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FPGA-Based Design of Chaotic Systems with Quadratic Nonlinearities

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Proceedings of Data Analytics and Management (ICDAM 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 788))

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Abstract

This paper presents a systematized methodology to implement chaotic systems with quadratic nonlinearities on digital platform using Runge–Kutta 4 (RK4) numerical method. Field programmable gate arrays (FPGAs), because of their flexibility, reconfigurability, and parallelism, have been used for the implementation using Verilog hardware description language (HDL) and the state machine control. The synthesis results based on Xilinx Artix device 7a200tffv1156-1, and simulation results using inbuilt simulator of Vivado design suite have been presented. The simulation results have been validated by python-based numerical simulations as well. The implemented chaotic systems have been evaluated based on hardware utilization and time delay.

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References

  1. Paliwal A, Mohindroo B, Suneja K (2020) Hardware design of image encryption and decryption using CORDIC based chaotic generator. In: 2020 5th IEEE international conference on recent advances and innovations in engineering (ICRAIE), Jaipur, India, pp 1–5. https://doi.org/10.1109/ICRAIE51050.2020.9358354

  2. Tang Z, Yu S (2012) Design and realization of digital image encryption and decryption based on multi-wing butterfly chaotic attractors. In: 2012 5th international congress on image and signal processing, Chongqing, China, pp 1143–1147. https://doi.org/10.1109/CISP.2012.6469744

  3. Negi A, Saxena D, Suneja K (2020) High level synthesis of chaos based text encryption using modified hill cipher algorithm. In: 2020 IEEE 17th India Council International Conference (INDICON), New Delhi, India, pp 1–5. https://doi.org/10.1109/INDICON49873.2020.9342591

  4. Gomar S, Ahmadi M (2019) A digital pseudo random number generator based on a chaotic dynamic system. In: 2019 26th IEEE international conference on electronics, circuits and systems (ICECS), Genoa, Italy, pp 610–613. https://doi.org/10.1109/ICECS46596.2019.8964861

  5. Suchit S, Suneja K (2022) Implementation of secure communication system using chaotic masking. In: 2022 IEEE global conference on computing, power and communication technologies (GlobConPT), New Delhi, India, pp 1–5. https://doi.org/10.1109/GlobConPT57482.2022.9938303

  6. Yang T, Wu CW, Chua LO (1997) Cryptography based on chaotic systems. IEEE Trans Circ Syst I Fundam Theor Appl 44(5):469–472. https://doi.org/10.1109/81.572346

    Article  Google Scholar 

  7. Tuna M, Alçın M, Koyuncu I, Fidan CB, Pehlivan I (2019) High speed FPGA-based chaotic oscillator design. Microproces Microsyst 66:72–80

    Google Scholar 

  8. Tuna M, Fidan CB (2016) Electronic circuit design, implementation and FPGA-based realization of a new 3D chaotic system with single equilibrium point. Optik 127(24):11786–11799

    Article  Google Scholar 

  9. Chen S, Yu S, Lü J, Chen G, He J (2018) Design and FPGA-based realization of a chaotic secure video communication system. IEEE Trans Circ Syst Video Technol 28(9):2359–2371. https://doi.org/10.1109/TCSVT.2017.2703946

    Article  Google Scholar 

  10. Nuñez-Perez JC, Adeyemi VA, Sandoval-Ibarra Y, Pérez-Pinal FJ, Tlelo-Cuautle E (2021) FPGA realization of spherical chaotic system with application in image transmission. Math Probl Eng. Article ID 5532106, 16p

    Google Scholar 

  11. Schmitz J, Zhang L (2017) Rössler-based chaotic communication system implemented on FPGA. In: 2017 IEEE 30th Canadian conference on electrical and computer engineering (CCECE), pp 1–4. https://doi.org/10.1109/CCECE.2017.7946729

  12. Tolba MF, Elwakil AS, Orabi H, Elnawawy M, Aloul F, Sagahyroon A, Radwan AG (2020) FPGA implementation of a chaotic oscillator with odd/even symmetry and its application. Integration 72:163–170

    Article  Google Scholar 

  13. Shi QY, Huang X, Yuan F, Li YX (2021) Design and FPGA implementation of multi-wing chaotic switched systems based on a quadratic transformation. Chin Phys 30(2):020507-1–020507-10

    Google Scholar 

  14. Koyuncu I, Özcerit A, Pehlivan I (2014) Implementation of FPGA-based real time novel chaotic oscillator. Nonlinear Dyn 7:49–59

    Article  MathSciNet  Google Scholar 

  15. Garg A, Yadav B, Sahu K, Suneja K (2021) An FPGA based real time implementation of Nosé hoover chaotic system using different numerical techniques. In: 2021 7th international conference on advanced computing and communication systems (ICACCS), Coimbatore, India, pp 108–113. https://doi.org/10.1109/ICACCS51430.2021.9441923

  16. Cartwright JHE, Piro O (1992) The dynamics of Runge-Kutta methods. Int J Bifurcation Chaos 2:427–449

    Article  MathSciNet  Google Scholar 

  17. Sadoudi S, Tanougast C, Azzaz MS et al (2013) Design and FPGA implementation of a wireless hyperchaotic communication system for secure real-time image transmission. J Image Video Proc 2013:43. https://doi.org/10.1186/1687-5281-2013-43

    Article  Google Scholar 

  18. Rössler OE (1976) An equation for continuous chaos. Phys Lett A 57(5):397–398

    Article  Google Scholar 

  19. Lorenz EN (1963) Deterministic non-periodic flows. J Atmos Sci 20:130–141

    Article  Google Scholar 

  20. Pehlivan I, Uyaroğlu Y (2010) A new chaotic attractor from general Lorenz system family and its electronic experimental implementation. Turkish J Electr Eng Comput Sci 18(2):171–184. https://doi.org/18. https://doi.org/10.3906/elk-0906-67

  21. Li XF, Chlouverakis KE, Xu DL (2009) Nonlinear dynamics and circuit realization of a new chaotic flow: a variant of Lorenz, Chen and Lü. Nonlinear Anal Real World Appl 10(4):2357–2368

    Article  MathSciNet  Google Scholar 

  22. Qi G, Chen G, Du S, Chen Z, Yuan Z (2005) Analysis of a new chaotic system. Physica A: Stat Mechan Appl 352(2–4):295–308

    Article  Google Scholar 

  23. Méndez-Ramírez R, Cruz-Hernández C, Arellano-Delgado A, Martínez-Clark R (2017) A new simple chaotic Lorenz-type system and its digital realization using a TFT touch-screen display embedded system. Complexity 6820492

    Google Scholar 

  24. Yang Q, Chen G (2008) A chaotic system with one saddle and two stable node-foci. Int J Bifur Chaos 18:1393–1414

    Article  MathSciNet  Google Scholar 

  25. Liu Y, Yang Q (2010) Dynamics of a new Lorenz-like chaotic system. Nonlinear Anal Real World Appl 11(4):2563–2572

    Article  MathSciNet  Google Scholar 

  26. Li XF, Chlouverakis KE, Xu DL (2009) Nonlinear dynamics and circuit realization of a new chaotic flow: a variant of Lorenz, Chen and Lü. Nonlinear Anal Real World Appl 10:2357–2368

    Article  MathSciNet  Google Scholar 

  27. Pikovski AS, Rabinovich MI, Trakhtengerts VY (1978) Onset of stochasticity in decay confinement of parametric instability. Soviet Physics JETP 47:715–719

    Google Scholar 

  28. Kocamaz UE, Uyaroğlu Y, Kizmaz H (2014) Control of Rabinovich chaotic system using sliding mode control. Int J Adapt Control Signal Proces 28(12), 1413–1421

    Google Scholar 

  29. Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurcat Chaos 9:1465–1466

    Article  MathSciNet  Google Scholar 

  30. Lu J, Chen G (2002) A new chaotic attractor coined. I J Bifurcat Chaos 12:659–661. https://doi.org/10.1142/S0218127402004620

    Article  MathSciNet  Google Scholar 

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Correspondence to Kriti Suneja .

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Suneja, K., Pandey, N., Pandey, R. (2023). FPGA-Based Design of Chaotic Systems with Quadratic Nonlinearities. In: Swaroop, A., Polkowski, Z., Correia, S.D., Virdee, B. (eds) Proceedings of Data Analytics and Management. ICDAM 2023. Lecture Notes in Networks and Systems, vol 788. Springer, Singapore. https://doi.org/10.1007/978-981-99-6553-3_12

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