Skip to main content

Advertisement

Log in

Modified bernoulli map-based scramble and s-box supported colour image encryption

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

The exponential growth of digital image sharing has amplified concerns regarding data privacy and security, especially for colour images of varying sizes and resolutions. Traditional encryption algorithms often fall short in balancing speed, scalability, and robust security for such diverse image datasets. Addressing this gap, we introduce a novel colour image encryption scheme that synergizes modified Bernoulli map-based random number generation for pixel scrambling with an S-Box-supported diffusion process. Our approach first employs a chaotic random number generator to effectively reorder pixel positions, enhancing confusion. This is followed by a diffusion phase utilizing a robust Khan S-Box to introduce nonlinearity and further obfuscate pixel values. To evaluate the security and efficiency of our method, we conducted extensive tests including differential cryptanalysis using NPCR (Number of Pixel Change Rate) and UACI (Unified Average Changing Intensity) metrics. The results demonstrate that our encryption system exhibits high resistance to differential attacks and achieves superior performance compared to existing methods. By combining fast random number generation with strong S-Box diffusion, our scheme offers a scalable and secure solution for real-time colour image encryption, contributing significant advancements to the field of cryptographic image processing.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9 
Fig. 10 
Fig. 11 
Fig. 12 
Fig. 13 

Similar content being viewed by others

Data Availability

No datasets were generated or analysed during the current study.

References

  1. Abdallah, A.A., Farhan, A.K.: New S-Box Design for Image Encryption Based on Multi-Chaotic System. Engineering and Technology Journal. 41, 1211–1219 (2023). https://doi.org/10.30684/etj.2023.139076.1416

  2. Winarno, E., Nugroho, K., Adi, P.W., Setiadi, D.R.I.M.: Integrated dual hyperchaotic and Josephus traversing based 3D confusion-diffusion pattern for image encryption. Journal of King Saud University - Computer and Information Sciences. 35, 101790 (2023). https://doi.org/10.1016/J.JKSUCI.2023.101790

  3. Ravi, R.V., Goyal, S.B., Singla, S.: Colour Image Cryptography using Chaotic Pixel Shuffling and 3D Logistic Diffusion. ACM International Conference Proceeding Series. (2022). https://doi.org/10.1145/3590837.3590871

    Article  MATH  Google Scholar 

  4. Zhao, H., Wang, S., Fu, Z.: A new image encryption algorithm based on cubic fractal matrix and L-LCCML system. Chaos Solitons Fractals 185, 115076 (2024). https://doi.org/10.1016/J.CHAOS.2024.115076

    Article  Google Scholar 

  5. Neugebauer, F., Polian, I., Hayes, J.P.: S-box-based random number generation for stochastic computing. Microprocess. Microsyst. 61, 316–326 (2018). https://doi.org/10.1016/j.micpro.2018.06.009

    Article  Google Scholar 

  6. Etem, T., Kaya, T.: Fast image encryption algorithm with random structures. International Journal of Computers and Applications. 1–12 (2023). https://doi.org/10.1080/1206212X.2023.2260617

  7. Etem, T., Kaya, T.: A novel True Random Bit Generator design for image encryption. Physica A: Statistical Mechanics and its Applications. 540, (2020). https://doi.org/10.1016/j.physa.2019.122750

  8. Chase Harrison, R., Rhea, B.K., Oldag, A.R., Dean, R.N., Perkins, E.: Experimental Validation of a Chaotic Jerk Circuit Based True Random Number Generator. Chaos Theory and Applications. 4, 64–70 (2022). https://doi.org/10.51537/CHAOS.1112243

  9. Nitaj, A., Susilo, W., Tonien, J.: A New Improved AES S-box with Enhanced Properties. (2020)

  10. Avaroğlu, E., Tuncer, T.: A novel S-box-based postprocessing method for true random number generation. Turk. J. Electr. Eng. Comput. Sci. 28, 288–301 (2020). https://doi.org/10.3906/elk-1906-194

    Article  MATH  Google Scholar 

  11. Zhang, Y.: The unified image encryption algorithm based on chaos and cubic S-Box. Inf Sci (N Y). 450, 361–377 (2018). https://doi.org/10.1016/j.ins.2018.03.055

    Article  MathSciNet  MATH  Google Scholar 

  12. Yang, S., Tong, X., Wang, Z., Zhang, M.: Efficient color image encryption algorithm based on 2D coupled chaos and multi-objective optimized S-box. Phys. Scr. 97, 045204 (2022). https://doi.org/10.1088/1402-4896/AC59FA

    Article  MATH  Google Scholar 

  13. Gong, L.H., Zeng, J., Li, X.Z.: Image encryption algorithm based on the fractional Hermite transform. J. Mod. Opt. 68, 1026–1040 (2021). https://doi.org/10.1080/09500340.2021.1968054

    Article  MathSciNet  MATH  Google Scholar 

  14. Sang, Y., Sang, J., Alam, M.S.: Image encryption based on logistic chaotic systems and deep autoencoder. Pattern Recognit Lett. 153, 59–66 (2022). https://doi.org/10.1016/j.patrec.2021.11.025

    Article  MATH  Google Scholar 

  15. Dong, W., Li, Q., Tang, Y.: Image encryption-then-transmission combining random sub-block scrambling and loop DNA algorithm in an optical chaotic system. Chaos Solitons Fractals 153, 111539 (2021). https://doi.org/10.1016/j.chaos.2021.111539

    Article  MathSciNet  MATH  Google Scholar 

  16. Etem, T., Kaya, T.: Self-generated encryption model of acoustics. Appl. Acoust. 170, 107481 (2020). https://doi.org/10.1016/j.apacoust.2020.107481

    Article  MATH  Google Scholar 

  17. Grini, A., Chillali, A., Mouanis, H.: A new cryptosystem based on a twisted Hessian curve Ha,d4. J Appl Math Comput. 1–17 (2021). https://doi.org/10.1007/s12190-021-01624-8

  18. Lai, Q., Hu, G., Erkan, U., Toktas, A.: High-efficiency medical image encryption method based on 2D Logistic-Gaussian hyperchaotic map. Appl Math Comput. 442, (2023). https://doi.org/10.1016/J.AMC.2022.127738

  19. Song, C., Huang, R., Hu, S.: Private-preserving language model inference based on secure multi-party computation. Neurocomputing 592, 127794 (2024). https://doi.org/10.1016/J.NEUCOM.2024.127794

    Article  MATH  Google Scholar 

  20. Kumar, A., Mishra, A.: Evaluation of Cryptographically Secure Pseudo Random Number Generators for Post Quantum Era. 2022 IEEE 7th International conference for Convergence in Technology, I2CT 2022. (2022). https://doi.org/10.1109/I2CT54291.2022.9824543

  21. Cai, X.Q., Liu, Z.F., Wang, T.: yin: Measurement-device-independent quantum homomorphic encryption. Phys. Lett. A 513, 129609 (2024). https://doi.org/10.1016/J.PHYSLETA.2024.129609

    Article  MATH  Google Scholar 

  22. Kocak, O., Erkan, U., Toktas, A., Gao, S.: PSO-based image encryption scheme using modular integrated logistic exponential map. Expert Syst. Appl. 237, 121452 (2024). https://doi.org/10.1016/J.ESWA.2023.121452

    Article  MATH  Google Scholar 

  23. Toktas, F., Erkan, U., Yetgin, Z.: Cross-channel color image encryption through 2D hyperchaotic hybrid map of optimization test functions. Expert Syst. Appl. 249, 957–4174 (2024). https://doi.org/10.1016/j.eswa.2024.123583

    Article  MATH  Google Scholar 

  24. Feng, W., Wang, Q., Liu, H., Ren, Y., Zhang, J., Zhang, S., Qian, K., Wen, H.: Exploiting Newly Designed Fractional-Order 3D Lorenz Chaotic System and 2D Discrete Polynomial Hyper-Chaotic Map for High-Performance Multi-Image Encryption. Fractal and Fractional 2023, Vol. 7, Page 887. 7, 887 (2023). https://doi.org/10.3390/FRACTALFRACT7120887

  25. Feng, W., Zhao, X., Zhang, J., Qin, Z., Zhang, J., He, Y.: Image Encryption Algorithm Based on Plane-Level Image Filtering and Discrete Logarithmic Transform. Mathematics 2022, Vol. 10, Page 2751. 10, 2751 (2022). https://doi.org/10.3390/MATH10152751

  26. Feng, W., Zhang, J., Chen, Y., Qin, Z., Zhang, Y., Ahmad, M., Woźniak, M.: Exploiting robust quadratic polynomial hyperchaotic map and pixel fusion strategy for efficient image encryption. Expert Syst. Appl. 246, 123190 (2024). https://doi.org/10.1016/J.ESWA.2024.123190

    Article  MATH  Google Scholar 

  27. Wen, H., Lin, Y.: Cryptanalysis of an image encryption algorithm using quantum chaotic map and DNA coding. Expert Syst. Appl. 237, 121514 (2024). https://doi.org/10.1016/J.ESWA.2023.121514

    Article  MATH  Google Scholar 

  28. Wen, H., Lin, Y.: Cryptanalyzing an image cipher using multiple chaos and DNA operations. Journal of King Saud University - Computer and Information Sciences. 35, 101612 (2023). https://doi.org/10.1016/J.JKSUCI.2023.101612

  29. Khan, M., Shah, T., Mahmood, H., Gondal, M.A., Hussain, I.: A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems. Nonlinear Dyn. 70, 2303–2311 (2012). https://doi.org/10.1007/S11071-012-0621-X/TABLES/10

    Article  MathSciNet  MATH  Google Scholar 

  30. Sharma, P.K., Ahmad, M., Khan, P.M.: Cryptanalysis of image encryption algorithm based on pixel shuffling and chaotic S-box transformation. Communications in Computer and Information Science. 467, 173–181 (2014). https://doi.org/10.1007/978-3-662-44966-0_16

    Article  MATH  Google Scholar 

  31. Zhang, H., Sun, W., Lu, L.: Chaotic encryption algorithm with scrambling diffusion based on the Josephus cycle. Front. Phys. 11, 1191793 (2023). https://doi.org/10.3389/FPHY.2023.1191793/BIBTEX

    Article  MATH  Google Scholar 

  32. Wu, Y., Noonan, J.P., Agaian, S.: NPCR and UACI Randomness Tests for Image Encryption. Journal of Selected Areas in Telecommunications (JSAT). April Edit, 31–38 (2011)

  33. Xu, L., Gou, X., Li, Z., Li, J.: A novel chaotic image encryption algorithm using block scrambling and dynamic index based diffusion. Opt. Lasers Eng. 91, 41–52 (2017). https://doi.org/10.1016/j.optlaseng.2016.10.012

    Article  MATH  Google Scholar 

  34. Alarood, A.A., Alsolami, E., Al-Khasawneh, M.A., Ababneh, N., Elmedany, W.: IES: Hyper-chaotic plain image encryption scheme using improved shuffled confusion-diffusion. Ain Shams Engineering Journal. 13, 101583 (2022). https://doi.org/10.1016/J.ASEJ.2021.09.010

    Article  Google Scholar 

  35. Kadir, A., Aili, M., Sattar, M.: Color image encryption scheme using coupled hyper chaotic system with multiple impulse injections. Optik (Stuttg). 129, 231–238 (2017). https://doi.org/10.1016/j.ijleo.2016.10.036

    Article  Google Scholar 

  36. Ghebleh, M., Kanso, A.: A novel efficient image encryption scheme based on chained skew tent maps. Neural Comput. Appl. 31, 2415–2430 (2019). https://doi.org/10.1007/s00521-017-3199-x

    Article  MATH  Google Scholar 

  37. Yuan, H.M., Liu, Y., Gong, L.H., Wang, J.: A new image cryptosystem based on 2D hyper-chaotic system. Multimed Tools Appl. 76, 8087–8108 (2017). https://doi.org/10.1007/s11042-016-3454-7

    Article  MATH  Google Scholar 

  38. Raghuvanshi, K.K., Kumar, S., Kumar, S., Kumar, S.: Development of new encryption system using Brownian motion based diffusion. Multimed Tools Appl. (2021). https://doi.org/10.1007/s11042-021-10665-x

    Article  MATH  Google Scholar 

  39. Chen, X., Qian, S., Yu, F., Zhang, Z., Shen, H., Huang, Y., Cai, S., Deng, Z., Li, Y., Du, S.: Pseudorandom Number Generator Based on Three Kinds of Four-Wing Memristive Hyperchaotic System and Its Application in Image Encryption. Complexity. 2020, (2020). https://doi.org/10.1155/2020/8274685

  40. Khan, J.S., Ahmad, J.: Chaos based efficient selective image encryption. Multidimens Syst Signal Process. 30, 943–961 (2019). https://doi.org/10.1007/s11045-018-0589-x

    Article  MathSciNet  MATH  Google Scholar 

  41. Chai, X., Fu, X., Gan, Z., Lu, Y., Chen, Y.: A color image cryptosystem based on dynamic DNA encryption and chaos. Signal Process. 155, 44–62 (2019). https://doi.org/10.1016/j.sigpro.2018.09.029

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This study has been produced from the doctoral dissertation of Taha Etem.

Author information

Authors and Affiliations

Authors

Contributions

T.E. conceived and designed the analysis, collected the data, contributed analysis tools and wrote paper. T.K. edited paper, controlled analysis and made supervision.

Corresponding author

Correspondence to Taha Etem.

Ethics declarations

Conflict of interests

The authors declare no competing interests.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Etem, T., Kaya, T. Modified bernoulli map-based scramble and s-box supported colour image encryption. SIViP 19, 59 (2025). https://doi.org/10.1007/s11760-024-03572-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11760-024-03572-9

Keywords

Navigation