Skip to main content
SpringerLink
Log in

A new perturbation-feedback hybrid control method for reducing the dynamic degradation of digital chaotic systems and its application in image encryption

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

Abstract

In a finite precision computing environment, the trajectories of all chaotic sequences enter a cycle leading to degradation of their dynamics. In this paper a new perturbation feedback hybrid control method to reduce the influence of finite precision. A traditional logistic map is introduced as a pseudo-random sequence generator for time-varying perturbation to perturb the coefficients of chaotic map and make them iteratively changed in the chaotic region. The nonlinear feedback mechanism has high complexity. Numerical analysis results show that the perturbation-feedback hybrid control method can effectively attenuate the dynamic degradation of digital chaotic systems. Further, we propose a simple encryption algorithm based on the perturbation-feedback hybrid control method and apply it to image encryption. The NPCR and UACI of our encryption method are 0.99609 and 0.33464, respectively and the information entropy is as high as 7.9976. All the numerical experiments results prove that the proposed algorithm is highly secure, resistant to multiple attacks, and is more competitive than other encryption algorithms.

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
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Alawida M, Samsudin A, Teh J (2019) S. Enhancing unimodal digital chaotic maps through hybridization [J]. Nonlinear Dyn 96(1):601–613

    Article  MATH  Google Scholar 

  2. Arpaci B, Kurt E, Celik K, Ciylan B (2020) Colored image encryption and decryption with a new algorithm and a Hyperchaotic electrical circuit [J]. J Electric Eng Technol 15(3):1413–1429

    Article  Google Scholar 

  3. Artiles Jose AP, Chaves Daniel PB, Pimentel C (2019) Image encryption using block cipher and chaotic sequences [J]. Signal Process Image Communication 79:24–31

    Article  Google Scholar 

  4. Asgari-Chenaghlu M, Balafar M-A, Feizi-Derakhshi M-R (2019) A novel image encryption algorithm based on polynomial combination of chaotic maps and dynamic function generation [J]. Signal Process 157:1–13

    Article  Google Scholar 

  5. Azzaz MS, Tanougast C, Sadoudi S et al (2013) A new auto-switched chaotic system and its FPGA implementation [J]. Commun Nonlinear Sci Numer Simul 18(7):1792–1804

    Article  MathSciNet  MATH  Google Scholar 

  6. Ben Farah MA, Kachouri A, Samet M (2011) Improvement of cryptosystem based on iterating chaotic map [J]. Commun Nonlinear Sci Numer Simul 16(6):2543–2553

    Article  Google Scholar 

  7. Ben Farah MA, Guesmi R, Kachouri A et al (2020) A new design of cryptosystem based on S-box and chaotic permutation [J]. Multimed Tools Appl 79(27–28):19129–19150

    Article  Google Scholar 

  8. Chen JX, Zhu ZL, Zhang LB et al (2018) Exploiting self-adaptive permutation-diffusion and DNA random encoding for secure and efficient image encryption [J]. Signal Process 142:340–353

    Article  Google Scholar 

  9. Chen C, Sun KH, Peng YX et al (2019) A novel control method to counteract the dynamical degradation of a digital chaotic sequence [J]. Eur Phys J Plus 134(1):31

    Article  Google Scholar 

  10. Dastgheib MA, Farhang M (2017) A digital pseudo-random number generator based on sawtooth chaotic map with a guaranteed enhanced period [J]. Nonlinear Dyn 89(4):2957–2966

    Article  MathSciNet  MATH  Google Scholar 

  11. Gopalakrishnan T, Ramakrishnan S (2017) Chaotic image encryption with hash keying as key generator [J]. IETE J Res 63(2):172–187

    Article  Google Scholar 

  12. Gopalakrishnan T, Ramakrishnan S (2019) Image encryption using hyper-chaotic map for permutation and diffusion by multiple hyper-chaotic maps [J]. Wirel Pers Commun 109(1):437–454

    Article  Google Scholar 

  13. Gustafson H, Dawson E, Nielsen L, Caelli W (1994) A computer package for measuring the strength of encryption algorithms [J]. Computer & Security 13(8):687–697

    Article  Google Scholar 

  14. Hamza R (2017) A novel pseudo random sequence generator for image-cryptographic applications [J]. J Inform Secur Appl 35:119–127

    Google Scholar 

  15. Hua ZY, Zhou YC (2018) One-dimensional nonlinear model for producing Chaos [J]. IEEE Trans Circuits Syst I-Regul Pap 65(1):235–246

    Article  Google Scholar 

  16. Hua ZY, Zhou YC, Pun CM et al (2015) 2D sine logistic modulation map for image encryption[J]. Inf Sci 297:80–94

    Article  Google Scholar 

  17. Jiang N, Zhao A, Xue CP et al (2019) Physical secure optical communication based on private chaotic spectral phase encryption/decryption [J]. Opt Lett 44(7):1536–1539

    Article  Google Scholar 

  18. Khan M (2015) A novel image encryption scheme based on multiple chaotic S-boxes [J]. Nonlinear Dyn 82(1–2):527–533

    Article  MathSciNet  Google Scholar 

  19. Lambic D, Nikolic M (2017) Pseudo-random number generator based on discrete-space chaotic map [J]. Nonlinear Dyn 90(1):223–232

    Article  MathSciNet  Google Scholar 

  20. Li X, Wang Y, Wang QH et al (2019) Modified integral imaging reconstruction and encryption using an improved SR reconstruction algorithm [J]. Opt Lasers Eng 112(SI):162–169

    Article  Google Scholar 

  21. Li CQ, Feng BB, Li SJ et al (2019) Dynamic analysis of digital chaotic maps via state-mapping networks [J]. IEEE Trans Circuits Syst I-Regul Pap 66(6):2322–2335

    Article  MathSciNet  Google Scholar 

  22. Liu LF, Miao SX (2015) A universal method for improving the dynamical degradation of a digital chaotic system[J]. Phys Scr 90(8):085205

    Article  Google Scholar 

  23. Liu LF, Miao SX (2017) Delay-introducing method to improve the dynamical degradation of a digital chaotic map [J]. Inf Sci 396:1–13

    Article  Google Scholar 

  24. Liu LF, Hu HP, Deng YS (2015) An analogue-digital mixed method for solving the dynamical degradation of digital chaotic systems [J]. IMA J Math Control Inf 32(4):703–715

    MathSciNet  MATH  Google Scholar 

  25. Liu LF, Lin J, Miao SX et al (2017) A double perturbation method for reducing dynamical degradation of the digital baker map [J]. Int J Bifurcat Chaos 27(07):174102–174396

    Article  MathSciNet  Google Scholar 

  26. Liu YQ, Luo YL, Song SX et al (2017) Counteracting dynamical degradation of digital chaotic Chebyshev map via perturbation [J]. Int J Bifurcat Chaos 27(03):1750033

    Article  MathSciNet  MATH  Google Scholar 

  27. Murillo-Escobar MA, Cruz-Hernandez C, Cardoza-Avendao L et al (2017) A novel pseudorandom number generator based on pseudorandomly enhanced logistic map [J]. Nonlinear Dyn 87(1):407–425

    Article  MathSciNet  Google Scholar 

  28. Nagaraj N, Shastry MC, Vaidya PG (2008) Increasing average period lengths by switching of robust chaos maps in finite precision [J]. Eur Phys J Spec Top 165(1):73–83

    Article  Google Scholar 

  29. Nesa N, Ghosh T, Banerjee I (2019) Design of a chaos-based encryption scheme for sensor data using a novel logarithmic chaotic map [J]. Journal of Information Security and Applications 47:320–328

    Article  Google Scholar 

  30. Persohn KJ, Povinelli R (2012) Analyzing logistic map pseudo-random number generators for periodicity induced by finite precision floating-point representation [J]. Chaos, Solitons Fractals 45(3):238–245

    Article  Google Scholar 

  31. Rajagopalan S, Poori S, Narasimhan M, Rethinam S, Vallipalayam Kuppusamy C, Balasubramanian R, Moorthi Paramasivam Annamalai V, Rengarajan A (2020) Chua's diode and strange attractor: a three-layer hardware–software co-design for medical image confidentiality [J]. IET Image Process 14(7):1354–1365

    Article  Google Scholar 

  32. Ravichandran D, Praveenkumar P, Rayappan JBB, Amirtharajan R (2017) DNA Chaos blend to secure medical privacy [J]. IEEE Trans Nanobiosci 16(8):850–858

    Article  Google Scholar 

  33. Tang JY, Yu ZN, Liu LF (2019) A delay coupling method to reduce the dynamical degradation of digital chaotic maps and its application for image encryption [J]. Multimed Tools Appl 78(17):24765–24788

    Article  Google Scholar 

  34. Tong XJ, Wang Z, Zhang M et al (2015) An image encryption algorithm based on the perturbed high-dimensional chaotic map [J]. Nonlinear Dyn 80(3):1493–1508

    Article  MathSciNet  MATH  Google Scholar 

  35. Wang XY, Li ZM (2019) A color image encryption algorithm based on Hopfield chaotic neural network [J]. Opt Lasers Eng 115:107–118

    Article  Google Scholar 

  36. Wang XY, Wang Q (2014) A fast image encryption algorithm based on only blocks in cipher text [J]. Chinese Physics B 23(3):1674–1056

    Article  Google Scholar 

  37. Wang SH, Liu WR, Lu HP et al (2004) Periodicity of chaotic trajectories in realizations of finite computer precisions and its implication in chaos communications [C]. Int J Moder Phys B 18(17–19):2617–2622

    Article  Google Scholar 

  38. Wang XY, Wang Q, Zhang YQ (2015) A fast image algorithm based on rows and columns switch [J]. Nonlinear Dyn 79(2):1141–1149

    Article  MathSciNet  Google Scholar 

  39. Wu Y, Zhou YC, Bao L (2014) Discrete wheel-switching chaotic system and applications [J]. IEEE Trans Circuits Syst I-Regul Pap 61(12):3469–3477

    Article  Google Scholar 

  40. Xie YY, Li JC, Kong ZF et al (2016) Exploiting optics Chaos for image encryption-then-transmission [J]. J Lightwave Technol 34(22):5101–5109

    Article  Google Scholar 

  41. Yuan ZS, Li HT, Zhu XH (2015) A digital-analog hybrid random number generator based on memristor [J]. Acta Phys Sin 64(24):240503

    Article  Google Scholar 

  42. Zhou YC, Hua ZY, Pun CM et al (2015) Cascade chaotic system with applications [J]. IEEE Trans Cybern 45(9):2001–2012

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (61862042, 61601215); 2019 Innovation Special Fund of Jiangxi Province (YC2019-S101).

Author information

Authors and Affiliations

  1. School of Software, Nanchang University, Nanchang, 330031, People’s Republic of China

    Hongyue Xiang & Lingfeng Liu

Authors
  1. Hongyue Xiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lingfeng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lingfeng Liu.

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

Xiang, H., Liu, L. A new perturbation-feedback hybrid control method for reducing the dynamic degradation of digital chaotic systems and its application in image encryption. Multimed Tools Appl 80, 19237–19261 (2021). https://doi.org/10.1007/s11042-021-10680-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-021-10680-y

Keywords

Search

Navigation