Skip to main content

Advertisement

Springer Nature Link
Log in

Dynamical analysis of four-dimensional chaotic system and its application in image encryption

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

Abstract

In this paper, a phase diagram of a four-dimensional chaotic system is established by introducing cosine function into Lorenz system. Then 0-1 test, complexity, and offset boosting, National Institute of Standards and Technology (NIST) test is conducted on the pseudo-random sequence generated by the system. Result shows that the system is suitable for image encryption. Combining with the proposed system, an image encryption algorithm based on hash and deoxyribonucleic acid (DNA) is designed. In this algorithm, through the plaintext hash value generated by the system initial values and the number of iterations to generate chaos sequence. By reordering the sequence of indexes to scrambling plaintext. In the diffusion module, we use XOR and cyclic left shift to get the final ciphertext. After simulation and security analysis, the algorithm has good encryption efficiency and security. It can resist most common attacks.

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
Algorithm 1
Algorithm 2
Algorithm 3
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Data Availability

The datasets analyzed during the current study are available from the corresponding author on reasonable resquest.

References

  1. Alawida M, Teh JS, et al. (2019) An image encryption scheme based on hybridizing digital chaos and finite state machine. Signal Process 164:249–266

    Article  Google Scholar 

  2. Babu NR, Kalpana M, et al. (2021) A novel audio encryption approach via finite-time synchronization of fractional order hyperchaotic system. Multimed Tools Appl 80:18043–18067

    Article  Google Scholar 

  3. Bao H, Hua Z, et al. (2021) Initials-boosted coexisting chaos in a 2-D sine map and its hardware implementation. IEEE Trans Industr Inform 17:1132–1140

    Article  Google Scholar 

  4. BenFarah MA, Farah A, et al. (2020) An image encryption scheme based on a new hybrid chaotic map and optimized substitution box. Nonlinear Dyn 99:3041–3064

    Article  Google Scholar 

  5. Chai X (2017) An image encryption algorithm based on bit level Brownian motion and new chaotic systems. Multimed Tools Appl 76:1159–1175

    Article  Google Scholar 

  6. Chen M, Ren X, et al. (2019) Periodically varied initial offset boosting behaviors in a memristive system with cosine memductance. Front Inform Technol Electron Eng 20:1706–1716

    Article  Google Scholar 

  7. Dong W, Li Q et al (2021) A robust and multi chaotic DNA image encryption with pixel-value pseudorandom substitution scheme. Opt Commun 499:127211

    Article  Google Scholar 

  8. Feudjio ER, Tamba VK et al Dynamic analysis of a hyperchaotic hyperjerk circuit, FPGA implementation and its application in RNG for medical images encryption. Transactions of the Indian National Academy of Engineering. https://doi.org/10.1007/s41403-022-00326-2

  9. Gong L, Qiu K, et al. (2019) An image compression and encryption algorithm based on chaotic system and compressive sensing. Opt Laser Technol 115:257–267

    Article  Google Scholar 

  10. Gong L, Qiu K, et al. (2019) An optical image compression and encryption scheme based on compressive sensing and RSA algorithm. Opt Lasers Eng 121:169–180

    Article  Google Scholar 

  11. Himeur Y, Boukabou A (2018) A robust encryption, secure key-frames based video watermarking system using chaotic. Multimed Tools Appl 77:8603–8627

    Article  Google Scholar 

  12. Hua ZY, Zhou YC (2016) Image encryption using 2D logistic-adjusted-sine map. Inform Sci 339:237–253

    Article  Google Scholar 

  13. Huang H, Yang S, et al. (2020) Efficient symmetric image encryption by using a novel 2D chaotic system. IET Image Process 14:1157–1163

    Article  Google Scholar 

  14. Li H, Wang Y, Zuo Z (2019) Chaos-based image encryption algorithm with orbit perturbation and dynamic state variable selection mechanisms. Opt Lasers Eng 115:197–207

    Article  Google Scholar 

  15. Liao X, Li K, et al. (2020) Robust detection of image operator chain with two-stream convolutional neural network. IEEE J Selected Topics Signal Process 14:955–968

    Article  Google Scholar 

  16. Liao X, Yin J, et al. (2022) Adaptive payload distribution in multiple images steganography based on image texture features. IEEE Trans Depend Ana Secur Comput 19:897–911

    Google Scholar 

  17. Liao X, Yu Y, et al. (2020) A new payload partition strategy in color image steganography. IEEE Trans Circ Syst Vid Technol 30:685–696

    Article  Google Scholar 

  18. Liu Y, Tang J, Xie T (2014) Cryptanalyzing a RGB image encryption algorithm based on DNA encoding and chaos map. Opt Laser Technol 60:111–115

    Article  Google Scholar 

  19. Mansouria A, Wang X (2021) A novel one-dimensional chaotic map generator and its application in a new index representation-based image encryption scheme. Inform Sci 563:91–110

    Article  MathSciNet  Google Scholar 

  20. Moon S, Baik J et al (2021) Chaos synchronization in generalized Lorenz systems and an application to image encryption. Commun Nonlinear Sci Numer Simulat 96:105708

    Article  MathSciNet  MATH  Google Scholar 

  21. Muthukumar P, Babu NR, et al. (2021) Detecting critical point of fractional-order chemical system with synchronization and application to image enhancement technique. Proceedings of the National Academy of Sciences India Section A: Physical Sciences 91:661–674

    Article  MathSciNet  MATH  Google Scholar 

  22. Nezhad SYD, Safdarian N et al (2020) New method for fingerprint images encryption using DNA sequence and chaotic tent map. Optik - International Journal for Light and Electron Optics 224:165661

    Article  Google Scholar 

  23. Roohi M, Zhang C, et al. (2020) Adaptive model free synchronization of different fractional order neural networks with an application in cryptography. Nonlinear Dyn 100:3979–4001

    Article  Google Scholar 

  24. Sahasrabuddhe A, Laiphrakpam DS (2021) Multiple images encryption based on 3D scrambling and hyper-chaotic system. Inform Sci 550:252–267

    Article  MathSciNet  MATH  Google Scholar 

  25. Shakiba A (2019) A novel randomized one-dimensional chaotic Chebyshev mapping for chosen plaintext attack secure image encryption with a novel chaotic breadth first traversal. Multimed Tools Appl 78:34773–34799

    Article  Google Scholar 

  26. Shannon CE (1948) A mathematical theory of communication. Bell System Tech J 27:379–423

    Article  MathSciNet  MATH  Google Scholar 

  27. Talhaouia MZ, Wang X (2021) A new fractional one dimensional chaotic map and its application in high-speed image encryption. Inform Sci 550:13–26

    Article  MathSciNet  Google Scholar 

  28. Wang X, Chen S et al (2021) A chaotic image encryption algorithm based on random dynamic mixing. Opt Laser Technol 138:106837

    Article  Google Scholar 

  29. Wang M, Deng Y, et al. (2019) Dynamics and circuit implementation of a four-wing memristive chaotic system with attractor rotation. Int J Non-Linear Mech 111:149–159

    Article  Google Scholar 

  30. Wang X, Feng L, et al. (2019) A fast image encryption algorithm based on non-adjacent dynamically coupled map lattice model. Nonlinear Dyn 95:2797–2824

    Article  MATH  Google Scholar 

  31. Wang X, Gao S (2020) Image encryption algorithm for synchronously updating Boolean networks based on matrix semi-tensor product theory. Inform Sci 507:16–36

    Article  MathSciNet  MATH  Google Scholar 

  32. Wang X, Wang Y et al (2020) A novel chaotic algorithm for image encryption utilizing one-time pad based on pixel level and DNA level. Opt Lasers Eng 125:105851

    Article  Google Scholar 

  33. Xian Y, Wang X (2021) Fractal sorting matrix and its application on chaotic image encryption. Inform Sci 547:1154–1169

    Article  MathSciNet  MATH  Google Scholar 

  34. Xin B, Peng W et al (2020) A discrete fractional-order Cournot duopoly game. Physica A 558:124993

    Article  MathSciNet  MATH  Google Scholar 

  35. Yan S, Wang E et al (2021) Analysis, circuit implementation and synchronization control of a hyperchaotic system. Phys Scr 96:125257

    Article  Google Scholar 

  36. Yang Y, Wanga L et al (2021) Dynamical analysis and image encryption application of a novel memristive hyperchaotic system. Opt Laser Technol 133:106553

    Article  Google Scholar 

  37. Ye X, Wang X, et al. (2020) A new chaotic circuit with multiple memristors and its application in image encryption. Nonlinear Dyn 99:1489–1506

    Article  Google Scholar 

  38. Ye X, Wang X et al (2020) A new random diffusion algorithm based on the multi-scroll Chua’s chaotic circuit system. Opt Lasers Eng 127:105905

    Article  Google Scholar 

  39. Yildirim M (2021) Optical color image encryption scheme with a novel DNA encoding algorithm based on a chaotic circuit. Chaos, Solitons Fractals. https://doi.org/10.1016/j.chaos.2021.111631

  40. Zhang Y (2018) The unified image encryption algorithm based on chaos and cubic S-Box. Inform Sci 450:361–377

    Article  MathSciNet  MATH  Google Scholar 

  41. Zhang S, Zheng J et al (2021) A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability. Chaos Solitons Fractals 145:110761

    Article  MathSciNet  MATH  Google Scholar 

  42. Zhou L, Tan F (2019) A chaotic secure communication scheme based on synchronization of double-layered and multiple complex networks. Nonlinear Dyn 96:869–883

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This research is supported by the Natural Science Foundation of Gansu Province(No.20JR5RA531).

Author information

Author notes

    Authors and Affiliations

    1. College of Physics and Electronic Engineering, Northwest Normal University, 967 Anning East Road, Lanzhou, 730070, Gansu, China

      Shaohui Yan, Binxian Gu, Yu Ren, Xi Sun & Ertong Wang

    2. Gansu Intelligent Information Technology and Application Engineering Research Center, Lanzhou, 730070, Gansu, China

      Shaohui Yan

    Authors
    1. Shaohui Yan
      View author publications

      You can also search for this author inPubMed Google Scholar

    2. Binxian Gu
      View author publications

      You can also search for this author inPubMed Google Scholar

    3. Yu Ren
      View author publications

      You can also search for this author inPubMed Google Scholar

    4. Xi Sun
      View author publications

      You can also search for this author inPubMed Google Scholar

    5. Ertong Wang
      View author publications

      You can also search for this author inPubMed Google Scholar

    Corresponding author

    Correspondence to Shaohui Yan.

    Ethics declarations

    Conflict of Interests

    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.

    Binxian Gu, Yu Ren, Xi Sun and Ertong Wang contributed equally to this work.

    Rights and permissions

    Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

    Reprints and permissions

    About this article

    Check for updates. Verify currency and authenticity via CrossMark

    Cite this article

    Yan, S., Gu, B., Ren, Y. et al. Dynamical analysis of four-dimensional chaotic system and its application in image encryption. Multimed Tools Appl 82, 21509–21534 (2023). https://doi.org/10.1007/s11042-022-14026-0

    Download citation

    • Received:

    • Revised:

    • Accepted:

    • Published:

    • Issue Date:

    • DOI: https://doi.org/10.1007/s11042-022-14026-0

    Keywords