Log in

Discrete memristive neuron model and its interspike interval-encoded application in image encryption

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

Bursting is a diverse and common phenomenon in neuronal activation patterns and it indicates that fast action voltage spiking periods are followed by resting periods. The interspike interval (ISI) is the time between successive action voltage spikes of neuron and it is a key indicator used to characterize the bursting. Recently, a three-dimensional memristive Hindmarsh-Rose (mHR) neuron model was constructed to generate hidden chaotic bursting. However, the properties of the discrete mHR neuron model have not been investigated, yet. In this article, we first construct a discrete mHR neuron model and then acquire different hidden chaotic bursting sequences under four typical sets of parameters. To make these sequences more suitable for the application, we further encode these hidden chaotic sequences using their ISIs and the performance comparative results show that the ISI-encoded chaotic sequences have much more complex chaos properties than the original sequences. In addition, we apply these ISI-encoded chaotic sequences to the application of image encryption. The image encryption scheme has a symmetric key structure and contains plain-text permutation and bidirectional diffusion processes. Experimental results and security analyses prove that it has excellent robustness against various possible attacks.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /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 includes VAT (Germany)

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Chen M, Mao S, Liu Y. Big data: A survey. Mobile Netw Appl, 2014, 19: 171–209

    Article  Google Scholar 

  2. Yang C, Huang Q, Li Z, et al. Big data and cloud computing: Innovation opportunities and challenges. Int J Digit Earth, 2017, 10: 13–53

    Article  Google Scholar 

  3. Yu S D, Liu L L, Wang Z Y, et al. Transferring deep neural networks for the differentiation of mammographic breast lesions. Sci China Tech Sci, 2019, 62: 441–447

    Article  Google Scholar 

  4. Su L, Wang L Y, Li K, et al. Automated X-ray recognition of solder bump defects based on ensemble-ELM. Sci China Tech Sci, 2019, 62: 1512–1519

    Article  Google Scholar 

  5. Tawalbeh L, Muheidat F, Tawalbeh M, et al. IoT privacy and security: Challenges and solutions. Appl Sci, 2020, 10: 4102

    Article  Google Scholar 

  6. Baptista M S. Cryptography with chaos. Phys Lett A, 1998, 240: 50–54

    Article  MathSciNet  MATH  Google Scholar 

  7. Kocarev L. Chaos-based cryptography: A brief overview. IEEE Circ Syst Mag, 2001, 1: 6–21

    Article  Google Scholar 

  8. Fadhel S, Shafry M, Farook O. Chaos image encryption methods: A survey study. Bull EEI, 2017, 6: 99–104

    Article  Google Scholar 

  9. Hua Z, Zhu Z, Chen Y, et al. Color image encryption using orthogonal Latin squares and a new 2D chaotic system. Nonlinear Dyn, 2021, 104: 4505–4522

    Article  Google Scholar 

  10. Bao B C, Zhu Y X, Ma J, et al. Memristive neuron model with an adapting synapse and its hardware experiments. Sci China Tech Sci, 2021, 64: 1107–1117

    Article  Google Scholar 

  11. Rajamani V, Kim H, Chua L. Morris-Lecar model of third-order barnacle muscle fiber is made of volatile memristors. Sci China Inf Sci, 2018, 61: 060426

    Article  MathSciNet  Google Scholar 

  12. Chen M, Qi J W, Wu H G, et al. Bifurcation analyses and hardware experiments for bursting dynamics in non-autonomous memristive FitzHugh-Nagumo circuit. Sci China Tech Sci, 2020, 63: 1035–1044

    Article  Google Scholar 

  13. Lu L L, Jia Y, Xu Y, et al. Energy dependence on modes of electric activities of neuron driven by different external mixed signals under electromagnetic induction. Sci China Tech Sci, 2019, 62: 427–440

    Article  Google Scholar 

  14. Du L, Cao Z L, Lei Y M, et al. Electrical activities of neural systems exposed to sinusoidal induced electric field with random phase. Sci China Tech Sci, 2019, 62: 1141–1150

    Article  Google Scholar 

  15. Lv M, Ma J, Yao Y G, et al. Synchronization and wave propagation in neuronal network under field coupling. Sci China Tech Sci, 2019, 62: 448–457

    Article  Google Scholar 

  16. Aihara K, Takabe T, Toyoda M. Chaotic neural networks. Phys Lett A, 1990, 144: 333–340

    Article  MathSciNet  Google Scholar 

  17. Hodgkin A L, Huxley A F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol, 1952, 117: 500–544

    Article  Google Scholar 

  18. Bao H, Liu W, Chen M. Hidden extreme multistability and dimensionality reduction analysis for an improved non-autonomous memristive FitzHugh-Nagumo circuit. Nonlinear Dyn, 2019, 96: 1879–1894

    Article  MATH  Google Scholar 

  19. Xu Q, Tan X, Zhu D, et al. Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit. Chaos Soliton Fract, 2020, 141: 110353

    Article  MathSciNet  Google Scholar 

  20. Bao H, Zhu D, Liu W, et al. Memristor synapse-based Morris-Lecar model: Bifurcation analyses and FPGA-based validations for periodic and chaotic bursting/spiking firings. Int J Bifurcat Chaos, 2020, 30: 2050045

    Article  MathSciNet  MATH  Google Scholar 

  21. Lin H, Wang C, Sun Y, et al. Firing multistability in a locally active memristive neuron model. Nonlinear Dyn, 2020, 100: 3667–3683

    Article  Google Scholar 

  22. Hindmarsh J L, Rose R M. A model of the nerve impulse using two first-order differential equations. Nature, 1982, 296: 162–164

    Article  Google Scholar 

  23. Rose R M, Hindmarsh J L. The assembly of ionic currents in a thalamic neuron I. The three-dimensional model. Proc Royal Soc Lond B, 1989, 237: 267–288

    Article  Google Scholar 

  24. Tlelo-Cuautle E, Díaz-Muñoz J D, González-Zapata A M, et al. Chaotic image encryption using hopfield and Hindmarsh-Rose neurons implemented on FPGA. Sensors, 2020, 20: 1326

    Article  Google Scholar 

  25. Yang Y, Wang L, Duan S, et al. Dynamical analysis and image encryption application of a novel memristive hyperchaotic system. Optics Laser Tech, 2021, 133: 106553

    Article  Google Scholar 

  26. Hu G, Li B. Coupling chaotic system based on unit transform and its applications in image encryption. Signal Process, 2021, 178: 107790

    Article  Google Scholar 

  27. Khan M, Masood F. A novel chaotic image encryption technique based on multiple discrete dynamical maps. Multimed Tools Appl, 2019, 78: 26203–26222

    Article  Google Scholar 

  28. Wang S C, Wang C H, Xu C. An image encryption algorithm based on a hidden attractor chaos system and the Knuth-Durstenfeld algorithm. Optics Lasers Eng, 2020, 128: 105995

    Article  Google Scholar 

  29. Hua Z Y, Zhou B H, Zhang Y X, et al. Modular chaotification model with FPGA implementation. Sci China Tech Sci, 2021, doi: https://doi.org/10.1007/s11431-020-1717-1

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

    Article  Google Scholar 

  31. Wang X, Guan N, Zhao H, et al. A new image encryption scheme based on coupling map lattices with mixed multi-chaos. Sci Rep, 2020, 10: 9784

    Article  Google Scholar 

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

    Article  Google Scholar 

  33. Li H, Hua Z, Bao H, et al. Two-dimensional memristive hyperchaotic maps and application in secure communication. IEEE Trans Ind Electron, 2021, doi: https://doi.org/10.1109/TIE.2020.3022539

  34. Bao H, Hu A, Liu W, et al. Hidden bursting firings and bifurcation mechanisms in memristive neuron model with threshold electromagnetic induction. IEEE Trans Neural Netw Learn Syst, 2020, 31: 502–511

    Article  Google Scholar 

  35. Yang Y, Liao X. Filippov Hindmarsh-Rose neuronal model with threshold policy control. IEEE Trans Neural Netw Learn Syst, 2019, 30: 306–311

    Article  Google Scholar 

  36. Bao B, Hu A, Bao H, et al. Three-dimensional memristive Hindmarsh-Rose neuron model with hidden coexisting asymmetric behaviors. Complexity, 2018, 2018: 1–11

    Google Scholar 

  37. Djeundam S R D, Yamapi R, Kofane T C, et al. Deterministic and stochastic bifurcations in the Hindmarsh-Rose neuronal model. Chaos, 2013, 23: 033125

    Article  MathSciNet  MATH  Google Scholar 

  38. Lakshmanan S, Lim C P, Nahavandi S, et al. Dynamical analysis of the Hindmarsh-Rose neuron with time delays. IEEE Trans Neural Netw Learn Syst, 2017, 28: 1953–1958

    Article  MathSciNet  Google Scholar 

  39. Li B, He Z. Bifurcations and chaos in a two-dimensional discrete Hindmarsh-Rose model. Nonlinear Dyn, 2014, 76: 697–715

    Article  MathSciNet  MATH  Google Scholar 

  40. Jafari S, Sprott J C, Golpayegani S M R H. Elementary quadratic chaotic flows with no equilibria. Phys Lett A, 2013, 377: 699–702

    Article  MathSciNet  MATH  Google Scholar 

  41. Gu H, Pan B, Chen G, et al. Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models. Nonlinear Dyn, 2014, 78: 391–407

    Article  MathSciNet  Google Scholar 

  42. Bao H, Chen M, Wu H G, et al. Memristor initial-boosted coexisting plane bifurcations and its extreme multi-stability reconstitution in two-memristor-based dynamical system. Sci China Tech Sci, 2020, 63: 603–613

    Article  Google Scholar 

  43. Bandt C, Pompe B. Permutation entropy: A natural complexity measure for time series. Phys Rev Lett, 2002, 88: 174102

    Article  Google Scholar 

  44. Richman J S, Moorman J R. Physiological time-series analysis using approximate entropy and sample entropy. Am J Physiol Heart Circ Physiol, 2000, 278: 2039–2049

    Article  Google Scholar 

  45. Lorenz E N. Deterministic nonperiodic flow. J Atmos Sci, 1963, 20: 130–141

    Article  MathSciNet  MATH  Google Scholar 

  46. Chen G, Ueta T. Yet another chaotic attractor. Int J Bifurcat Chaos, 1999, 09: 1465–1466

    Article  MathSciNet  MATH  Google Scholar 

  47. Xu C, Sun J, Wang C. A novel image encryption algorithm based on bit-plane matrix rotation and hyper chaotic systems. Multimed Tools Appl, 2020, 79: 5573–5593

    Article  Google Scholar 

  48. Wang B, Zhang B F, Liu X W. An image encryption approach on the basis of a time delay chaotic system. Optik, 2021, 225: 165737

    Article  Google Scholar 

  49. Hua Z, Zhu Z, Yi S, et al. Cross-plane colour image encryption using a two-dimensional logistic tent modular map. Inf Sci, 2021, 546: 1063–1083

    Article  MathSciNet  Google Scholar 

  50. Ye G, Huang X. Spatial image encryption algorithm based on chaotic map and pixel frequency. Sci China Inf Sci, 2018, 61: 058104

    Article  MathSciNet  Google Scholar 

  51. Pak C, Huang L. A new color image encryption using combination of the 1D chaotic map. Signal Process, 2017, 138: 129–137

    Article  Google Scholar 

  52. Preishuber M, Hutter T, Katzenbeisser S, et al. Depreciating motivation and empirical security analysis of chaos-based image and video encryption. IEEE Trans Inform Forensic Secur, 2018, 13: 2137–2150

    Article  Google Scholar 

  53. Gan Z, Chai X, Han D, et al. A chaotic image encryption algorithm based on 3-D bit-plane permutation. Neural Comput Applic, 2019, 31: 7111–7130

    Article  Google Scholar 

  54. Alvarez G, Li S. Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurcat Chaos, 2006, 16: 2129–2151

    Article  MathSciNet  MATH  Google Scholar 

  55. Luo Y, Du M, Liu J. A symmetrical image encryption scheme in wavelet and time domain. Commun Nonlinear Sci Numer Simul, 2015, 20: 447–460

    Article  Google Scholar 

  56. Wang N, Li C, Bao H, et al. Generating multi-scroll Chua’s attractors via simplified piecewise-linear Chua’s diode. IEEE Trans Circ Syst I, 2019, 66: 4767–4779

    Google Scholar 

  57. Wu Y, Noonan J P, Agaian S. NPCR and UACI randomness tests for image encryption. Cyber J Multidiscip J Sci Tech, 2011, 1: 31–38

    Google Scholar 

  58. Yuan J, Wu Y, Lu X, et al. Recent advances in deep learning based sentiment analysis. Sci China Tech Sci, 2020, 63: 1947–1970

    Article  Google Scholar 

  59. ** H, Cao Y, Wang T, et al. Recent advances of neural text generation: Core tasks, datasets, models and challenges. Sci China Tech Sci, 2020, 63: 1990–2010

    Article  Google Scholar 

  60. Zhang J, Zong C. Neural machine translation: Challenges, progress and future. Sci China Tech Sci, 2020, 63: 2028–2050

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Han Bao.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51777016, 51607013 and 62071142).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bao, H., Hua, Z., Liu, W. et al. Discrete memristive neuron model and its interspike interval-encoded application in image encryption. Sci. China Technol. Sci. 64, 2281–2291 (2021). https://doi.org/10.1007/s11431-021-1845-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-021-1845-x

Keywords

Navigation