Color image encryption method based on 2D-variational mode decomposition

  • Shouqiang Kang
  • Yaqi Liang
  • Yujing WangEmail author
  • Mikulovich V I


In order to reduce the correlation between adjacent pixels in a plaintext image, and to solve the small key space problem of image encryption algorithms when a low-dimension chaotic map is used, a new encryption method for color images is proposed based on two-dimensional variational mode decomposition (2D-VMD) combined with eight-dimensional (8D) hyper-chaotic systems. 2D-VMD decomposes R, G and B components of a color image respectively. The 8D hyper-chaotic system is constructed by means of variable coupling. After improving and combining the original sequences obtained by iterating the system, two groups of key sequences associated with the plain-image are obtained. One group is used to scramble each mode image obtained by 2D-VMD; the other is used to replace the pixel values of the scrambled mode images. For different mode images, different key sequences are adopted. The encrypted images whose number is equal to the number of the modes can then be obtained. The experimental results show that, compared with the existing methods, the correlation coefficients between the pixels in the spatial domain of the plain-image can be reduced by 2D-VMD, as it’s more difficult to crack. In addition, the encryption method has better statistical and differential characteristics, as well as large enough key space, and better plain-image sensitivity.


Color image Two-dimensional variational mode decomposition Hyper-chaotic system Encryption method Image decomposition 



This research is supported by The Natural Science Foundation of Heilongjiang Province (Grant No. QC2014C075), University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province (Grant No. UNPYSCT-2017091), and Program for the Top Young Innovative Talents of Harbin University of Science and Technology (Grant No. 201511).


  1. 1.
    Abdurahman K, Askar H, Guo WQ (2014) Color image encryption using skew tent map and hyper chaotic system of 6th-order CNN. Optik-Int J Light Electron Optics 125(5):1671–1675CrossRefGoogle Scholar
  2. 2.
    Bassham LE III, Andrew R, Juan S et al. (2010) A statistical test suite for random and pseudorandom number generators for cryptographic applications. Technical report SP 800-22, National Institute of standards & TechnologyGoogle Scholar
  3. 3.
    Dragomiretskiy K, Zosso D (2015) two-dimensional Variational mode decomposition. 10th international conference, EMMCVPR 2015, Hong Kong, ChinaGoogle Scholar
  4. 4.
    Gao TG, Chen ZQ (2008) A new image encryption algorithm based on hyper-chaos. Phys Lett A 372(4):394–400zbMATHCrossRefGoogle Scholar
  5. 5.
    García-martínez M, Ontañón-garcía LJ, Campos-cantón E (2015) Hyperchaotic encryption based on multi-scroll piecewise linear systems. Appl Mathe Comput 270:413–424MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gu G, Ling J (2014) A fast image encryption method by using chaotic 3D cat maps. Optik-Int J Light Electron Optics 125(17):4700–4705CrossRefGoogle Scholar
  7. 7.
    He YT, Huang HQ (2016) Chaotic encryption algorithm of digital image based on EMD. J Ningxia Univ: Nat Sci Ed 37(4):424–428zbMATHGoogle Scholar
  8. 8.
    Hsiao HI, Lee J (2015) Fingerprint image cryptography based on multiple chaotic systems. Signal Process 113:169–181CrossRefGoogle Scholar
  9. 9.
    Hua ZY, Zhou YC (2016) Image encryption using 2D logistic-adjusted-sine map. Inform Sci Int J 339:237–253CrossRefGoogle Scholar
  10. 10.
    Li CQ, Liu YS, Xie T (2013) Breaking a novel image encryption scheme based on improved hyperchaotic sequences. Nonlinear Dynam 73(3):2083–2089MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Liu ZJ, Xu L, Liu T (2011) Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains. Opt Commun 284(1):123–128CrossRefGoogle Scholar
  12. 12.
    Liu Q, Li P, Zhang M (2015) A novel image encryption algorithm based on chaos maps with Markov properties. Commun Nonlinear Sci Numer Simul 20(2):506–515zbMATHCrossRefGoogle Scholar
  13. 13.
    Liu WH, Sun KH, Zhu CX (2016) A fast image encryption algorithm based on chaotic map. Optics Lasers Eng 84:26–36CrossRefGoogle Scholar
  14. 14.
    Lü J, Zhang BY, Zhu JL (2013) Four-dimensional secondary Hyperchaotic system and its hardware implementation. J Harbin Univ Sci Technol 18(1):95–98Google Scholar
  15. 15.
    Mao Y, Chen G, Lian S (2004) A novel fast image encryption scheme based on 3D chaotic baker maps. Int J Bifurcation Chaos 14(10):3613–3624MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Özkaynak F, Özer AB, Yavuz S (2012) Cryptanalysis of a novel image encryption scheme based on improved hyperchaotic sequences. Opt Commun 285(24):4946–4948CrossRefGoogle Scholar
  17. 17.
    Rhouma R, Safya B (2008) Cryptanalysis of a new image encryption algorithm based on hyper-chaos. Phys Lett A 372(33):5973–5978zbMATHCrossRefGoogle Scholar
  18. 18.
    Sui LS, Xin MT, Tian AL (2013) Single-channel color image encryption using phase retrieve algorithm in fractional Fourier domain. Optics Lasers Eng 51(12):1297–1309CrossRefGoogle Scholar
  19. 19.
    Tedmori S, Al-najdawi N (2014) Image cryptographic algorithm based on the Haar wavelet transform. Inf Sci 269(11):21–34MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Wang XY, Wang Q (2014) A novel image encryption algorithm based on dynamic S-boxes constructed by chaos. Nonlinear Dynam 75(3):567–576CrossRefGoogle Scholar
  21. 21.
    Wang XY, Xu DH (2014) Image encryption using genetic operators and intertwining logistic map. Nonlinear Dynam 78(4):2975–2984MathSciNetCrossRefGoogle Scholar
  22. 22.
    Wang W, Tan HY, Pang Y (2016) A novel encryption algorithm based on DWT and multichaos mapping. J Sensors 2016(5):1–7Google Scholar
  23. 23.
    Ye GD (2014) A block image encryption algorithm based on wave transmission and chaotic systems. Nonlinear Dyn 75(3):417–427CrossRefGoogle Scholar
  24. 24.
    Zhang Q, Guo L, Wei X (2013) A novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system. Optik-Int J Light Electron Optics 124(18):3596–3600CrossRefGoogle Scholar
  25. 25.
    Zhang W, Yu H, Zhao Y, Zhu Z (2016) Image encryption based on three-dimensional bit matrix permutation. Signal Process 118:36–50CrossRefGoogle Scholar
  26. 26.
    Zhu CX (2012) A novel image encryption scheme based on improved hyperchaotic sequences. Opt Commun 285(1):29–37CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Shouqiang Kang
    • 1
  • Yaqi Liang
    • 1
  • Yujing Wang
    • 1
    Email author
  • Mikulovich V I
    • 2
  1. 1.School of Electrical and Electronic EngineeringHarbin University of Science and TechnologyHarbinPeople’s Republic of China
  2. 2.Radiophysics and Electronic DepartmentBelarusian State UniversityMinskBelarus

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