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Image encryption using the new two-dimensional Beta chaotic map

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Abstract

To further improve the security of the image encryption methods based on chaotic maps, we created a new two-dimensional chaotic map called two Dimensional Beta Chaotic Map(2D-BCM) driven from the one-dimensional Beta chaotic map(1D-BCM). This paper describes a new image encryption approach based on 2D-BCM. The new 2D-BCM is used to produce chaotic sequences. These sequences were used to create the encryption key. The proposed algorithm is composed of three main steps: Permutation, diffusion, and substitution. For the proposed scheme, the generally used metrics of security, and sensitivity to initial conditions are effectively determined with the help of a selection of standard simulation results. In comparison to prior schemes, the obtained results of various types of security analysis show that the newly created 2D-BCM has high sensitivity and security.

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Data availability

The datasets analyzed during the current study are available In: https://sipi.usc.edu/database/database.php?volume=misc.

References

  1. Belazi A, Abd El-Latif A, Belghith S (2016) A novel image encryption scheme based on substitution-permutation network and chaos. Signal Process 128:155–170. https://doi.org/10.1016/j.sigpro.2016.03.021

    Article  Google Scholar 

  2. Cao C, Sun K, Liu W (2017) Signal Process 143. https://doi.org/10.1016/j.sigpro.2017.08.020

  3. Chen G, Mao Y, Chui C (2004) A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Solitons Fractals 21:749. https://doi.org/10.1016/j.chaos.2003.12.022

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen JX, Zhu ZL, Fu C, Yu H, Zhang LB (2015) A fast chaos-based image encryption scheme with a dynamic state variables selection mechanism. Commun Nonlinear Sci Numer Simul 20:846860. https://doi.org/10.1016/j.cnsns.2014.06.032

    Article  Google Scholar 

  5. De S, Bhaumik J, Giri D (2022) A secure image encryption scheme based on three different chaotic maps. Multimed Tools Appl 81:81–5514. https://doi.org/10.1007/s11042-021-11696-0

    Article  Google Scholar 

  6. Elghandour A, Salah A, Karawia A (2021) A new cryptographic algorithm via a two-dimensional chaotic map. Ain Shams Eng J 13:101489. https://doi.org/10.1016/j.asej.2021.05.004

    Article  Google Scholar 

  7. Elkhalil N, Zahmoul R, Ejbali R, Zaied M (2019) A joint encryption-compression technique for images based on beta chaotic maps and SPIHT coding. ICSEA, p 130

  8. Gao X (2021) Opt Laser Technol 142:107252. https://doi.org/10.1016/j.optlastec.2021.107252

    Article  Google Scholar 

  9. Hamdi M, Rhouma R, Belghith S (2016) A selective compression-encryption of images based on SPIHT coding and Chirikov Standard Map. Signal Process 131:514–526. https://doi.org/10.1016/j.sigpro.2016.09.011

    Article  Google Scholar 

  10. Hsiao HI, Lee J (2015) Color image encryption using chaotic nonlinear adaptive filter. Signal Process 117:281–309. https://doi.org/10.1016/j.sigpro.2015.06.007

    Article  Google Scholar 

  11. Hua Z, Zhou Y (2016) Image encryption using 2D Logistic-adjusted-Sine map. Inf Sci 339:237–253. https://doi.org/10.1016/j.ins.2016.01.017

    Article  Google Scholar 

  12. Hua Z, Zhou Y, Pun CM, Chen C (2014) Information Sciences 297. https://doi.org/10.1016/j.ins.2014.11.018

  13. Hua Z, Zhou Y, Pun CM, Chen C (2014) 2D Sine Logistic modulation map for image encryption. Inf Sci 297:80–94. https://doi.org/10.1016/j.ins.2014.11.018

    Article  Google Scholar 

  14. Hussein W, Al-Saidi N, Kadhim H (2018) pp 265–269. https://doi.org/10.1109/SCEE.2018.8684083

  15. Karawia A (2019) IET Image Process 13. https://doi.org/10.1049/iet-ipr.2018.5142

  16. Kumar V, Girdhar A (2021) A 2D logistic map and Lorenz-Rossler chaotic system based RGB image encryption approach. Multimed Tools Appl 80:3749–3773. https://doi.org/10.1007/s11042-020-09854-x

    Article  Google Scholar 

  17. 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. Results Opt 1:100031. https://doi.org/10.1016/j.rio.2020.100031

    Article  Google Scholar 

  18. Li C, Luo G, Qin K, Li C (2017) Nonlinear Dyn 87. https://doi.org/10.1007/s11071-016-3030-8

  19. Liao X, Lai S, Zhou Q (2010) A novel image encryption algorithm based on self-adaptive wave transmission. Signal Process 90:2714. https://doi.org/10.1016/j.sigpro.2010.03.022

    Article  MATH  Google Scholar 

  20. Liu W, Sun K, Zhu C (2016) A fast image encryption algorithm based on chaotic map. Opt Lasers Eng 84:26. https://doi.org/10.1016/j.optlaseng.2016.03.019

    Article  Google Scholar 

  21. Malik D, Shah T (2020) Color multiple image encryption scheme based on 3D-chaotic maps. Math Comput Simul 178:646–666. https://doi.org/10.1016/j.matcom.2020.07.007

    Article  MathSciNet  MATH  Google Scholar 

  22. Masood F, Ahmad J, Shah SA, Sajjad S, Jamal SS, Hussain I (2020) A novel hybrid secure image encryption based on julia set of fractals and 3D Lorenz chaotic map. Entropy 22:274. https://doi.org/10.3390/e22030274

    Article  MathSciNet  Google Scholar 

  23. Matthews R (1989) On the derivation of a “chaotic” encryption algorithm. Cryptologia 13:29–42. https://doi.org/10.1080/0161-118991863745

    Article  MathSciNet  Google Scholar 

  24. Rim Z, Zaied M (2016) pp 004,052–004,057. https://doi.org/10.1109/SMC.2016.7844867

  25. Rim Z, Ejbali R, Zaied M (2017) Image encryption based on new Beta chaotic maps. Opt Lasers Eng 96:39. https://doi.org/10.1016/j.optlaseng.2017.04.009

    Article  Google Scholar 

  26. Rim Z, Afef A, Ejbali R, Zaied M (2020) Beta Chaotic Map Based Image Steganography, pp 97–104. https://doi.org/10.1007/978-3-030-20005-310

  27. Rim Z, Ejbali R, Zaied M (2021) An improved partial image encryption scheme based on lifting wavelet transform, wide range Beta chaotic map and Latin square. Multimed Tools Appl 80:15173–15191. https://doi.org/10.1007/s11042-020-10263-3

    Article  Google Scholar 

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

    Article  Google Scholar 

  29. Sheela S, Kaggere S, Tandur D (2018) Image encryption based on modified Henon map using hybrid chaotic shift transform. Multimed Tools Appl 77:25223–25251. https://doi.org/10.1007/s11042-018-5782-2

    Article  Google Scholar 

  30. Souden H, Ejbali R, Zaied M (2019) p 116. https://doi.org/10.1117/12.2523482

  31. Wu Y, Yang G, ** H, Noonan J (2012) Image encryption using the two-dimensional logistic chaotic map. J Electron Imaging 21:3014. https://doi.org/10.1117/1.JEI.21.1.013014

    Article  Google Scholar 

  32. Wu J, Liao X, Yang B (2017) Color image encryption based on chaotic systems and elliptic curve ElGamal scheme. Signal Process 141:109–124. https://doi.org/10.1016/j.sigpro.2017.04.006

    Article  Google Scholar 

  33. Yavuz E, Yazc R, Kasapba MC, Yamac E (2016) A chaos-based image encryption algorithm with simple logical functions. Comput Electr Eng 54:471. https://doi.org/10.1016/j.compeleceng.2015.11.008

    Article  Google Scholar 

  34. Zaied M, Ben Amar C, Alimi A (2003) International conference on signal, system and design, SSD03, Tunisia 1, 185

Download references

Acknowledgements

The authors would like to acknowledge the financial support of this work by grants from General Direction of Scientific Research (DGRST), Tunisia, under the ARUB program.

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Correspondence to Najet Elkhalil.

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Elkhalil, N., Weddy, Y.C. & Ejbali, R. Image encryption using the new two-dimensional Beta chaotic map. Multimed Tools Appl 82, 31575–31589 (2023). https://doi.org/10.1007/s11042-023-15105-6

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