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Construction of a non-degeneracy 3D chaotic map and application to image encryption with keyed S-box

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Abstract

In recent years, chaotic maps have been widely used in image encryption. In order to solve the common problems in chaotic encryption schemes, we designed a novel image encryption scheme based on chaotic map and S-Box. (1) To solve the weaknesses in some 1D chaotic maps, we constructed a non-degenerate 3D hyper chaotic map (3D-HCM), and its dynamic analysis results demonstrated that, compared with 1D seed maps, the 3D-HCM has ergodicity, better randomness and a larger chaotic range. (2) To counteract dynamic degradation, we adjusted the exponent in real time in each iteration. (3) Based on 3D-HCM, we constructed a keyed S-Box without fixed point, reverse fixed point or short period ring. (4) To enhance the ability of the image encryption scheme for resisting common attacks, we blurred the plain image tinily before encryption and applied cross-plane permutation and diffusion to shuffle all the pixels. Experimental and security analysis results demonstrated that the proposed image encryption scheme has higher security, and it can resist to common attacks.

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References

  1. Batool S, Waseem H (2019) A novel image encryption scheme based on Arnold scrambling and Lucas series[J]. Multimed Tools Appl 78(19):27611–27637

    Article  Google Scholar 

  2. Beg S, Ahmad N, Anjum A, Ahmad M, Khan A, Baig F, Khan A (2020) S-box design based on optimize LFT parameter selection: a practical approach in recommendation system domain. Multimed Tools Appl 79:11667–11684

    Article  Google Scholar 

  3. Chen L, Yin H, Yuan L, Lopes AM, Machado JAT, Wu RC (2020) A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations[J]. Front Inf Technol Electron Eng 21(6):866–879

    Article  Google Scholar 

  4. Dimitrov M (2020) On the Design of Chaos-Based S-boxes[J]. IEEE Access 99:117173–117181

    Article  Google Scholar 

  5. El-Latif A, Abd-El-Atty B, Amin M et al (2020) Quantum-inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications[J]. Sci Rep 10:1930

    Article  Google Scholar 

  6. Fadhil M, Farhan A, Fadhil M (2021) Designing substitution box based on the 1D logistic map chaotic system[J]. IOP Conf Ser Mater Sci Eng 1076(1):12041–12053

    Article  Google Scholar 

  7. Faheem Z, Ali A, Khan M et al (2020) Highly dispersive substitution box (S-box) design using chaos[J]. ETRI J 42(4):619–632

    Article  Google Scholar 

  8. Farah MAB, Guesmi R, Kachouri A, Samet M (2020) A new design of cryptosystem based on S-box and chaotic permutation. Multimed Tools Appl 79:19129–19150

    Article  Google Scholar 

  9. Gao X (2021) Image encryption algorithm based on 2D hyperchaotic map[J]. Opt Laser Technol 142(4):107252

    Article  Google Scholar 

  10. Ge M, Ye R (2019) A novel image encryption scheme based on 3D bit matrix and chaotic map with markov properties. Egypt Inf J 20:45–54

    Google Scholar 

  11. Guo Y, Lu Y, Liu R et al (2020) Low-light image enhancement with regularized illumination optimization and deep noise suppression[J]. IEEE Access 99:145297–145315

    Article  Google Scholar 

  12. He Y, Zhang Y, Wang Y (2020) A new image encryption algorithm based on two-dimensional spatiotemporal chaotic system. Neural Comput & Applic 32(2):247–260

    Article  Google Scholar 

  13. Hua Z, Zhou Y (2015) Dynamic parameter-control chaotic system[J]. IEEE Trans Cybern 46(12):3330–3341

    Article  Google Scholar 

  14. Hua Z, Zhou Y, Huang H (2019) Cosine-transform-based chaotic system for image encryption[J]. Inf Sci 480:403–419

    Article  Google Scholar 

  15. Hua Z, Zhang Y, Zhou Y (2020) Two-dimensional modular chaotification system for improving chaos complexity[J]. IEEE Trans Signal Process 68:1937–1949

    Article  MathSciNet  MATH  Google Scholar 

  16. Hua Z, Zhang Y, Bao H, Huang H, Zhou Y (2021) N-dimensional polynomial chaotic system with applications[J]. IEEE Trans Circ Syst I: Regular Papers 69(2):784–797

    Google Scholar 

  17. Hua Z, Zhu Z, Yi S, Zhang Z, Huang H (2021) Cross-plane colour image encryption using a two-dimensional logistic tent modular map[J]. Inf Sci 546:1063–1083

    Article  MathSciNet  Google Scholar 

  18. Hussain I (2020) True-chaotic substitution box based on boolean functions. Eur Phys J Plus 135:663

    Article  Google Scholar 

  19. Kang X, Guo Z (2019) A new color image encryption scheme based on DNA encoding and spatiotemporal chaotic system[J]. Signal Process Image Commun 80:115760–115770

    Google Scholar 

  20. Kumar D, Joshi A, Mishra V (2020) Optical and digital double color-image encryption algorithm using 3D chaotic map and 2D-multiple parameter fractional discrete cosine transform[J]. Results Opt 1:100031

    Article  Google Scholar 

  21. Lambi D (2020) A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design[J]. Nonlinear Dyn 100(2):677–711

    Google Scholar 

  22. Li Q, Wang X, Wang H, Ye X, Zhou S, Gao S, Shi Y (2021) A secure image protection algorithm by steganography and encryption using the 2D-TSCC. Chin Phys B 30:149–160

    Google Scholar 

  23. Li X, Mou J, Banerjee S, Cao Y (2022) An optical image encryption algorithm based on fractionalorder laser hyperchaotic system. Int J Bifurcation Chaos 32(2):2250035

    Article  MATH  Google Scholar 

  24. Liu H, Kadir A et al (2015) Asymmetric color image encryption scheme using 2D discrete-time map[J]. Signal Process 113:104–112

    Article  Google Scholar 

  25. Liu H, Wen F, Kadir A (2018) Construction of a new 2D Chebyshev-sine map and its application to color image encryption[J]. Multimed Tools Appl 78(12):15997–16010

    Article  Google Scholar 

  26. Liu H, Zhang Y, Kadir A, Xu Y (2019) Image encryption using complex hyper chaotic system by injecting impulse into parameters[J]. Appl Math Comput 360:83–93

    MathSciNet  MATH  Google Scholar 

  27. Liu H, Kadir A, Xu C (2020) Color image encryption with cipher feedback and coupling chaotic map[J]. Int J Bifurcation Chaos 30(12):2050173

    Article  MathSciNet  MATH  Google Scholar 

  28. Liu H, Kadir A, Xu C (2020) Cryptanalysis and constructing S-box based on chaotic map and backtracking[J]. Appl Math Comput 376:125153–125163

    MathSciNet  MATH  Google Scholar 

  29. Maazouz M, Toubal A, Bengherbia B, Houhou O, Batel N (2022) FPGA implementation of a chaosbased image encryption algorithm. J King Saud Univ-Comput Inf Sci, https://doi.org/10.1016/j.jksuci.2021.12.022

  30. Mc Cullough BD (2006) A review of TESTU01[J]. J Appl Econ 21(5):677–682

    Article  Google Scholar 

  31. Naim M, Pacha A, Serief C (2021) A novel satellite image encryption algorithm based on hyperchaotic systems and josephus problem. Adv Space Res 67(7):2077–2103

    Article  Google Scholar 

  32. Naseer Y, Shah T, Attaullah, et al. (2020) Advance image encryption technique utilizing compression, dynamical system and S-boxes[J]. Math Comput Simul (MATCOM) 178:207–217

    Article  MathSciNet  MATH  Google Scholar 

  33. Peng J, Jin S, Zhang D et al (2021) S-box construction method based on the combination of quantum chaos and PWLCM chaotic map[J]. Int J Cogn Inf Nat Intell 15(4):1–17

    Article  Google Scholar 

  34. Rafiq A, Khan M (2019) Construction of new S-boxes based on triangle groups and its applications in copyright protection[J]. Multimed Tools Appl 78:15527–15544

    Article  Google Scholar 

  35. Rashidi B (2021) Compact and efficient structure of 8-bit S-box for lightweight cryptography[J]. Integration 76:172–182

    Article  Google Scholar 

  36. Si Y, Liu H, Chen Y (2021) Constructing keyed strong S-box using an enhanced quadratic map[J]. Int J Bifurcation Chaos 31(10):2150146

    Article  MathSciNet  MATH  Google Scholar 

  37. Teng L, Wang X, Yang F, Xian Y (2021) Color image encryption based on cross 2D hyperchaotic map using combined cycle shift scrambling and selecting diffusion[J]. Nonlinear Dyn 105:1859–1876

    Article  Google Scholar 

  38. Tian Y, Lu Z (2018) Chaotic S-box: six-dimensional fractional Lorenz-duffing chaotic system and O-shaped path scrambling[J]. Nonlinear Dyn 94:2115–2126

    Article  Google Scholar 

  39. Wang X, Li P, Zhang Y et al (2018) A novel color image encryption scheme using DNA permutation based on the Lorenz system[J]. Multimed Tools Appl 77(5):6243–6265

    Article  Google Scholar 

  40. Wang X, Qin X, Liu C (2019) Color image encryption algorithm based on customized globally coupled map lattices[J]. Multimed Tools Appl 78:6191–6209

    Article  Google Scholar 

  41. Wen H, Yu S, Lv J (2017) Encryption algorithm based on Hadoop and non-degenerate high-dimensional hyperchaotic system[J]. Acta Phys Sin 66(23):230503 (in Chinese)

    Article  Google Scholar 

  42. Zhang Q, Han J (2021) A novel color image encryption algorithm based on image hashing, 6D hyperchaotic and DNA coding[J]. Multimed Tools Appl 15:13841–13864

    Article  Google Scholar 

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Acknowledgments

This research is supported by the Natural Science Foundation of Shandong Province (No: ZR2022MF232), the Science and Technology Program of University of Jinan (No: XKY2070).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Jinan, Jinan, 250022, Shandong, China

    Mengchen Wang, Hongjun Liu & Mengdi Zhao

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  1. Mengchen Wang
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  2. Hongjun Liu
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  3. Mengdi Zhao
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Correspondence to Hongjun Liu.

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Wang, M., Liu, H. & Zhao, M. Construction of a non-degeneracy 3D chaotic map and application to image encryption with keyed S-box. Multimed Tools Appl 82, 34541–34563 (2023). https://doi.org/10.1007/s11042-023-14988-9

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  • DOI: https://doi.org/10.1007/s11042-023-14988-9

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