Skip to main content
SpringerLink
Log in

An image encryption algorithm using a dynamic S-box and chaotic maps

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

This paper presents an image encryption algorithm based on dynamic S-box. Encryption algorithm includes four stages: generation of encryption keys, the construction of the S-box, image permutation and image diffusion. The encryption keys are generated by the initial keys and the grey-scale values of the image. The generated encryption keys are used as the initial values and control parameters of the 2D Logistic-Sine-Coupling Map (2D-LACM) and the Logistic Map. And these two chaotic maps are iterated to generate two key sequences and one key sequence, respectively. The construction of S-box is to use the key sequence generated by Logistic map to get a 16 × 16 random matrix with values from 0 to 255 and non-duplicate values. And the idea of confusion is applied to the construction of S-box. The S-box is obtained by using two key sequences generated by 2D-LACM to confuse the matrix. In the permutation phase, the pixel points in the image are first traversed in a random order according to the first key sequence generated by the iterative 2D-LACM, and then each pixel is replaced by the traversal sequence. In the diffusion phase, the permuted image is traversed in the same traversal order as described above, and the result of the traversal is XOR operated with the second key sequence of 2D-LACM. The XOR result is then replaced once by an S-box to get the final encrypted image. The simulation results and security analysis show that the algorithm has high encryption efficiency. It has good key space and can resist various attacks effectively.

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

Similar content being viewed by others

References

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

    Article  MathSciNet  Google Scholar 

  2. Moatsum A et al (2019) A new hybrid digital chaotic system with applications in image encryption. Signal Process 160:45–48

    Article  Google Scholar 

  3. Kumar CM, Vidhya R, Brindha M (2021) An efficient chaos based image encryption algorithm using enhanced thorp shuffle and chaotic convolution function. Appl Intell. https://doi.org/10.1007/s10489-021-02508-x

  4. Chai XL et al (2019) A novel image encryption scheme based on DNA sequence operations and chaotic systems. Neural Comput Appl 31(1):219–237

    Article  Google Scholar 

  5. Vidhya R, Brindha M, Gounden AN (2020) Analysis of zig-zag scan based modified feedback convolution algorithm against differential attacks and its application to image encryption. Appl Intell 50:3101–3124

    Article  Google Scholar 

  6. Chen JX, Zhu ZL, Fu C et al (2015) An image encryption scheme using nonlinear inter-pixel computing and swapping based permutation approach. Commun Nonlinear Sci Numer Simul 23(1–3):294–310

    Article  MathSciNet  Google Scholar 

  7. Teng L, Wang X, Meng J (2018) A chaotic color image encryption using integrated bit-level permutation. Multimed Tools Appl 77:883–6896

    Article  Google Scholar 

  8. Zhang Y, Tang Y (2018) A plaintext-related image encryption algorithm based on chaos. Multimed Tools Appl 77:6647–6669

    Article  Google Scholar 

  9. Alhadawi HS, Majid MA, Lambi D et al (2021) A novel method of S-box design based on discrete chaotic maps and cuckoo search algorithm. Multimed Tools Appl 80:7333–7350

    Article  Google Scholar 

  10. Manjula G, Mohan H (2016) Constructing key dependent dynamic S-box for AES block cipher system. 2016 2nd international conference on applied and theoretical computing and communication technology (iCATccT) 613–617. https://doi.org/10.1109/ICATCCT.2016.7912073

  11. Wang TT, Zhang C (2017) Image encryption algorithm based on Diophantus model and dynamic S box. Comput Eng Design 38(10):3678–3685 (in Chinese)

    Google Scholar 

  12. Zhu CX, Wang GJ, Sun KH (2018) Cryptanalysis and improvement on an image encryption algorithm design using a novel Chaos based S-box. Symmetry 10(9). https://doi.org/10.3390/sym10090399

  13. Uis J, Ugalde E, Salazar G (1998) A cryptosystem based on cellular automata. Chaos 8(4):819–822

    Article  Google Scholar 

  14. Wang XY, Yang JJ (2020) A novel image encryption scheme of dynamic S-boxes and random blocks based on spatiotemporal chaotic system. Optik:217. https://doi.org/10.1016/j.ijleo.2020.164884

  15. Farah MAB, Farah A, Farah T (2019) An image encryption scheme based on a new hybrid chaotic map and optimized substitution box. Nonlinear Dynamics 99:3041–3064

    Article  Google Scholar 

  16. Farah A, Belazi A (2018) A novel chaotic Jaya algorithm for unconstrained numerical optimization. Nonlinear Dynamics 93:1451–1480

    Article  Google Scholar 

  17. Wang X et al (2019) S-box based image encryption application using a chaotic system without equilibrium. Appl Sci 9(4). https://doi.org/10.3390/app9040781

  18. Arslan S, Ahmed J (2021) Dynamic substitution based encryption algorithm for highly correlated data. Multidim Syst Sign Process 32:91–114

    Article  Google Scholar 

  19. Liu HJ et al (2018) Chaos based adaptive double-image encryption scheme using hash function and S-boxes. Multimed Tools Appl 77:1391–1407

    Article  Google Scholar 

  20. Idrees B et al (2020) Image encryption algorithm using S-box and dynamic Hénon bit level permutation. Multimed Tools Appl 79:6135–6162

    Article  Google Scholar 

  21. Wang Y, Li A, Wang SQ et al (2020) Image encryption algorithm based on the combination of CNN and traditional S box. Electro-Optical and Control 28(3):34–38, 57

  22. Liu H, Zhao B, Huang L (2019) Quantum image encryption scheme using Arnold transform and S-box scrambling. Entropy 21(4). https://doi.org/10.3390/e21040343

  23. Hua ZY et al (2018) 2D logistic-sine-coupling map for image encryption. Signal Process 149:148–161

    Article  Google Scholar 

  24. Cassal-Quiroga BB, Campos-Cantón E (2020) Geration of dynamical S-boxes for block ciphers via extended logistic map. Math Probl Eng. https://doi.org/10.1155/2020/2702653

  25. Webster AF, Tavares SE (1986) On the Design of S-Boxes. In: Williams H.C. (eds) Advances in Cryptology — CRYPTO ‘85 Proceedings. CRYPTO 1985. Lecture notes in computer science, vol 218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39799-X_41

  26. Adams C, Tavares S (1990) The structured design of cryptographically good S-boxes. J Cryptol 3:27–41

    Article  MathSciNet  Google Scholar 

  27. Ahmed HA, Zolkipli MF, Ahmad M (2018) A novel efficient substitution-box design based on firefly algorithm and discrete chaotic map. Neural Comput Applic 31:7201–7210

    Article  Google Scholar 

  28. Al Solami E, Ahmad M, Volos C, Doja M, Beg M (2018) A new hyperchaotic system-based design for efficient bijective substitution-boxes. Entropy 20(7). https://doi.org/10.3390/e20070525

  29. Khan M, Asghar Z (2018) A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S 8 permutation. Neural Comput Applic 29:993–999

    Article  Google Scholar 

  30. Belazi A, AAA E-L, Belghith S (2016) A novel image encryption scheme based on substitution-permutation network and chaos. Signal Process 128(155–170)

Download references

Conflict of interest

The authors declare that they have no conflicts of interest.

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Jiming Zheng & Qingxia Zeng

  2. Key Lab of Intelligent Analysis and Decision Complex System, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Jiming Zheng

Authors
  1. Jiming Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qingxia Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiming Zheng.

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

Zheng, J., Zeng, Q. An image encryption algorithm using a dynamic S-box and chaotic maps. Appl Intell 52, 15703–15717 (2022). https://doi.org/10.1007/s10489-022-03174-3

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-022-03174-3

Keywords

Search

Navigation