Skip to main content
Log in

A secure image encryption scheme based on three different chaotic maps

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

Abstract

In the current decade, chaos based image encryption has distinctly captured a remarkable position in multimedia data security. In this paper, a hybrid chaos based image encryption scheme has been developed. A two-dimensional ecological chaotic map, namely Beddington, Free and Lawton (BFL) map has been combined with logistic map and Chebyshev map to generate a pseudo-random keystream for image encryption. In addition, an image substitution technique based on logistic map has been proposed. The random nature of keystream has been successfully tested by employing DIEHARD and NIST randomness test suites. Furthermore, the scheme has also been verified by histogram, correlation, global entropy, local entropy, key sensitivity and differential attack analyses. The proposed scheme achieves average \(41.6\%\) and \(8.5\%\) improvement in correlation value of cipher image and plaintext sensitivity, respectively, compared to Sheela et al.’s scheme.

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

Access this article

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
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

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

    Article  MathSciNet  Google Scholar 

  2. Beddington JR, Free CA, Lawton JH (1975) Dynamic complexity in predator-prey models framed in difference equations. Nature 255:58–60

    Article  Google Scholar 

  3. Chen JX, Zhu ZL, Fu C, Yu H, Zhang LB (2015) An efficient image encryption scheme using gray code based permutation approach. Optics and Lasers in Engineering 67:191–204

    Article  Google Scholar 

  4. Chen JX, Zhu ZL, Fu C, Yu H (2015) Optical image encryption scheme using 3-D chaotic map based joint image scrambling and random encoding in gyrator domains. Optics Communications 341:263–270

    Article  Google Scholar 

  5. Dey D, Giri D, Jana B, Maitra T, Mohapatra RN (2018) Linear-feedback shift register-based multi-ant cellular automation and chaotic map-based image encryption. Security and Privacy 1(6):1–11

    Google Scholar 

  6. Fu C, Chen JJ, Zou H, Meng WH, Zhan YF, Yu YW (2012) A chaos-based digital image encryption scheme with an improved diffusion strategy. Optics Express 20(3):2363–2378

    Article  Google Scholar 

  7. Funt, et al. HDR Dataset Computational Vision Lab Computing Science, Simon Fraser University, Burnaby, BC, Canada. http://www.cs.sfu.ca/ colour/data/funt_hdr/. Accessed 02 May 2017

  8. Geisel T, Fairen V (1984) Statistical Properties of Chaos in Chebyshev Maps. Physics Letters A 105(6):263–266

    Article  MathSciNet  Google Scholar 

  9. Hikal NA, Eid MM (2020) A new approach for palmprint image encryption based on hybrid chaotic maps. Journal of King Saud University - Computer and Information Sciences 32(7):870–882

    Article  Google Scholar 

  10. Hua Z, Zhou Y, Huang H (2019) Cosine-transform-based chaotic system for image encryption. Information Sciences 480:403–419

    Article  Google Scholar 

  11. Huang X (2012) Image encryption algorithm using chaotic Chebyshev generator. Nonlinear Dynamics 67:2411–2417

    Article  MathSciNet  Google Scholar 

  12. Li C, Luo G, Li C (2018) A parallel image encryption algorithm based on chaotic Duffing oscillators. Multimed Tools Appl 77:19193–19208

    Article  Google Scholar 

  13. Mendoza SA, Matt EW, Guimarães-Blandón DR (2018) Parrondo’s paradox or chaos control in discrete two-dimensional dynamic systems. Chaos, Solitons & Fractals 106:86–93

    Article  MathSciNet  Google Scholar 

  14. Nicholson AJ, Bailey VA (1935) The balance of animal populations - Part I. Proc Zool Soc London 105(3):551–598

    Article  Google Scholar 

  15. Nottingham Trent University, UK, “UCID Image Database”. http://jasoncantarella.com/downloads/ucid.v2.tar.gz. Accessed 02 May 2018

  16. Ricker WE (1954) Stock and recruitment. Journal of the Fisheries Research Board of Canada 11(5):559–623

    Article  Google Scholar 

  17. Seyedzadeh SM, Norouzi B, Mosavi MR, Mirzakuchaki S (2015) A novel color image encryption algorithm based on spatial permutation and quantum chaotic map. Nonlinear Dynamics 81(1–2):511–529

    Article  MathSciNet  Google Scholar 

  18. Sheela SJ, Suresh KV, Tandur D (2018) Image encryption based on modified Henon map using hybrid chaotic shift transform. Multimed Tools Appl 77:25223–25251

    Article  Google Scholar 

  19. Stinson D (2002) Cryptography: Theory and Practice. Second ed. CRC/C&H

  20. Taneja N, Raman B, Gupta I (2011) Selective image encryption in fractional wavelet domain. International Journal of Electronics and Communications 65(4):338–344

    Article  Google Scholar 

  21. Taneja N, Raman B, Gupta I (2011) Chaos Based Partial Encryption of SPIHT Compressed Images. International Journal of Wavelets, Multiresolution and Information Processing 9(2):317–331

    Article  Google Scholar 

  22. Taneja N, Raman B, Gupta I (2012) Combinational domain encryption for still visual data. Multimed Tools Appl 59:775–793

    Article  Google Scholar 

  23. Taneja N, Raman B, Gupta I (2012) Chaos based cryptosystem for still visual data. Multimed Tools Appl 61:281–298

    Article  Google Scholar 

  24. Tong XJ, Wang Z, Zhang M, Liu Y, Xu H, Ma J (2015) An image encryption algorithm based on the perturbed high-dimensional chaotic map. Nonlinear Dynamics 80:1493–1508

    Article  MathSciNet  Google Scholar 

  25. University of California, San Diego, “STARE Image Database”. https://cecas.clemson.edu/ ahoover/stare/. Accessed 02 May 2018

  26. University of Southern California, “The USC-SIPI Image Database”. http://sipi.usc.edu/database/database.php. Accessed 02 May 2018

  27. Wang X, Xu D (2015) A novel image encryption scheme using chaos and Langton’s Ant cellular automaton. Nonlinear Dynamics 79:2449–2456

    Article  MathSciNet  Google Scholar 

  28. Wu Y Noonan JP Agaian S (2011) NPCR and UACI randomness tests for image encryption. Cyber Journals: Multidisciplinary Journals in Science and Technology, Journal of Selected Areas in Telecommunications (JSAT) : 31–38

  29. Wu Y, Zhou Y, Saveriades G, Agaian S, Noonan JP, Natarajan P (2013) Local Shannon entropy measure with statistical tests for image randomness. Information Sciences 222:323–342

    Article  MathSciNet  Google Scholar 

  30. Zhang X, Mao Y, Zhao Z (2014) An efficient chaotic image encryption based on alternate circular S-boxes. Nonlinear Dynamics 78:359–369

    Article  Google Scholar 

  31. Zhang X, Zhao Z, Wang J (2014) Chaotic image encryption based on circular substitution box and key stream buffer. Signal Processing: Image Communication 29(8):902–913

    Google Scholar 

  32. Zhu S, Zhu C (2018) Image encryption algorithm with an avalanche effect based on a six-dimensional discrete chaotic system. Multimed Tools Appl 77:29119–29142

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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

De, S., Bhaumik, J. & Giri, D. A secure image encryption scheme based on three different chaotic maps. Multimed Tools Appl 81, 5485–5514 (2022). https://doi.org/10.1007/s11042-021-11696-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-021-11696-0

Keywords

Navigation