle Scholar
  2. 2.
    Akhshani A, Akhavan A, Mobaraki A et al (2014) Pseudo random number generator based on quantum chaotic map[J]. Commun Nonlinear Sci Numer Simul 19(1):101–111CrossRefzbMATHGoogle Scholar
  3. 3.
    Arroyo D, Rhouma R, Alvarez G et al (2008) On the security of a new image encryption scheme based on chaotic map lattices[J]. Chaos 18(3):033112CrossRefGoogle Scholar
  4. 4.
    Banerjee S, Yorke JA, Grebogi C (1998) Robust chaos[J]. Phys Rev Lett 80(14):3049CrossRefzbMATHGoogle Scholar
  5. 5.
    Belazi A, Khan M, El-Latif AAA et al (2017) Efficient cryptosystem approaches: S-boxes and permutation–substitution-based encryption[J]. Nonlinear Dyn 87(1):337–361CrossRefGoogle Scholar
  6. 6.
    Cong L, Wu X, Sun S (1999) A general efficient method for chaotic signal estimation[J]. IEEE Trans Signal Process 47(5):1424–1428CrossRefGoogle Scholar
  7. 7.
    Gao Z, Chen D, Zhang W et al (2017) Colour image encryption algorithm using one-time key and FrFT[J]. IET Image Process 12(4):472–478CrossRefGoogle Scholar
  8. 8.
    Hamza AB, Krim H (2003) Jensen-Rényi divergence measure: theoretical and computational perspectives[C]//Information Theory, 2003. Proceedings. IEEE International Symposium on. IEEE, p 257–257Google Scholar
  9. 9.
    Hussain I, Shah T, Gondal MA (2012) Image encryption algorithm based on PGL(2,GF(28)) S-boxes and TD-ERCS chaotic sequence. Nonlinear Dyn 70(1):181–187CrossRefGoogle Scholar
  10. 10.
    Kadir A, Aili M, Sattar M (2017) Color image encryption scheme using coupled hyper chaotic system with multiple impulse injections. Optik 129:231–238CrossRefGoogle Scholar
  11. 11.
    Kurian AP, Leung H (2009) Weak signal estimation in chaotic clutter using model-based coupled synchronization[J]. IEEE Trans Circuits Syst I 56(4):820–828MathSciNetCrossRefGoogle Scholar
  12. 12.
    L'Ecuyer P, Simard R (2013) TestU01: a software library in ANSI C for empirical testing of random number generators--user’s guide, Compact Version[J]Google Scholar
  13. 13.
    Liu H, Kadir A, Sun X (2017) Chaos-based fast colour image encryption scheme with true random number keys from environmental noise[J]. IET Image Process 11(5):324–332CrossRefGoogle Scholar
  14. 14.
    Luo C, Wang X (2014) Adaptive modified function projective lag synchronization of hyperchaotic complex systems with fully uncertain parameters[J]. J Vib Control 20(12):1831–1845MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Rozenbaum EB, Ganeshan S, Galitski V (2017) Lyapunov exponent and out-of-time-ordered correlator’s growth rate in a chaotic system[J]. Phys Rev Lett 118(8):086801CrossRefGoogle Scholar
  16. 16.
    Seyedzadeh SM, Mirzakuchaki S (2012) A fast color image encryption algorithm based on coupled two-dimensional piecewise chaotic map. Signal Process 92(5):1202–1215CrossRefGoogle Scholar
  17. 17.
    Shanon CE (1949) Communication theory of secrecy systems. Bell Syst Tech J 28(4):656–715MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wang X, Guo K (2014) A new image alternate encryption algorithm based on chaotic map[J]. Nonlinear Dyn 76(4):1943–1950CrossRefzbMATHGoogle Scholar
  19. 19.
    Wang XY, Zhang YQ, Zhao YY (2015) A novel image encryption scheme based on 2-D logistic map and DNA sequence operations[J]. Nonlinear Dyn 82(3):1269–1280MathSciNetCrossRefGoogle Scholar
  20. 20.
    Wang X, Wang S, Zhang Y et al (2018) A one-time pad color image cryptosystem based on SHA-3 and multiple chaotic systems[J]. Opt Lasers Eng 103:1–8CrossRefGoogle Scholar
  21. 21.
    Wang C, Wang X, Xia Z, Zhang C (2019) Ternary radial harmonic Fourier moments based robust stereo image zero-watermarking algorithm. Inf Sci 470:109–120CrossRefGoogle Scholar
  22. 22.
    Xiao D, Zhang YS (2014) Self-adaptive permutation and combined global diffusion for chaotic color image encryption. AEU Int J Electron Commun 68(4):361–368CrossRefGoogle Scholar
  23. 23.
    Ye G, Huang X (2017) An efficient symmetric image encryption algorithm based on an intertwining logistic map[J]. Neurocomputing 251:45–53CrossRefGoogle Scholar
  24. 24.
    Ye G, Zhao H, Chai H (2016) Chaotic image encryption algorithm using wave-line permutation and block diffusion[J]. Nonlinear Dyn 83(4):2067–2077MathSciNetCrossRefGoogle Scholar
  25. 25.
    Zhang Y, Xiao D (2014) An image encryption scheme based on rotation matrix bit-level permutation and block diffusion[J]. Commun Nonlinear Sci Numer Simul 19(1):74–82CrossRefzbMATHGoogle Scholar
  26. 26.
    Zhen P, Zhao G, Min L, Jin X (2016) Chaos-based image encryption scheme combining DNA coding and entropy. Multimed Tools Appl 75(11):6303–6319CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of JinanJinanChina
  2. 2.Shandong Famous Teacher’s WorkshopWeifang Vocational CollegeWeifangChina
  3. 3.School of Computer Science and EngineeringXinjiang University of Finance and EconomicsUrumqiChina

Personalised recommendations