Skip to main content
SpringerLink
Log in

A novel fractional order chaos-based image encryption using Fisher Yates algorithm and 3-D cat map

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

This paper presents a novel image encryption scheme using 3-D Arnold cat map and Fisher-Yates shuffling algorithm. A plain image is divided into various slices of equal size and then the 3-D representation of the image is shuffled by the 3-D chaotic map. A fractional order system of nonlinear differential equations is used to implement the diffusion in the intensity values of the shuffled image pixels. The solution of this fractional order system develops a strange attractor which is the onset of the chaos. Fisher-Yates is used to make a chaotic matrix which is used for arranging the data points. Experimental results are given on various images with comprehensive analysis which demonstrates the high security and sensitivity of the scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Ahmada M, Shamsi U, Khan IR (2015) An enhanced image encryption algorithm using fractional chaotic systems. Procedia Computer Science 57:852–859

    Article  Google Scholar 

  2. Belazi A, Abd El-Latif AA, Belghith S (2016) A novel image encryption scheme based on substitution-permutation network and chaos. Signal Proc 128:155–170

    Article  Google Scholar 

  3. Bhatnagar G, Kumar S, Raman B, Sukavanam N (2009) Stereo image coding via digital watermarking. J Electron Imaging (SPIE) 18(3):033012

    Article  Google Scholar 

  4. Bhatnagar G, Saha A, Wu QMJ, Atrey PK (2014) Analysis and extension of multiresolution singular value decomposition. Inf Sci 277:247—262

    Article  Google Scholar 

  5. Chen G, Mao Y, Chui C (2004) A symmetric image encryption scheme based on 3d chaotic cat maps. Chaos, Solitons Fractals 21:749–761

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurcation Chaos 9:1465–1466

    Article  MathSciNet  MATH  Google Scholar 

  7. Diethelm K, Ford NJ, Freed AD (2002) A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynam 29:3–22

    Article  MathSciNet  MATH  Google Scholar 

  8. Dosselmann R, Yang XD et al (2008) A formal assessment of the structural similarity index. University of Regina. Department of Computer Science

  9. Durstenfeld R (1964) Algorithm 235: random permutation. Commun ACM 7:420

    Article  Google Scholar 

  10. Ford J, Mantica G, Ristow GH (1991) The Arnol’d cat: failure of the correspondence principle. Physica D: Nonlinear Phenomena 50(3):493–520

    Article  MathSciNet  MATH  Google Scholar 

  11. Fouda J, Effa J, Sabat S, Ali M (2014) A fast chaotic block cipher for image encryption. Commun Nonlinear Sci Numer Simul 19:578–588

    Article  MathSciNet  Google Scholar 

  12. Fridrich J (1998) Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifurcat Chaos 8:1259–1284

    Article  MathSciNet  MATH  Google Scholar 

  13. Hirsch M, Smale S, Devaney RL (2004) Differential equations, dynamical systems, and an introduction to Chaos. Elsevier Academic Press, New York

    MATH  Google Scholar 

  14. Hua Z, Zhou Y, Pun CM, Chen CLP (2015) 2D sine logistic modulation map for image encryption. Inf Sci 297:80–94

    Article  Google Scholar 

  15. Huang CK, Nien H (2009) Multi chaotic systems based pixel shuffle for image encryption. Opt Commun 282(11):2123–2127

    Article  Google Scholar 

  16. Institute ANS, Committee I.C.S.S, Board IS (1985) IEEE standard for binary floating point arithmetic: IEEE

  17. Kanso A, Ghebleh M (2012) A novel image encryption algorithm based on a 3d chaotic map. Commun Nonlinear Sci Numer Simul 17(7):2943–2959

    Article  MathSciNet  MATH  Google Scholar 

  18. Kocarev L (2008) Intelligent computing based on chaos. Springer, Berlin

    Google Scholar 

  19. Li C, Peng G (2004) Chaos in Chen’s system with a fractional order. Chaos, Solitons and Fractals 22:443–450

    Article  MathSciNet  MATH  Google Scholar 

  20. Liu H, Wang X (2011) Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt Commun 284(15-17):3895–3903

    Article  Google Scholar 

  21. Liu Y, Zhang L, Nie L, Yan Y (2016) Fortune teller : predicting your career path. AAAI conference on artificial intelligence thirtieth AAAI conference on artificial intelligence

  22. Liu Y, Zheng Y, Liang Y, Liu S, Rosenblum DS (2016) Urban water quality prediction based on multi-task multi-view learning. In: Proceedings of the twenty-fifth international joint conference on artificial intelligence (IJCAI-16)

  23. Liu Y, Nie L, Liu L, Rosenblum DS (2016) From action to activity: sensor-based activity recognition. Neurocomputing 181:108–115

    Article  Google Scholar 

  24. Mao Y, Chen G (2005) Chaos-based image encryption. Springer, Berlin, pp 231–265

    Google Scholar 

  25. Mao Y, Chen G (2004) A novel fast image encryption scheme based on 3d chaotic baker maps. Int J Bifurcat Chaos 14(10):3613–3624

    Article  MathSciNet  MATH  Google Scholar 

  26. May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261(5560):459–467

    Article  MATH  Google Scholar 

  27. Musanna F, Rani A, Kumar S (2018) Image encryption using chaotic 3-D arnold’s cat map and logistic map. In: Chaudhuri B, Kankanhalli M, Raman B (eds) Proceedings of 2nd international conference on computer vision & image processing. Advances in intelligent systems and computing, vol 704. Springer, Singapore

  28. Pareek N, Patidar V, Sud K (2006) Image encryption using chaotic logistic map. Image Vis Comput 24(9):926–934

    Article  Google Scholar 

  29. Rani A, Raman B, Kumar S (2014) A robust watermarking scheme exploiting balanced neural tree for rightful ownership protection. Multimedia Tools and Applications 72(3):2225–2248

    Article  Google Scholar 

  30. Rivest RL, Shamir A, Adleman L (1978) On digital signatures and public key cryptosystems. Commun Ass Comput 21:120–126

    MathSciNet  MATH  Google Scholar 

  31. Rukhin A, Soto J, Nechvatal J, Smid M, Barker E (2001) A statistical test suite for random and pseudorandom number generators for cryptographic applications. Nat. Inst. Standard Technol., Gaithersburg, MD, USA, NIST Special Pub. 800-22, Revision 1a

  32. Smid ME, Branstad DK (1988) Data encryption standard: past and future. Proc IEEE 76(5):550–559

    Article  Google Scholar 

  33. Stallings W (2002) The advanced encryption standard. Cryptologia 26(3):165–188

    Article  Google Scholar 

  34. Volos CK, Kyprianidis IM, Stouboulos IN (2013) Image encryption process based on chaotic synchronization phenomena. Signal Process 93(5):1328–1340

    Article  Google Scholar 

  35. Wang XY, Zhang YQ, Bao XM (2015) A novel chaotic image encryption scheme using dna sequence operations. Opt Lasers Eng 73:53–61

    Article  Google Scholar 

  36. Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13 (4):600–612

    Article  Google Scholar 

  37. Wolf A, Swift JB, Swinney H, Vastano L, John A (1985) Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena 16:285–317

    Article  MathSciNet  MATH  Google Scholar 

  38. Wong KW (2008) Image encryption using chaotic maps. Springer 14:333–355

    MATH  Google Scholar 

  39. Wu Y, Noonan J, Agaian S (2011) Npcr and uaci randomness tests for image encryption. Multidisciplinary Journals in Science and Technology, Journal of Selected Areas in Telecommunications (JSAT) 1(2):31–38

    Google Scholar 

  40. Xu Y, Hua W, Yongge L (2014) Image encryption based on synchronization of fractional chaotic systems. Commun Nonlinear Sci Numer Simulat 19(10):3735–3744

    Article  MathSciNet  Google Scholar 

  41. Zhang W, Hai Y, Zhao Y, Zhu Z (2016) Image encryption based on three-dimensional bit matrix permutation. Signal Process 118:36–50

    Article  Google Scholar 

  42. Zhang Y, Wang X (2014) A symmetric image encryption algorithm based on mixed linear-nonlinear coupled map lattice. Inf Sci 273(20):329–51

    Article  Google Scholar 

  43. Zhou Y, Bao L, Chen C (2013) Image encryption using a new parametric switching chaotic system. Signal Process 93(11):3039–3052

    Article  Google Scholar 

  44. Zhu Z, Zhang W, Wong K, Yu H (2011) A chaos-based symmetric image encryption scheme using a bit-level permutation. Inf Sci 181:1171–1186

    Article  Google Scholar 

Download references

Acknowledgements

One of the authors, Farhan Musanna is thankful to IIT Roorkee and Ministry of Human Resource Development (MHRD), Government of India for the financial support for carrying out this work. This work is also supported by the Indian Space Research Organization through their project OGP-150 (RESPOND).

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Farhan Musanna & Sanjeev Kumar

Authors
  1. Farhan Musanna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sanjeev Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Farhan Musanna.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Musanna, F., Kumar, S. A novel fractional order chaos-based image encryption using Fisher Yates algorithm and 3-D cat map. Multimed Tools Appl 78, 14867–14895 (2019). https://doi.org/10.1007/s11042-018-6827-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-018-6827-2

Keywords

Search

Navigation