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2D hyperchaotic Styblinski-Tang map for image encryption and its hardware implementation

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Abstract

A novel 2D chaotic system is presented, which is inspired by Styblinski Tang (ST) function employed as optimization test function. It is a challenge function because of having many local optima. The performance of the chaotic system namely 2D Styblinski Tang (2D-ST) map is corroborated through an extensive comparison with the literature in terms of the sensitive chaos metrics as well as its randomness is verified over TestU0. The 2D-ST map manifests the best hyperchaotic behavior due to higher ergodicity and complexity characteristics. Moreover, the 2D-ST map is implemented to a microcontroller hardware, and it is seen that the results manifests that the proposed 2D-ST can be a potential practical candidate thanks to excellent hyperchaotic performance.

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References

  1. Erkan U, Toktas A, Enginoğlu S et al (2022) An image encryption scheme based on chaotic logarithmic map and key generation using deep CNN. Multimed Tools Appl 81:7365–7391. https://doi.org/10.1007/s11042-021-11803-1

    Article  Google Scholar 

  2. Vaidyanathan S, Volos C (2016) Advances and applications in chaotic systems. Springer, Cham. https://doi.org/10.1007/978-3-319-30279-9

  3. Zhao M, Liu H, Niu Y (2023) Batch generating keyed strong S-Boxes with high nonlinearity using 2D hyper chaotic map. Integration 92:91–98. https://doi.org/10.1016/j.vlsi.2023.05.006

    Article  Google Scholar 

  4. Si Y, Liu H, Zhao M (2023) Constructing keyed strong S-Box with higher nonlinearity based on 2D hyper chaotic map and algebraic operation. Integration 88:269–277. https://doi.org/10.1016/j.vlsi.2022.10.011

    Article  Google Scholar 

  5. Liu H, Wang X, Zhao M, Niu Y (2022) Constructing strong S-Box by 2D chaotic map with application to irreversible parallel key expansion. Int J Bifurc Chaos 32:2250163. https://doi.org/10.1142/S0218127422501632

    Article  MathSciNet  Google Scholar 

  6. Liu H, Liu J, Ma C (2023) Constructing dynamic strong S-Box using 3D chaotic map and application to image encryption. Multimed Tools Appl 82:23899–23914. https://doi.org/10.1007/s11042-022-12069-x

    Article  Google Scholar 

  7. Zhao M, Liu H (2023) A Nondegenerate n-Dimensional hyperchaotic map model with application in a keyed parallel hash function. Int J Bifurc Chaos 33:2350070. https://doi.org/10.1142/S0218127423500700

    Article  MathSciNet  Google Scholar 

  8. Wang L, Jiang S, Ge M-F et al (2021) Finite-/fixed-time synchronization of memristor chaotic systems and image encryption application. IEEE Trans Circuits Syst I Regul Pap 68:4957–4969. https://doi.org/10.1109/TCSI.2021.3121555

    Article  Google Scholar 

  9. Wang X, Gao S (2021) A chaotic image encryption algorithm based on a counting system and the semi-tensor product. Multimed Tools Appl 80:10301–10322. https://doi.org/10.1007/s11042-020-10101-6

    Article  Google Scholar 

  10. Chan JCL, Lee TH, Tan CP (2022) Secure communication through a chaotic system and a sliding-mode observer. IEEE Trans Syst Man Cybern Syst 52:1869–1881. https://doi.org/10.1109/TSMC.2020.3034746

    Article  Google Scholar 

  11. Zhang Y, Hua Z, Bao H et al (2022) An n-Dimensional chaotic system generation method using parametric pascal matrix. IEEE Trans Ind Inform 1. https://doi.org/10.1109/TII.2022.3151984

  12. Zhou S, Wang X, Zhang Y et al (2022) A novel image encryption cryptosystem based on true random numbers and chaotic systems. Multimed Syst 28:95–112. https://doi.org/10.1007/s00530-021-00803-8

    Article  Google Scholar 

  13. Toktas A, Erkan U, Ustun D, Wang X (2023) Parameter optimization of chaotic system using Pareto-based triple objective artificial bee colony algorithm. Neural Comput Appl. https://doi.org/10.1007/s00521-023-08434-y

    Article  Google Scholar 

  14. Chen G, Huang Y (2011) Chaotic maps: dynamics, fractals, and rapid fluctuations. Morgan & Claypool Publishers, Williston

    Book  Google Scholar 

  15. Han ZH, Zhang KS (2012) Surrogate-based optimization. Real-World Applications of Genetic Algorithms, InTech. https://doi.org/10.5772/36125

  16. Xu M, Han M, Chen CLP, Qiu T (2020) Recurrent broad learning systems for time series prediction. IEEE Trans Cybern 50:1405–1417. https://doi.org/10.1109/TCYB.2018.2863020

    Article  Google Scholar 

  17. Erkan U, Toktas A, Lai Q (2023) Design of two dimensional hyperchaotic system through optimization benchmark function. Chaos Solit Fractals 167:113032. https://doi.org/10.1016/j.chaos.2022.113032

    Article  MathSciNet  Google Scholar 

  18. Erkan U, Toktas A, Lai Q (2023) 2D hyperchaotic system based on Schaffer function for image encryption. Expert Syst Appl 213:119076. https://doi.org/10.1016/j.eswa.2022.119076

    Article  Google Scholar 

  19. Lai Q, Lai C (2022) Design and implementation of a new hyperchaotic memristive map. IEEE Trans Circuits Syst II Express Briefs 69:2331–2335. https://doi.org/10.1109/TCSII.2022.3151802

    Article  Google Scholar 

  20. Hua Z, Jin F, Xu B, Huang H (2018) 2D Logistic-Sine-coupling map for image encryption. Signal Process 149:148–161. https://doi.org/10.1016/j.sigpro.2018.03.010

    Article  Google Scholar 

  21. Wu Y, Zhou Y, Bao L (2014) Discrete wheel-switching chaotic system and applications. IEEE Trans Circuits Syst I Regul Pap 61:3469–3477. https://doi.org/10.1109/TCSI.2014.2336512

    Article  Google Scholar 

  22. Zhou Y, Hua Z, Pun C-M, Philip Chen CL (2015) Cascade chaotic system with applications. IEEE Trans Cybern 45:2001–2012. https://doi.org/10.1109/TCYB.2014.2363168

    Article  Google Scholar 

  23. Zheng J, Hu H (2022) A highly secure stream cipher based on analog-digital hybrid chaotic system. Inf Sci (Ny) 587:226–246. https://doi.org/10.1016/j.ins.2021.12.030

    Article  Google Scholar 

  24. Wang Y, Liu Z, Zhang LY, Pareschi F, Setti G, Chen G (2021) From chaos to pseudorandomness: a case study on the 2-D coupled map lattice. IEEE Trans Cybern: 53:1324–1334. https://doi.org/10.1109/TCYB.2021.3129808

  25. Cao W, Mao Y, Zhou Y (2020) Designing a 2D infinite collapse map for image encryption. Signal Process 171:107457. https://doi.org/10.1016/j.sigpro.2020.107457

  26. Hua Z, Zhu Z, Chen Y (2021) Li Y (2021) Color image encryption using orthogonal Latin squares and a new 2D chaotic system. Nonlinear Dyn 1044(104):4505–4522. https://doi.org/10.1007/S11071-021-06472-6

    Article  Google Scholar 

  27. Gao X (2021) Image encryption algorithm based on 2D hyperchaotic map. Opt Laser Technol 142:107252. https://doi.org/10.1016/J.OPTLASTEC.2021.107252

    Article  Google Scholar 

  28. Teng L, Wang X, Yang F, Xian Y (2021) Color image encryption based on cross 2D hyperchaotic map using combined cycle shift scrambling and selecting diffusion. Nonlinear Dyn 105:1859–1876. https://doi.org/10.1007/S11071-021-06663-1

    Article  Google Scholar 

  29. Hua Z, Chen Y, Bao H, Zhou Y (2022) Two-dimensional parametric polynomial chaotic system. IEEE Trans Syst Man Cybern Syst 52:4402–4414. https://doi.org/10.1109/TSMC.2021.3096967

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  31. Sun J (2021) 2D-SCMCI hyperchaotic map for image encryption algorithm. IEEE Access 9:59313–59327. https://doi.org/10.1109/ACCESS.2021.3070350

    Article  Google Scholar 

  32. Zhu L, Jiang D, Ni J et al (2022) A stable meaningful image encryption scheme using the newly-designed 2D discrete fractional-order chaotic map and Bayesian compressive sensing. Signal Process 195:108489. https://doi.org/10.1016/j.sigpro.2022.108489

    Article  Google Scholar 

  33. Wang X, Chen X, Zhao M (2023) A new two-dimensional sine-coupled-logistic map and its application in image encryption. Multimed Tools Appl. https://doi.org/10.1007/s11042-023-14674-w

    Article  Google Scholar 

  34. Liu X, Sun K, Wang H (2023) A novel image encryption scheme based on 2D SILM and improved permutation-confusion-diffusion operations. Multimed Tools Appl 82:23179–23205. https://doi.org/10.1007/s11042-022-14133-y

    Article  Google Scholar 

  35. Moon S, Baik J-J, Seo JM (2021) Chaos synchronization in generalized Lorenz systems and an application to image encryption. Commun Nonlinear Sci Numer Simul 96:105708. https://doi.org/10.1016/j.cnsns.2021.105708

    Article  MathSciNet  Google Scholar 

  36. Styblinski MA, Tang T-S (1990) Experiments in nonconvex optimization: Stochastic approximation with function smoothing and simulated annealing. Neural Netw 3:467–483. https://doi.org/10.1016/0893-6080(90)90029-K

    Article  Google Scholar 

  37. Hua Z, Zhou Y, Huang H (2019) Cosine-transform-based chaotic system for image encryption. Inf Sci (Ny) 480:403–419. https://doi.org/10.1016/j.ins.2018.12.048

    Article  Google Scholar 

  38. Butusov DN, Pesterev DO, Tutueva AV et al (2021) New technique to quantify chaotic dynamics based on differences between semi-implicit integration schemes. Commun Nonlinear Sci Numer Simul 92:105467. https://doi.org/10.1016/j.cnsns.2020.105467

    Article  MathSciNet  Google Scholar 

  39. Richman JS, Moorman JR (2000) Physiological time-series analysis using approximate and sample entropy. Am J Physiol - Hear Circ Physiol 278:2039–2049. https://doi.org/10.1152/ajpheart.2000.278.6.h2039

    Article  Google Scholar 

  40. Bandt C, Pompe B (2002) Permutation entropy: a natural complexity measure for time series. Phys Rev Lett 88:4. https://doi.org/10.1103/PhysRevLett.88.174102

    Article  Google Scholar 

  41. Gottwald GA, Melbourne I (2004) A new test for chaos in deterministic systems. Proceedings: Mathematical, Physical and Engineering Sciences 460:603–611

  42. Theiler J (1987) Efficient algorithm for estimating the correlation dimension from a set of discrete points. Phys Rev A 36:4456–4462. https://doi.org/10.1103/PhysRevA.36.4456

    Article  MathSciNet  Google Scholar 

  43. Grassberger P, Procaccia I (1983) Estimation of the Kolmogorov entropy from a chaotic signal. Phys Rev A 28:2591–2593. https://doi.org/10.1103/PhysRevA.28.2591

    Article  Google Scholar 

  44. L’Ecuyer P, Simard R (2007) TestU01: a c library for empirical testing of random number generators. ACM Trans Math Softw 33. https://doi.org/10.1145/1268776.1268777

  45. Kocak O, Erkan U, Toktas A et al (2024) PSO-based image encryption scheme using modular integrated logistic exponential map. Expert Systems with Applications 237121452. https://doi.org/10.1016/j.eswa.2023.121452

  46. Erkan Uğur, Toktas Abdurrahim, Toktas Feyza et al (2022) 2D eπ-map for image encryption. Inf Sci 589:770–789. https://doi.org/10.1016/j.ins.2021.12.126

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Engineering, Tarsus University, Tarsus, Mersin, Türkiye

    Deniz Ustun

  2. Department of Computer Engineering, Faculty of Engineering, Karamanoglu Mehmetbey University, 70200, Karaman, Türkiye

    Uğur Erkan

  3. Department of Artificial Intelligence and Data Engineering, Engineering Faculty, Ankara University, Gölbaşı, 06830, Ankara, Türkiye

    Abdurrahim Toktas

  4. School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang, 330013, China

    Qiang Lai & Liang Yang

Authors
  1. Deniz Ustun
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  4. Qiang Lai
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  5. Liang Yang
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Correspondence to Uğur Erkan.

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Ustun, D., Erkan, U., Toktas, A. et al. 2D hyperchaotic Styblinski-Tang map for image encryption and its hardware implementation. Multimed Tools Appl 83, 34759–34772 (2024). https://doi.org/10.1007/s11042-023-17054-6

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