Skip to main content
SpringerLink
Log in

An Efficient Digital Confidentiality Scheme Based on Commutative Chaotic Polynomial

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

One of the most critical aspects of this technologically progressive era is the propagation of information through an unsecured communication channel. The information is electronically transported as binary bits. One of the most important issues in the existing world is the secrecy of these digital contents. In this paper, we used Chebyshev’s polynomial-based, chaotic maps to propose a new technique for encrypting images. The proposed encryption brings confusion as well as diffusion to the system presented, which is one of the utmost essential aspects of the encryption method. The confusion process is performed in two stages, XORing the original image with the Chebyshev polynomial generated matrices and scrambling, the chaotic scrambling matrix is also generated by the Chebyshev polynomial generated matrix, which increases the sensitivity of the cryptosystem to the key which initialize the parameters for Chebyshev polynomial. We checked our planned scheme against various performance analyses and contrasted them with established outcomes. The scheme is accomplished by offering excellent privacy to digital images.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Alghafis A, Firdousi F, Batool SI, Amin M (2020) An efficient image encryption scheme based on chaotic and deoxyribonucleic acid sequencing. Mathematics and Computers in Simulation (MATCOM), Elsevier 177, no. C: 441–466

    Article  MathSciNet  Google Scholar 

  2. Ali KM, Khan M (2019) A new construction of confusion component of block ciphers. Multimed Tools Appl 78:32585–32604

    Article  Google Scholar 

  3. Alvarez G, Li S (2006) Some basic cryptographic requirements for Chaos-based systems. International Journal of Bifurcation and Chaos 16(8):2129–2151

    Article  MathSciNet  Google Scholar 

  4. Atty BA-E, Abd El-Latif AA, Venegas-Andraca SE (2019) An encryption protocol for NEQR images based on one-particle quantum walks on a circle. Quantum Information Processing, vol. 18

  5. Bssssrahim AH, Pacha AA, Said NH (2021) A new image encryption scheme based on a hyperchaotic system & multi specific S-boxes. Information Security Journal: A Global Perspective. A new image encryption scheme based on a hyperchaotic system & multi specific S-boxes

  6. Chatterjee S, Roy S, Das AK, Chattopadhyay S, Kumar N, Vasilakos AV (2018) Secure biometric-based authentication scheme using Chebyshev chaotic map for multi-server environment. IEEE Transactions on Dependable and Secure Computing, 15 (15): 824–839

  7. El-Latif AAA, Atty BA, Mazurczyk W, Fung C, SEV (2020) Secure data encryption based on quantum walks for 5G internet of things scenario. IEEE Transactions on Network and Service Management

  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 243:19129–19150

    Article  Google Scholar 

  9. Gan Z, Chai X, Zhang M, Lu Y (2018) A double color image encryption scheme based on three-dimensional brownian motion. Multimed Tools Appl 77:27919–27953

    Article  Google Scholar 

  10. Geisel T, Fairén V (1984) Statistical properties of chaos in Chebyshev maps. Phys Lett A 105(6):263–266

    Article  MathSciNet  Google Scholar 

  11. Guesmi R, Farah MAB, Kachouri A, Samet M (2015) Chaos-based designing of a highly nonlinear S-box using Boolean functions, in IEEE SSD international multi-conference on systems, Signals and Devices

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

    Article  Google Scholar 

  13. Jarin I, Fattah SA, Shahnaz C (2018) Natural and medical image encryption using self-adaptive permutation and DNA encoding, in IEEE international WIE conference on electrical and computer engineering (WIECON-ECE)

  14. Kang X, Luo X, Zhang X, Jiang J (2019) Homogenized Chebyshev-Arnold map and its application to color image encryption IEEE Access 7, 7,114459–114471

  15. Kaur M, Kumar V (2020) A comprehensive review on image encryption techniques. Archives of Computational Methods in Engineering 27:15–43

    Article  MathSciNet  Google Scholar 

  16. Khan M (2015) A novel image encryption scheme based on multiple chaotic S-boxes. Nonlinear Dynamics 82(1):527–533

    Article  MathSciNet  Google Scholar 

  17. Khan M, Asghar Z (2018) A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S8 permutation. Neural Comput & Applic 29:993–999

    Article  Google Scholar 

  18. Khan M, Shah T (2014) A construction of novel chaos base nonlinear component of block cipher. Nonlinear Dynamics 76:377–382

    Article  MathSciNet  Google Scholar 

  19. Khan M, Shah T (2015) An efficient chaotic image encryption scheme. Neural Comput & Applic 26:1137–1148

    Article  Google Scholar 

  20. Khan M, Shah T, Batool SI (2017) A new approach for image encryption and watermarking based on substitution box over the classes of chain rings. Multimed Tools Appl, 76, 24027–24062

  21. Khan S, Han L, Lu H, Lu H, Butt KK, Bachira G, Khan NU (2019) A new hybrid image encryption algorithm based on 2D-CA, FSM-DNA rule generator, and FSBI. IEEE Access 7:81333–81350

    Article  Google Scholar 

  22. Kocarev L, Makraduli J, Amato P (2015) Public-key encryption based on Chebyshev polynomials. Circuits Syst Signal Process 24:497–517

    Article  MathSciNet  Google Scholar 

  23. Lai H, Orgun MA, Xiao J, Pieprzyk J, Xue L, Yang Y (2014) Provably secure three-party key agreement protocol using Chebyshev chaotic maps in the standard model. Nonlinear Dynamics 77(4):1427–1439

    Article  MathSciNet  Google Scholar 

  24. Lei Z, Li L, Xianwei G (2011) Design and realization of image encryption system. International Congress on Image and Signal Processing 4:741–744

    Google Scholar 

  25. Tang WKS, Liu Y (2011) Formation of high-dimensional chaotic maps and their uses in cryptography, springer, Berlin, Heidelberg, 354: 99–136

  26. Norouzi B, Mirzakuchaki S (2017) An image encryption algorithm based on DNA sequence operations and cellular neural network. Multimed Tools Appl 76:13681–13701

    Article  Google Scholar 

  27. Said L, Hazzazi MM, Khan M, Jamal SS (2021) A novel image encryption based on rossler map diffusion and particle swarm optimization generated highly non-linear substitution boxes. Chin J Phys 72:558–574

    Article  MathSciNet  Google Scholar 

  28. Shannon CE (1949) Communication theory of secrecy systems. Bell Syst Tech J 28(4):656–715

    Article  MathSciNet  Google Scholar 

  29. Younas I, Khan M (2018) A new efficient digital image encryption based on inverse left almost semi group and Lorenz chaotic system. Entropy. 20(913)

  30. Zhong YR, Liu HY, Sun XY (2018) Image encryption using 2d sine-piecewise linear chaotic map, in Proceeding s of 2018 International Conference on Wavelet Analysis and Pattern Recognition. Chengdu, China

    Google Scholar 

Download references

Acknowledgments

One of the author Dr. Sajjad Shaukat Jamal extends his gratitude to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under grant number R. G. P. 1/399/42.

Author information

Authors and Affiliations

  1. Department of Avionics Engineering, Institute of Space Technology, Islamabad, Pakistan

    Lal Said Khan & Muhammad Amin

  2. Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, Pakistan

    Majid Khan

  3. Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia

    Sajjad Shaukat Jamal

Authors
  1. Lal Said Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Majid Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sajjad Shaukat Jamal
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muhammad Amin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Majid Khan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, L.S., Khan, M., Jamal, S.S. et al. An Efficient Digital Confidentiality Scheme Based on Commutative Chaotic Polynomial. Multimed Tools Appl 81, 33591–33611 (2022). https://doi.org/10.1007/s11042-022-13078-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-022-13078-6

Keywords

Search

Navigation