Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Advertisement

Springer Nature Link
Log in

A new one-dimensional chaotic map and its application in a novel permutation-less image encryption scheme

  • Original article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

In this paper, we propose a new real one-dimensional cosine fractional (1-DCF) chaotic map. Several chaos-theory analysis tests demonstrate that the proposed map has many good cryptography properties, such as a highly chaotic behavior, a large chaotic range, an infinite number of unstable fixed points, and a widely superior sensitivity to the initial conditions than most of the low-dimensional chaotic maps. Regarding these attractive features, we use the 1-DCF map to design a novel fast image encryption scheme for real-time image processing. Unlike most of the existing encryption schemes, we adopt a permutation-less architecture to increase the encryption speed. Regardless of the permutation phase absence, a high-security level is obtained by using a substitution process with a high sensitivity to the plain image. Moreover, we replace the natural row-order encryption with a more secure random-like encryption order generated from the secret key. Experimentation and simulations show that the new scheme is better than many recently proposed encryption schemes in both security and rapidity.

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

Access this article

Log in via an institution

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.

Institutional subscriptions

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Rijmen, V., Daemen, J.: Advanced encryption standard. In: Proceedings of Federal Information Processing Standards Publications. National Institute of Standards and Technology, pp. 19–22 (2001)

  2. Coppersmith, D.: The data encryption standard (DES) and its strength against attacks. IBM J. Res. Dev. 38(3), 243–250 (1994)

    Article  Google Scholar 

  3. Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)

    Article  MathSciNet  Google Scholar 

  4. Talhaoui, M.Z., Wang, X., Midoun, M.A.: Fast image encryption algorithm with high security level using the bülban chaotic map. J. Real-Time Image Process. (2020). https://doi.org/10.1007/s11554-020-00948-1

    Article  Google Scholar 

  5. Artiles, J.A., Chaves, D.P., Pimentel, C.: Image encryption using block cipher and chaotic sequences. Sig. Process. Image Commun. 79, 24–31 (2019)

    Article  Google Scholar 

  6. El Assad, S., Farajallah, M.: A new chaos-based image encryption system. Sig. Process. Image Commun. 41, 144–157 (2016)

    Article  Google Scholar 

  7. Li, Y., Wang, C., Chen, H.: A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation. Opt. Lasers Eng. 90, 238–246 (2017)

    Article  Google Scholar 

  8. Xuejing, K., Zihui, G.: A new color image encryption scheme based on dna encoding and spatiotemporal chaotic system. Sig. Process. Image Commun. 80, 115670 (2020)

    Article  Google Scholar 

  9. Chai, X., Chen, Y., Broyde, L.: A novel chaos-based image encryption algorithm using DNA sequence operations. Opt. Lasers Eng. 88, 197–213 (2017)

    Article  Google Scholar 

  10. Akhshani, A., Akhavan, A., Lim, S.-C., Hassan, Z.: An image encryption scheme based on quantum logistic map. Commun. Nonlinear Sci. Numer. Simul. 17(12), 4653–4661 (2012)

    Article  MathSciNet  Google Scholar 

  11. Zhou, N.R., Hua, T.X., Gong, L.H., Pei, D.J., Liao, Q.H.: Quantum image encryption based on generalized Arnold transform and double random-phase encoding. Quantum Inf. Process. 14(4), 1193–1213 (2015)

    Article  MathSciNet  Google Scholar 

  12. Yang, Y.-G., Tian, J., Lei, H., Zhou, Y.-H., Shi, W.-M.: Novel quantum image encryption using one-dimensional quantum cellular automata. Inf. Sci. 345, 257–270 (2016)

    Article  Google Scholar 

  13. Chen, W., Chen, X., Sheppard, C.J.: Optical image encryption based on diffractive imaging. Opt. Lett. 35(22), 3817–3819 (2010)

    Article  Google Scholar 

  14. Shao, Z., Liu, X., Yao, Q., Qi, N., Shang, Y., Zhang, J.: Multiple-image encryption based on chaotic phase mask and equal modulus decomposition in quaternion gyrator domain. Sig. Process. Image Commun. 80, 115662 (2020)

    Article  Google Scholar 

  15. Boriga, R., Dăscălescu, A.C., Priescu, I.: A new hyperchaotic map and its application in an image encryption scheme. Sig. Process. Image Commun. 29(8), 887–901 (2014)

    Article  Google Scholar 

  16. Hua, Z., Zhou, Y., Bao, B.: Two-dimensional sine chaotification system with hardware implementation. IEEE Trans. Ind. Inf. 16(2), 887–897 (2019)

    Article  Google Scholar 

  17. Hua, Z., Zhang, Y., Zhou, Y.: Two-dimensional modular chaotification system for improving chaos complexity. IEEE Trans. Signal Process. (2020). https://doi.org/10.1109/TSP.2020.2979596

    Article  MathSciNet  Google Scholar 

  18. Wang, X., Zhao, H., Hou, Y., Luo, C., Zhang, Y., Wang, C.: Chaotic image encryption algorithm based on pseudo-random bit sequence and dna plane. Mod. Phys. Lett. B 33(22), 1950263 (2019)

    Article  MathSciNet  Google Scholar 

  19. Hua, Z., Xu, B., Jin, F., Huang, H.: Image encryption using josephus problem and filtering diffusion. IEEE Access 7, 8660–8674 (2019)

    Article  Google Scholar 

  20. Boriga, R., Dăscălescu, A.C., Diaconu, A.-V.: A new one-dimensional chaotic map and its use in a novel real-time image encryption scheme. Adv. Multimed. 2014, 6 (2014)

    Article  Google Scholar 

  21. Wang, B., Wei, X., Zhang, Q.: Cryptanalysis of an image cryptosystem based on logistic map. Opt.-Int. J. Light Electron Opt. 124(14), 1773–1776 (2013)

    Article  Google Scholar 

  22. Li, C., Xie, T., Liu, Q., Cheng, G.: Cryptanalyzing image encryption using chaotic logistic map. Nonlinear Dyn. 78(2), 1545–1551 (2014)

    Article  Google Scholar 

  23. He, D., He, C., Jiang, L.-G., Zhu, H.-W., Hu, G.-R.: Chaotic characteristics of a one-dimensional iterative map with infinite collapses. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48(7), 900–906 (2001)

    Article  MathSciNet  Google Scholar 

  24. Mansouri, A., Wang, X.: A novel one-dimensional sine powered chaotic map and its application in a new image encryption scheme. Inf. Sci. 520, 46–62 (2020)

    Article  MathSciNet  Google Scholar 

  25. Talhaoui, M.Z., Wang, X., Midoun, M.A.: A new one-dimensional cosine polynomial chaotic map and its use in image encryption. Vis. Comput. (2020). https://doi.org/10.1007/s00371-020-01822-8

    Article  Google Scholar 

  26. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining lyapunov exponents from a time series. Phys. D 16(3), 285–317 (1985)

    Article  MathSciNet  Google Scholar 

  27. Pincus, S.M.: Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. 88(6), 2297–2301 (1991)

    Article  MathSciNet  Google Scholar 

  28. Pincus, S.: Approximate entropy (apen) as a complexity measure. Chaos Interdiscipl. J. Nonlinear Sci. 5(1), 110–117 (1995)

    Article  MathSciNet  Google Scholar 

  29. Shannon, C.E.: Communication theory of secrecy systems*. Bell Syst. Technol. J. 28(4), 656–715 (1949). https://doi.org/10.1002/j.1538-7305.1949.tb00928.x

    Article  MathSciNet  MATH  Google Scholar 

  30. Tang, J., Yu, Z., Liu, L.: A delay coupling method to reduce the dynamical degradation of digital chaotic maps and its application for image encryption. Multimed. Tools Appl. (2019). https://doi.org/10.1007/s11042-019-7602-8

    Article  Google Scholar 

  31. Liu, L., Miao, S.: A new simple one-dimensional chaotic map and its application for image encryption. Multimed. Tools Appl. 77(16), 21445–21462 (2018)

    Article  Google Scholar 

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

    Article  Google Scholar 

  33. Wang, X., Feng, L., Li, R., Zhang, F.: A fast image encryption algorithm based on non-adjacent dynamically coupled map lattice model. Nonlinear Dyn. (2019). https://doi.org/10.1007/s11071-018-4723-y

    Article  MATH  Google Scholar 

  34. Hua, Z., Jin, F., Xu, B., Huang, H.: 2D Logistic-sine-coupling map for image encryption. Signal Process. 149, 148–161 (2018)

    Article  Google Scholar 

  35. Wu, Y., Zhou, Y., Saveriades, G., Agaian, S., Noonan, J.P., Natarajan, P.: Local Shannon entropy measure with statistical tests for image randomness. Inf. Sci. 222, 323–342 (2013). https://doi.org/10.1016/j.ins.2012.07.049

    Article  MathSciNet  MATH  Google Scholar 

  36. Castro, J.C.H., Sierra, J.M., Seznec, A., Izquierdo, A., Ribagorda, A.: The strict avalanche criterion randomness test. Math. Comput. Simul. 68(1), 1–7 (2005). https://doi.org/10.1016/j.matcom.2004.09.001

    Article  MathSciNet  MATH  Google Scholar 

  37. Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc. Chaos 16(08), 2129–2151 (2006)

    Article  MathSciNet  Google Scholar 

  38. Stallings, W.: Cryptography and network security: principles and practice. Int. J. Eng. Comput. Sci. 01(01), 121–136 (2012)

    Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (No. 61672124), the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund (No. MMJJ20170203), Liaoning Province Science and Technology Innovation Leading Talents Program Project (No. XLYC1802013), Key R&D Projects of Liaoning Province (No. 2019020105-JH2/103), Jinan City ’20 universities’ Funding Projects Introducing Innovation Team Program (No. 2019GXRC031).

Author information

Authors and Affiliations

  1. School of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China

    Xingyuan Wang

  2. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Mohamed Zakariya Talhaoui & Xingyuan Wang

  3. Department of FPST, Ecole Nationale Polytechnique d’Oran, Oran, 31000, Algeria

    Abdallah Talhaoui

Authors
  1. Mohamed Zakariya Talhaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xingyuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdallah Talhaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xingyuan Wang.

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

Talhaoui, M.Z., Wang, X. & Talhaoui, A. A new one-dimensional chaotic map and its application in a novel permutation-less image encryption scheme. Vis Comput 37, 1757–1768 (2021). https://doi.org/10.1007/s00371-020-01936-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-020-01936-z

Keywords

Search

Navigation