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An image encryption scheme proposed by modifying chaotic tent map using fuzzy numbers

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Abstract

Digital images play a crucial role in data communication through the internet or any mode, but their security is a formidable task. Multiple image encryption approaches were conceived, employing chaotic maps to accomplish the security level of digital images. Chaotic maps are deemed suitable for encryption techniques because of their intrinsic properties of randomness, unpredictable behavior, and ergodicity. In this paper, we modify a chaotic map utilizing a fuzzy number and confer the enhancement in chaotic behavior through a bifurcation diagram. Further, we conceive a distinctive image encryption scheme that can uniform the pixel value of a plain image during the diffusion process with the help of a pseudo-random sequence generated from modifying the map. The sum of diffused pixels is used in the discretized tent map to annihilate the correlation among contiguous pixels of the diffused image. Finally, various security and statistical analysis exemplify that our proposed encryption scheme is fast, secure, and efficient against a plethora of threats.

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References

  1. Bakhshandeh A, Eslami Z (2013) An authenticated image encryption scheme based on chaotic maps and memory cellular automata. Opt Lasers Eng 51 (6):665–673

    Article  Google Scholar 

  2. Bashir Z, Rashid T, Zafar S (2016) Hyperchaotic dynamical system based image encryption scheme with time-varying delays. Pac Sci Rev A: Nat Sci Eng 18(3):254–260

    Google Scholar 

  3. Bashir Z, Wa̧tróbski J, Rashid T, Zafar S, Sałabun W (2017) Chaotic dynamical state variables selection procedure based image encryption scheme. Symmetry 9(12):312

    Article  Google Scholar 

  4. Chakraverty S, Sahoo DM, Mahato NR (2019) Concepts of soft computing, Fuzzy and ANN with Programming. Springer, Singapore

    Book  MATH  Google Scholar 

  5. Elmanfaloty RA, Abou-Bakr E (2020) An image encryption scheme using a 1D chaotic double section skew tent map. Complexity

  6. Fridrich J (1994) On chaotic systems: fuzzified logistic mapping. Int J Gen Syst 22(4):369–380

    Article  MATH  Google Scholar 

  7. Gao W, Idrees B, Zafar S, Rashid T (2020) Construction of nonlinear component of block cipher by action of modular group PSL (2, Z) on projective line PL (GF (2 8)). IEEE Access 8:136736–136749

    Article  Google Scholar 

  8. Hanss M (2005) Applied fuzzy arithmetic. Springer, Berlin

    MATH  Google Scholar 

  9. Hong L, Sun JQ (2006) Bifurcations of fuzzy nonlinear dynamical systems. Commun Nonlinear Sci Numer Simul 11(1):1–12

    Article  MathSciNet  MATH  Google Scholar 

  10. Hua Z, Jin F, Xu B, Huang H (2018) 2D Logistic-Sine-coupling map for image encryption. Signal Process 149:148–161

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Idress B, Zafar S, Rashid T, Gao W (2020) Image encryption algorithm using S-box and dynamic Henon bit level permutation. Multimed Tools Appl 79 (9):6135–6162

    Article  Google Scholar 

  13. Kanso A (2011) Self-shrinking chaotic stream ciphers. Commun Nonlinear Sci Numer Simul 16(2):822–836

    Article  MathSciNet  MATH  Google Scholar 

  14. Li S, Ding W, Yin B, Zhang T, Ma Y (2018) A novel delay linear coupling logistics map model for color image encryption. Entropy 20(6):463

    Article  Google Scholar 

  15. Malik MGA, Bashir Z, Iqbal N, Imtiaz MA (2020) Color image encryption algorithm based on hyper-chaos and DNA computing. IEEE Access 8:88093–88107

    Article  Google Scholar 

  16. Matthews R (1989) On the derivation of a “chaotic” encryption algorithm. Cryptologia 13(1):29–42

    Article  MathSciNet  Google Scholar 

  17. Malik DS, Shah T (2020) Color multiple image encryption scheme based on 3Dchaotic maps. Math Comput Simul 178:646–666

    Article  MATH  Google Scholar 

  18. Masuda N, Aihara K (2002) Cryptosystems with discretized chaotic maps. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 49(1):28–40

    Article  MathSciNet  MATH  Google Scholar 

  19. Moysis L, Volos C, Jafari S, Munoz-Pacheco JM, Kengne J, Rajagopal K, Stouboulos I (2020) Modification of the logistic map using fuzzy numbers with application to pseudorandom number generation and image encryption. Entropy 22(4):474

    Article  MathSciNet  Google Scholar 

  20. Niu Y, Zhou Z, Zhang X (2020) An image encryption approach based on chaotic maps and genetic operations. Multimed Tools Appl 79:25613–25633

    Article  Google Scholar 

  21. Pak C, Huang L (2017) A new color image encryption using combination of the 1D chaotic map. Signal Process 138:129–137

    Article  Google Scholar 

  22. Rehman AU, Firdous A, Iqbal S, Abass ZM, Shahid MA, Wang H, Ullah F (2020) A Color Image encryption algorithm based on one time key, chaos theory, and concept of rotor machine. IEEE Access 8:172275–172295

    Article  Google Scholar 

  23. Tromer E, Osvik DA, Shamir A (2010) Efficient cache attacks on AES, and countermeasures. J Cryptol 23(1):37–71

    Article  MathSciNet  MATH  Google Scholar 

  24. Wang X, Zhu X, Zhang Y (2018) An image encryption algorithm based on Josephus traversing and mixed chaotic map. IEEE Access 6:23733–23746

    Article  Google Scholar 

  25. Wei Z (2011) Dynamical behaviors of a chaotic system with no equilibria. Phys Lett A 376(2):102–108

    Article  MathSciNet  MATH  Google Scholar 

  26. Zhang G, Ding W, Li L (2020) Image encryption algorithm based on tent delay-sine cascade with logistic map. Symmetry 12(3):355

    Article  Google Scholar 

  27. Zhang LY, Liu Y, Pareschi F, Zhang Y, Wong KW, Rovatti R, Setti G (2017) On the security of a class of diffusion mechanisms for image encryption. IEEE Trans Cybern 48(4):1163–1175

    Article  Google Scholar 

  28. Zhu S, Zhu C (2020) Secure image encryption algorithm based on hyperchaos and dynamic DNA coding. Entropy 22(7):772

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors are grateful to the reviewers for their comments and suggestions to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, University of Management and Technology, Lahore, 54770, State, Pakistan

    Muhammad Akraam, Tabasam Rashid & Sohail Zafar

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  1. Muhammad Akraam
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  2. Tabasam Rashid
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  3. Sohail Zafar
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Correspondence to Tabasam Rashid.

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Muhammad Akraam, Tabasam Rashid and Sohail Zafar contributed equally to this work.

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Akraam, M., Rashid, T. & Zafar, S. An image encryption scheme proposed by modifying chaotic tent map using fuzzy numbers. Multimed Tools Appl 82, 16861–16879 (2023). https://doi.org/10.1007/s11042-022-13941-6

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  • DOI: https://doi.org/10.1007/s11042-022-13941-6

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