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Image encryption based on a new 2D logistic adjusted logistic map

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Abstract

This paper proposes an encryption scheme based on a new 2-dimensional chaotic map. The new 2D chaotic map is derived from the idea of giving the two outputs of a 2D logistic map to two separate 1-dimensional logistic maps. The resulting 2D chaos based pseudo-random number generator is demonstrated to have significantly better randomness and unpredictability characteristics in terms of Lyapunov exponents as well as trajectory plots, in comparison to some recently proposed schemes based on other 2D chaotic maps. This new 2D chaotic map is then used to implement encryption of images. The proposed encryption scheme is demonstrated to be significantly better in terms of the required computational effort. For the proposed scheme, the commonly used measures of security, unpredictability and sensitivity to initial states are successfully established with the help of a set of standard simulation results.

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References

  1. Arnold VI, Avez A (1968) Ergodic problems in classical mechanics. Benjamin, New York

    MATH  Google Scholar 

  2. Bellinii P, Mesitii M, Nesii P, Perlasca P (2018) Protection and composition of crossmedia content in collaborative environments. Multimed Tools Appl 77(2):2083–2114

    Article  Google Scholar 

  3. Benettin G, Galgani L, Strelcyn JM (1976) Kolmogorov entropy and numerical experiments. Phys Rev A 14(6):2338–2345

    Article  Google Scholar 

  4. Bhardwaj R, Aggarwal A (2019) Hiding clinical information in medical images: an encrypted dual-image reversible data hiding algorithm with base-3 numeral framework. Optik 181:1099–1112

    Article  Google Scholar 

  5. Reggie B, Paul B, Abarbanel HDI (1991) Computing the Lyapunov spectrum of a dynamical system from an observed time series. Phys Rev A 43(6):2787–2806

    Article  MathSciNet  Google Scholar 

  6. Cao C, Sun K, Liu W (2018) A novel bit-level image encryption algorithm based on 2d-LICM hyperchaotic map. Signal Process 143:122–133

    Article  Google Scholar 

  7. Chai X (2017) An image encryption algorithm based on bit level Brownian motion and new chaotic systems. Multimed Tools Appl 76(1):1159–1175

    Article  Google Scholar 

  8. Chandrika BK, Aparna P, Sumam DS (2017) Perceptually lossless coder for volumetric medical image data. J Vis Commun Image Represent 46:23–32

    Article  Google Scholar 

  9. Guanrong C, Tetsushi U (1999) Yet another chaotic attractor. Int J Bifurcation Chaos 9(7):1465–1466

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  11. Chen J, Zhu Z, Fu C, Yu H, Zhang L (2015) A fast chaos-based image encryption scheme with a dynamic state variables selection mechanism. Commun Nonlinear Sci Numer Simul 20(3):846–860

    Article  Google Scholar 

  12. Cokal C, Solak E (2009) Cryptanalysis of a chaos-based image encryption algorithm. Phys Lett A 373(15):1357–1360

    Article  MathSciNet  Google Scholar 

  13. Fridrich J (1998) Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifurcation Chaos 8(6):1259–84

    Article  MathSciNet  Google Scholar 

  14. Fu C, Lin B, Miao Y, Liu X, Chen J (2011) A novel chaos-based bit-level permutation scheme for digital image encryption. Opt Commun 284(23):5415–5423

    Article  Google Scholar 

  15. Fu C, Chen J, Zou H, Meng W, Zhan Y, Yu Y (2012) A chaos-based digital image encryption scheme with an improved diffusion strategy. Opt Express 20 (3):2363–2378

    Article  Google Scholar 

  16. Guan ZH, Huang F, Guan W (2005) Chaos-based image encryption algorithm. Phys Lett A 346(1-3):153–157

    Article  Google Scholar 

  17. Hsiao H, Lee J (2015) Color image encryption using chaotic nonlinear adaptive filter. Signal Process 117:281–309

    Article  Google Scholar 

  18. Hua Z, Zhou Y, Pun C, Chen CLP (2015) 2D Sine Logistic modulation map for image encryption. Inf Sci 297:80–94

    Article  Google Scholar 

  19. Hua Z, Zhou Y (2016) Image encryption using 2D Logistic-adjusted-Sine map. Inf Sci 339:237–253

    Article  Google Scholar 

  20. Kindt EJ (2018) Having yes, using no? about the new legal regime for biometric data. Comput Law Secur Rev 34(3):523–538

    Article  Google Scholar 

  21. ”lena512.bmp”. https://www.ece.rice.edu/~wakin/images/lena512.bmp. Accessed 2 July 2018

  22. Li S, Li C, Lo KT, Chen G (2008) Cryptanalysis of an image scrambling scheme without bandwidth expansion. IEEE Trans Circ Syst Video Technol 18(3):338–349

    Article  Google Scholar 

  23. Li C, Lo KT (2011) Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process 91(4):949–954

    Article  Google Scholar 

  24. Li C, Luo G, Qin K, Li C (2016) An image encryption scheme based on chaotic tent map. Nonlinear Dyn 87(1):127–133

    Article  MathSciNet  Google Scholar 

  25. Liao X, Lai S, Zhou Q (2010) A novel image encryption algorithm based on self-adaptive wave transmission. Signal Process 90(9):2714–2722

    Article  Google Scholar 

  26. Liu W, Sun K, Zhu C (2016) A fast image encryption algorithm based on chaotic map. Opt Lasers Eng 84:26–36

    Article  Google Scholar 

  27. 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):3613–3624

    Article  MathSciNet  Google Scholar 

  28. Sheela SJ, Suresh KV, Tandur D (2018) Image encryption based on modified Henon map using hybrid chaotic shift transform. Multimed Tools Appl 77 (19):25223–25251

    Article  Google Scholar 

  29. USC-SIPI Image Database Website. http://sipi.usc.edu/database/database.php?volume=misc. Accessed 2 July 2018

  30. Villena S, Vega M, Mateos J, Rosenberg D, Katsaggelos AK (2018) Image super-resolution for outdoor digital forensics. Usability and legal aspects. Comput Ind 98:34–47

    Article  Google Scholar 

  31. Wang Y, Wong K, Liao X, Xiang T, Chen G (2009) A chaos-based image encryption algorithm with variable control parameters. Chaos Solitons Fractals 41(4):1773–1783

    Article  Google Scholar 

  32. Wu Y, Yang G, Jin H, Noonan JP (2012) Image encryption using the two-dimensional logistic chaotic map. J Electron Imaging 21(1):013–014

    Article  Google Scholar 

  33. Wu Y, Zhou Y, Saveriades G, Agaian S, Noonan JP, Natarajan P (2013) Local Shannon entropy measure with statistical tests for image randomness. Inf Sci 222(10):323–342

    Article  MathSciNet  Google Scholar 

  34. Wu Y, Zhou Y, Noonan JP, Agaian S (2014) Design of image cipher using latin squares. Inf Sci 264(0):317–339

    Article  MathSciNet  Google Scholar 

  35. Wu J, Liao X, Yang B (2017) Color image encryption based on chaotic systems and elliptic curve ElGamal scheme. Signal Process 141:109–124

    Article  Google Scholar 

  36. Erdem Y, Rifat Y, Cem KM, Ezgi Y (2016) A chaos-based image encryption algorithm with simple logical functions. Comput Electr Eng 54:471–483

    Article  Google Scholar 

  37. Zhang Y, Xiao D, Wen W, Li M (2014) Breaking an image encryption algorithm based on hyper-chaotic system with only one round diffusion process. Nonlinear Dyn 76(3):1645–1650

    Article  Google Scholar 

  38. Zhang W, Yu H, Zhao Y, Zhu Z (2015) Image encryption based on three-dimensional bit matrix permutation. Signal Process 118:36–50

    Article  Google Scholar 

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

    Article  Google Scholar 

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Correspondence to Madhu Sharma.

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Sharma, M. Image encryption based on a new 2D logistic adjusted logistic map. Multimed Tools Appl 79, 355–374 (2020). https://doi.org/10.1007/s11042-019-08079-x

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  • DOI: https://doi.org/10.1007/s11042-019-08079-x

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