[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Two-dimensional hyperchaotic effect coupled mapping lattice and its application in dynamic S-box generation

  • Research
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper presents a method for the construction of dynamic S-boxes using the Two-Dimensional Hyperchaotic Effect Coupled Map Lattice (2D-HECML) system. Initially, we design an Enhanced M-Sequence for the selection of coupled objects in 2D-HECML, as well as for linear transformation matrices and coordinate transformations in S-box substitution. Its excellent stochasticity and distributional properties are demonstrated by comparative analysis of the equilibrium and autocorrelation functions. Then, we integrate the novel spherical cavity hyperchaotic mapping into the 2D-HECML system to construct the modular space hyperchaotic effect. The rich nonlinear dynamical behavior and excellent performance of the system are verified by the comparative analysis of dynamical characteristic indices such as correlation coefficient and bifurcation diagrams. Based on the above, we design a dynamic S-box generation algorithm by exploiting the spatiotemporal chaotic property of the system. The test results of various cryptographic performance metrics confirm that the S-boxes generated by this algorithm can effectively resist various types of cryptanalytic attacks, including differential attacks and correlated key 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
£29.99 /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 (United Kingdom)

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Matsui, M.: Linear cryptanalysis method for DES cipher. In: Advances in Cryptology—EUROCRYPT’93: Workshop on the Theory and Application of Cryptographic Techniques Lofthus, Norway, May 23–27, 1993 Proceedings, vol. 12, pp. 386–397. Springer (1994)

  2. Biham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptol. 4, 3–72 (1991)

    MathSciNet  Google Scholar 

  3. Bard, G.: Algebraic Cryptanalysis. Springer, Berlin (2009)

    Google Scholar 

  4. Guo, S., Zhao, X., Zhang, F., Wang, T., Shi, Z.J., Standaert, F.-X., Ma, C.: Exploiting the incomplete diffusion feature: a specialized analytical side-channel attack against the AES and its application to microcontroller implementations. IEEE Trans. Inf. Forensics Secur. 9, 999–1014 (2014)

    Google Scholar 

  5. Ali, A.M.A., Sriram, S., Natiq, H., Ahmadi, A., Rajagopal, K., Jafari, S.: A novel multi-stable sinusoidal chaotic map with spectacular behaviors. Commun. Theor. Phys. 75(11), 115001 (2023)

    MathSciNet  Google Scholar 

  6. Sriram, G., Ali, A.M.A., Natiq, H., Ahmadi, A., Rajagopal, K., Jafari, S.: Dynamics of a novel chaotic map. J. Comput. Appl. Math. 436, 115453 (2024)

    MathSciNet  Google Scholar 

  7. Açikkapi, M.Ş, Özkaynak, F., Özer, A.B.: Side-channel analysis of chaos-based substitution box structures. IEEE Access. 7, 79030–79043 (2019)

    Google Scholar 

  8. Lambić, D.: A novel method of S-box design based on discrete chaotic map. Nonlinear Dyn. 87, 2407–2413 (2017)

    MathSciNet  Google Scholar 

  9. Özkaynak, F., Özer, A.B.: A method for designing strong S-Boxes based on chaotic Lorenz system. Phys. Lett. A 374(36), 3733–3738 (2010)

    Google Scholar 

  10. Çavuşoğlu, Ü., Zengin, A., Pehlivan, I., Kaçar, S.: A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system. Nonlinear Dyn. 87, 1081–1094 (2017)

    Google Scholar 

  11. Özkaynak, F., Yavuz, S.: Designing chaotic S-boxes based on time-delay chaotic system. Nonlinear Dyn. 74, 551–557 (2013)

    MathSciNet  Google Scholar 

  12. Özkaynak, F., Çelik, V., Özer, A.B.: A new S-box construction method based on the fractional-order chaotic Chen system. SIViP 11, 659–664 (2017)

    Google Scholar 

  13. Zheng, J., Bao, T.: An image encryption algorithm using cascade chaotic map and S-box. Entropy 24(12), 1827 (2022)

    Google Scholar 

  14. Yang, S., Tong, X., Wang, Z., Zhang, M.: S-box generation algorithm based on hyperchaotic system and its application in image encryption. Multimed. Tools Appl. 82, 1–25 (2023)

    Google Scholar 

  15. Ning, H., Zhao, G., Li, Z., Gao, S., Ma, Y., Dong, Y.: A novel method for constructing dynamic S-boxes based on a high-performance spatiotemporal chaotic system. Nonlinear Dyn. 112(2), 1487–1509 (2024)

    Google Scholar 

  16. Zhao, M., Yuan, Z., Li, L., Chen, X.B.: A novel efficient S-box design algorithm based on a new chaotic map and permutation. Multimed. Tools Appl. (2024). https://doi.org/10.1007/s11042-023-17720-9

    Article  Google Scholar 

  17. Waheed, A., Subhan, F.: S-box design based on logistic skewed chaotic map and modified Rabin–Karp algorithm: applications to multimedia security. Phys. Scr. 99(5), 055236 (2024)

    Google Scholar 

  18. Wu, W., Kong, L.: Image encryption algorithm based on a new 2D polynomial chaotic map and dynamic S-box. SIViP 18, 3213–3228 (2024)

    Google Scholar 

  19. Hua, Z., Li, J., Chen, Y., Yi, S.: Design and application of an S-box using complete Latin square. Nonlinear Dyn. 104, 807–825 (2021)

    Google Scholar 

  20. Zhou, S., Qiu, Y., Wang, X., Zhang, Y.: el image cryptosystem based on new 2D hyperchaotic map and dynamical chaotic S-box. Nonlinear Dyn. 111, 9571–9589 (2023)

    Google Scholar 

  21. Zheng, J., Zeng, Q.: An image encryption algorithm using a dynamic S-box and chaotic maps. Applied Intelligence. 52(13), 15703–15717 (2022)

    Google Scholar 

  22. Wang, M., Liu, H., Zhao, M.: Construction of a non-degeneracy 3D chaotic map and application to image encryption with keyed S-box. Multimed. Tools Appl. 82(22), 34541–34563 (2023)

    Google Scholar 

  23. Ding, C., Xue, R.: Signal-sensing dynamic S-box image encryption with 2D Griewank–sin map. Nonlinear Dyn. 111(24), 22595–22620 (2023)

    Google Scholar 

  24. Malik, A.W., Zahid, A.H., Bhatti, D.S., Kim, H.J., Kim, K.I.: Designing S-box using tent-sine chaotic system while combining the traits of tent and sine map. IEEE Access. 11, 79265–79274 (2023)

    Google Scholar 

  25. Jiang, Z., Ding, Q.: Construction of an S-box based on chaotic and bent functions. Symmetry. 13, 671 (2021)

    Google Scholar 

  26. Chen, G., Chen, Y., Liao, X.: An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps. Chaos Solitons Fractals 31, 571–579 (2007)

    MathSciNet  Google Scholar 

  27. Tang, G., Liao, X., Chen, Y.: A novel method for designing S-boxes based on chaotic maps. Chaos Solitons Fractals 23, 413–419 (2005)

    Google Scholar 

  28. Aslam, M., Beg, S., Anjum, A., Qadir, Z., Khan, S., Malik, S.U.R., et al.: A strong construction of S-box using Mandelbrot set an image encryption scheme. PeerJ Comput. Sci. 8, e892 (2022)

    Google Scholar 

  29. Çavuşoğlu, Ü., Kaçar, S., Pehlivan, I., Zengin, A.: Secure image encryption algorithm design using a novel chaos based S-Box. Chaos Solitons Fractals 95, 92–101 (2017)

    Google Scholar 

  30. Zhang, Y.Q., He, Y., Wang, X.Y.: Spatiotemporal chaos in mixed linear–nonlinear two-dimensional coupled logistic map lattice. Physica A 490, 148–160 (2018)

    MathSciNet  Google Scholar 

  31. Kaneko, K.: Spatiotemporal intermittency in coupled map lattices. Prog. Theor. Phys. 74(5), 1033–1044 (1985)

    MathSciNet  Google Scholar 

  32. Azam, N.A., Murtaza, G., Hayat, U.: A novel image encryption scheme based on elliptic curves and coupled map lattices. Optik 274, 170517 (2023)

    Google Scholar 

  33. Dong, Y., Zhao, G., Ma, Y., Pan, Z., Wu, R.: A novel image encryption scheme based on pseudo-random coupled map lattices with hybrid elementary cellular automata. Inf. Sci. 593, 121–154 (2022)

    Google Scholar 

  34. Lv, Z., Sun, F., Cai, C.: A new spatiotemporal chaotic system based on two-dimensional discrete system. Nonlinear Dyn. 109(4), 3133–3144 (2022)

    Google Scholar 

  35. Lai, Q., Yang, L., Liu, Y.: Design and realization of discrete memristive hyperchaotic map with application in image encryption. Chaos Solitons Fractals 165, 112781 (2022)

    Google Scholar 

  36. Lai, Q., Yang, L., Chen, G.: Design and performance analysis of discrete memristive hyperchaotic systems with stuffed cube attractors and ultraboosting behaviors. IEEE Trans. Ind. Electron. 71(7), 7819–7828 (2023)

    Google Scholar 

  37. Wu, Z., Zhang, Y., Bao, H., Lan, R., Hua, Z.: nD-CS: A circularly shifting chaotic map generation method. Chaos Solitons Fractals 181, 114650 (2024)

    Google Scholar 

  38. Dong, Y., Zhao, G.: A spatiotemporal chaotic system based on pseudo-random coupled map lattices and elementary cellular automata. Chaos Solitons Fractals 151, 111217 (2021)

    MathSciNet  Google Scholar 

  39. Zhou, P., Du, J., Zhou, K., Wei, S.: 2D mixed pseudo-random coupling PS map lattice and its application in S-box generation. Nonlinear Dyn. 103, 1151–1166 (2021)

    Google Scholar 

  40. Liu, Z., Wang, Y., Zhao, Y., Zhang, L.Y.: A stream cipher algorithm based on 2D coupled map lattice and partitioned cellular automata. Nonlinear Dyn. 101, 1383–1396 (2020)

    Google Scholar 

  41. Ning, H., Zhao, G., Dong, Y., Ma, Y.: A novel two-dimensional dynamic pseudo-random coupled map lattices system based on partitioned elementary cellular automata. Appl. Sci. 12(23), 12399 (2022)

    Google Scholar 

  42. Kaneko, K.: Spatiotemporal chaos in one-and two-dimensional coupled map lattices. Physica D 37(1–3), 60–82 (1989)

    MathSciNet  Google Scholar 

  43. Wang, X., Zhao, M., Feng, S., Chen, X.: An image encryption scheme using bit-plane cross-diffusion and spatiotemporal chaos system with nonlinear perturbation. Soft. Comput. 27(3), 1223–1240 (2023)

    Google Scholar 

  44. Zhang, G., Zheng, L., Su, Z., Zeng, Y., Wang, G.: M-sequences and sliding window based audio watermarking robust against large-scale cropping attacks. IEEE Trans. Inf. Forensics Secur. 18, 1182–1195 (2023)

    Google Scholar 

  45. Martínez-Cagigal, V., Santamaría-Vázquez, E., Pérez-Velasco, S., Marcos-Martínez, D., Moreno-Calderón, S., Hornero, R.: Non-binary m-sequences for more comfortable brain–computer interfaces based on c-VEPs. Expert Syst. Appl. 232, 120815 (2023)

    Google Scholar 

  46. Zhang, Y.Q., He, Y., Li, P., Wang, X.Y.: A new color image encryption scheme based on 2DNLCML system and genetic operations. Opt. Lasers Eng. 128, 106040 (2020)

    Google Scholar 

  47. Kantz, H.: A robust method to estimate the maximal Lyapunov exponent of a time series. Phys. Lett. A 185(1), 77–87 (1994)

    MathSciNet  Google Scholar 

  48. Li, S., Liu, Y., Ren, F., Yang, Z.: Design of a high throughput pseudorandom number generator based on discrete hyper-chaotic system. IEEE Trans. Circuits Syst. II Express Briefs 70(2), 806–810 (2022)

    Google Scholar 

  49. Shao, S., Li, J., Shao, P., Xu, G.: Chaotic image encryption using piecewise-logistic-sine map. IEEE Access. 11, 27477–27488 (2023)

    Google Scholar 

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

    MathSciNet  Google Scholar 

  51. Wang, X., Yang, J., Guan, N.: High-sensitivity image encryption algorithm with random cross diffusion based on dynamically random coupled map lattice model. Chaos Solitons Fractals 143, 110582 (2021)

    MathSciNet  Google Scholar 

  52. Zhang, Y.Q., Wang, X.Y.: Spatiotemporal chaos in Arnold coupled logistic map lattice. Nonlinear Anal. Model. Control. 18(4), 526–541 (2013)

    MathSciNet  Google Scholar 

  53. Ratner, B.: The correlation coefficient: its values range between? 1/- 1, or do they? J. Target. Meas. Anal. Mark. 17, 139–142 (2009)

    Google Scholar 

  54. Bassham III, L.E., Rukhin, A.L., Soto, J., Nechvatal, J.R., Smid, M.E., Barker, E.B., Leigh, S.D., Levenson, M., Vangel, M., Banks, D.L., et al.: Sp 800–22 rev. 1a. A statistical test suite for random and pseudorandom number generators for cryptographic applications V-1, pp. 2–40 (2010)

  55. Su, Y., Tong, X., Zhang, M., Wang, Z.: Efficient image encryption algorithm based on dynamic high-performance S-box and hyperchaotic system. Phys. Scr. 98(6), 065215 (2023)

    Google Scholar 

Download references

Funding

This research is supported by “the Fundamental Research Funds for the Central Universities”(Grant Number: 328202258), “the Fundamental Research Funds for the Central Universities”(Grant Number: 3282023054).

Author information

Authors and Affiliations

  1. Beijing Electronic Science and Technology Institute, Beijing, 100070, China

    Yingjie Ma, Yan Tian, Lei Zhang & Peiliang Zuo

Authors
  1. Yingjie Ma
    View author publications

    Search author on:PubMed Google Scholar

  2. Yan Tian
    View author publications

    Search author on:PubMed Google Scholar

  3. Lei Zhang
    View author publications

    Search author on:PubMed Google Scholar

  4. Peiliang Zuo
    View author publications

    Search author on:PubMed Google Scholar

Contributions

YM Conceptualization, Methodology, Writing—Original Draft, Writing—Review and Editing, Software, Formal Analysis, Investigation, Visualization, YT Conceptualization, Methodology, Writing—Original Draft, Writing—Review and Editing, Software, Formal Analysis. LZ Data Curation, Project Administration, Supervision, Writing—Review and Editing, Software. PZ Conceptualization, Visualization, Data Curation, Writing—Review and Editing.

Corresponding author

Correspondence to Yan Tian.

Ethics declarations

Competing interests

The authors declare no competing interests.

Conflict of interest

The authors declare that they have no conflict of interest.

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) 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

Ma, Y., Tian, Y., Zhang, L. et al. Two-dimensional hyperchaotic effect coupled mapping lattice and its application in dynamic S-box generation. Nonlinear Dyn 112, 17445–17476 (2024). https://doi.org/10.1007/s11071-024-09907-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-024-09907-y

Keywords