Multimedia Tools and Applications

, Volume 76, Issue 6, pp 8757–8779 | Cite as

Securing color images using Two-square cipher associated with Arnold map



This paper presents an image encryption scheme using modified Two-square cipher associated with Arnold map. The traditional Two-square cipher is modified to make it more secure and applicable on the image data. A new block-based scheme is considered for Arnold map to handle the images of any size. The proposed scheme is structured into a substitution-permutation framework such that it has an excessively huge key space, and the correct decoding is highly sensitive to the correct keys with their correct order. The experimental results are given to validate the feasibility and robustness of the proposed scheme. Further, the superiority of the proposed scheme is analyzed by comparing with the related work.


Image encryption Image decryption Arnold map Two-square cipher 


  1. 1.
    Antonini M, Barlaud M, Mathieu P, Daubechies I (1992) Image coding using wavelet transform. IEEE Trans Image Process 1(2):205–220CrossRefGoogle Scholar
  2. 2.
    Arnold VI, Avez A (1968) Ergodic problems of classical mechanics. New York, Benjamin [Translated from Russian]Google Scholar
  3. 3.
    Borujeni SE, Eshghi M (2009) Chaotic image encryption design using tompkins-paige algorithm. Hindawi J Math Problem Eng 2009:22MATHGoogle Scholar
  4. 4.
    Dyson FJ, Falk H (1992) Period of a discrete cat mapping. Amer Math Month 99(7):603–614MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Guo Q, Liu Z, Liu S (2010) Color image encryption by using arnold and discrete fractional random transforms in ihs space. Opt Lasers Eng 48(12):1174–1181CrossRefGoogle Scholar
  6. 6.
    Hennelly B, Sheridan JT (2003) Optical image encryption by random shifting in fractional fourier domains. Opt Lett 28(4):269–271CrossRefGoogle Scholar
  7. 7.
    Huang X, Ye G (2014) An image encryption algorithm based on hyper-chaos and dna sequence. Multimed Tools Appl 72(1):57–70CrossRefGoogle Scholar
  8. 8.
    Kumar M, Mishra DC, Sharma RK (2014) A first approach on an rgb image encryption. Opt Lasers Eng 52:27–34CrossRefGoogle Scholar
  9. 9.
    Kwok H, Tang WK (2007) A fast image encryption system based on chaotic maps with finite precision representation. Chaos Solitons Fractals 32(4):1518–1529MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Li H (2009) Image encryption based on gyrator transform and two-step phase-shifting interferometry. Opt Lasers Eng 47(1):45–50CrossRefGoogle Scholar
  11. 11.
    Li L, Ahmed AE, Niu X (2012) Elliptic curve elgamal based homomorphic image encryption scheme for sharing secret images. Signal Process 92(4):1069–1078CrossRefGoogle Scholar
  12. 12.
    Li M, Liang T, He YJ (2013) Arnold transform based image scrambling method. In: 3rd international conference on multimedia technology(ICMT 2013), pp 1309–1316Google Scholar
  13. 13.
    Liu Z, Chen H, Liu T, Li P, Dai J, Sun X, Liu S (2010) Double-image encryption based on the affine transform and the gyrator transform. J Opt 12(3):035,407CrossRefGoogle Scholar
  14. 14.
    Liu Z, Chen H, Liu T, Li P, Xu L, Dai J, Liu S (2011) Image encryption by using gyrator transform and arnold transform. J Electron Imag 20(1):013,020–1–013,020–6CrossRefGoogle Scholar
  15. 15.
    Liu Z, Xu L, Liu T, Chen H, Li P, Lin C, Liu S (2011) Color image encryption by using arnold transform and color-blend operation in discrete cosine transform domains. Opt Commun 284(1):123–128CrossRefGoogle Scholar
  16. 16.
    Liu Z, Gong M, Dou Y, Liu F, Lin S, Ahmad MA, Dai J, Liu S (2012) Double image encryption by using arnold transform and discrete fractional angular transform. Opt Lasers Eng 50(2):248–255CrossRefGoogle Scholar
  17. 17.
    Mao Y, Chen G (2005) Chaos-based image encryption. Handbook Geomet Comput:231–265Google Scholar
  18. 18.
    Pandurangan HT, Naveen Kumar SK (2014) Application of algebra and discrete wavelet transform in two-dimensional data (rgb-images) security. Int J Wavelets Multiresol Inf Process 12(6):1450,040–1–1450,040–25MathSciNetCrossRefGoogle Scholar
  19. 19.
    Scharinger J (1998) Fast encryption of image data using chaotic kolmogorov flows. J Electron Imag 7(2):318–325CrossRefGoogle Scholar
  20. 20.
    Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Sui L, Gao B (2013) Color image encryption based on gyrator transform and arnold transform. Opt Laser Technol 48:530–538CrossRefGoogle Scholar
  22. 22.
    Taneja N, Raman B, Gupta I (2012) Chaos based cryptosystem for still visual data. Multimed Tools Appl 61(2):281–298CrossRefGoogle Scholar
  23. 23.
    Tang Z, Zhang X (2011) Secure image encryption without size limitation using arnold transform and random strategies. J Multimed 6(2):202–206CrossRefGoogle Scholar
  24. 24.
    Tang Z, Zhang X, Lan W (2015) Efficient image encryption with block shuffling and chaotic map. Multimed Tools Appl 74(15):5429–5448CrossRefGoogle Scholar
  25. 25.
    Zhang Y, Zheng CH, Tanno N (2002) Optical encryption based on iterative fractional fourier transform. Opt Commun 202(4–6):277–285CrossRefGoogle Scholar
  26. 26.
    Zheng Y, Jin J (2015) A novel image encryption scheme based on hnon map and compound spatiotemporal chaos. Multimed Tools Appl 74(8):7803–7820CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia

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