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Silicon Valley Cybersecurity Conference

SVCC 2021: Silicon Valley Cybersecurity Conference pp 90–105Cite as

A Comprehensive Analysis of Chaos-Based Secure Systems

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1536))

Abstract

Chaos is a deterministic phenomenon that emerges under certain conditions in a nonlinear dynamic system when the trajectories of the state variables become periodic and highly sensitive to the initial conditions. Chaotic systems are flexible, and it has been shown that communication is possible using parametric feedback control. Chaos synchronization is the basis of using chaos in communication. Chaos synchronization refers to the characteristic that the trajectories of two identical chaotic systems, each with its own unique initial conditions, converge over time.

In this paper, data extraction is performed on different chaotic equations implemented as circuits. Lorenz is the base system implemented in this paper, followed by Modified Lorenz, Chua’s, L\(\ddot{u}\)’s, and R\(\ddot{o}\)ssler systems. Additionally, more recent systems (e.g., SprottD Attractor) are included in the data extraction process. The robust system implementations provide an alternative to software chaos and architectures, and will further reduce the required power and area. These chaotic systems serve as alternatives for quantum era computing, which will cause synchronous and asynchronous techniques to fail. The data extracted organize different modes of chaos implementation based on the ease of their fabrication in integrated circuits. Performance metrics including power consumption, area, design load, noise, and robustness to process and temperature variant are extracted for each system to demonstrate a figure of merit. The figure of merit showcases chaos equations fitting to be implemented as a transmitter/receiver with a mode of chaotic ciphering in communication.

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References

  1. Cuomo, K.M., Oppenheim, A.V., Strogatz, S.H.: Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circ. Syst. II Analog Digital Signal Process. 40(10), 626–633 (1993)

    Article  Google Scholar 

  2. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaotic dynamical systems. In Chaos: Soviet-American Perspective on Nonlinear Science, pp. 153–172. American Institute of Physics (1990)

    Google Scholar 

  3. Benioff, P.: The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computers as represented by turing machines. J. Stat. Phys. 22(5), 563–591 (1980)

    Article  MathSciNet  Google Scholar 

  4. Arute, F., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505–510 (2019)

    Article  Google Scholar 

  5. Kalai, G.: The argument against quantum computers. In: Quantum, Probability, Logic, pp. 399–422 (2020)

    Google Scholar 

  6. Smith, F.L., III.: Quantum technology hype and national security. Secur. Dialogue 5(1), 0967010620904922 (2020)

    Google Scholar 

  7. Elwakil, A.S., Kennedy, M.P.: Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 48(3), 289–307 (2001)

    Article  MathSciNet  Google Scholar 

  8. Delgado-Restituto, M., Rodriguez-Vazquez, A.: A CMOS analog chaotic oscillator for signal encryption. In: ESSCIRC 1993: Nineteenth European Solid-State Circuits Conference, vol. 1, pp. 110–113. IEEE (1993)

    Google Scholar 

  9. Delgado-Restituto, M., Rodriguez-Vazquez, A., Linan, M.: A modulator/demodulator CMOS IC for chaotic encryption of audio. In: ESSCIRC1995: Twenty-First European Solid-State Circuits Conference, pp. 170–173. IEEE (1995)

    Google Scholar 

  10. Elwakil, A.S., Salama, K.N., Kennedy, M.P.: An equation for generating chaos and its monolithic implementation. Int. J. Bifurcat. Chaos 12(12), 2885–2895 (2002)

    Article  Google Scholar 

  11. Trejo-Guerra, R., Tlelo-Cuautle, E., Cruz-Hernández, C., SÁnchez-LÓpez, C.: Chaotic communication system using Chua’s oscillators realized with CCII+S. Int. J. Bifurcat. Chaos 19(12), 4217–4226 (2009)

    Google Scholar 

  12. Sánchez-López, C., Trejo-Guerra, R., Munoz-Pacheco, J., Tlelo-Cuautle, E.: N-scroll chaotic attractors from saturated function series employing CCII+S. Nonlinear Dyn. 61(1–2), 331–341 (2010)

    Article  Google Scholar 

  13. Trejo-Guerra, R., et al.: Integrated circuit generating 3-and 5-scroll attractors. Commun. Nonlinear Sci. Numer. Simul. 17(11), 4328–4335 (2012)

    Article  MathSciNet  Google Scholar 

  14. Trejo-Guerra, R., Tlelo-Cuautle, E., Jiménez-Fuentes, M., Muñoz-Pacheco, J.M., Sánchez-López, C.: Multiscroll floating gate-based integrated chaotic oscillator. Int. J. Circuit Theory Appl. 41(8), 831–843 (2013)

    Article  Google Scholar 

  15. Gonzalez, O.A., Han, G., De Gyvez, J.P., et al.: CMOS cryptosystem using a Lorenz chaotic oscillator. In: ISCAS 1999, Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No. 99CH36349), vol. 5, pp. 442–445. IEEE (1999)

    Google Scholar 

  16. Wu, Y.-L., Yang, C.-H., Li, Y.-S., Wu, C.-H.: Nonlinear dynamic analysis and chip implementation of a new chaotic oscillator. In: 2015 IEEE 12th International Conference on Networking, Sensing and Control, pp. 554–559. IEEE (2015)

    Google Scholar 

  17. Xiong, L., Lu, Y.-J., Zhang, Y.-F., Zhang, X.-G., Gupta, P.: Design and hardware implementation of a new chaotic secure communication technique. PLoS One 11(8), e0158348 (2016)

    Article  Google Scholar 

  18. Liang, C., Zhang, Q., Ma, J., Li, K.: Research on neural network chaotic encryption algorithm in wireless network security communication. EURASIP J. Wirel. Commun. Netw. 2019(1), 1–10 (2019). https://doi.org/10.1186/s13638-019-1476-3

    Article  Google Scholar 

  19. Zhang, L.: Artificial neural network model design and topology analysis for FPGA implementation of Lorenz chaotic generator. In: IEEE 30th Canadian Conference on Electrical and Computer Engineering (CCECE), pp. 1–4. IEEE (2017)

    Google Scholar 

  20. Tuna, M., Alçın, M., Koyuncu, İ, Fidan, C.B., Pehlivan, İ: High speed FPGA-based chaotic oscillator design. Microprocess. Microsyst. 66, 72–80 (2019)

    Article  Google Scholar 

  21. Gonzales, O.A., Han, G., De Gyvez, J.P., Sánchez-Sinencio, E.: Lorenz-based chaotic cryptosystem: a monolithic implementation. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 47(8), 1243–1247 (2000)

    Article  MathSciNet  Google Scholar 

  22. Yu, S., Lü, J., Tang, W.K., Chen, G.: A general multiscroll Lorenz system family and its realization via digital signal processors. Chaos Interdisc. J. Nonlinear Sci. 16(3), 033126 (2006)

    Article  Google Scholar 

  23. Brown, D., Hedayatipour, A., Majumder, M.B., Rose, G.S., McFarlane, N., Materassi, D.: Practical realisation of a return map immune Lorenz-based chaotic stream cipher in circuitry. IET Comput. Digital Tech. 12(6), 297–305 (2018)

    Article  Google Scholar 

  24. Özoǧuz, S., Elwakil, A.S., Kennedy, M.P.: Experimental verification of the butterfly attractor in a modified Lorenz system. Int. J. Bifurcat. Chaos 12(07), 1627–1632 (2002)

    Article  Google Scholar 

  25. Radwan, A., Soliman, A., El-Sedeek, A.: MOS realization of the modified Lorenz chaotic system. Chaos, Solitons Fractals 21(3), 553–561 (2004)

    Article  Google Scholar 

  26. Wu, Y.-L., Yang, C.-H., Wu, C.-H.: Design of initial value control for modified Lorenz-Stenflo system. Math. Probl. Eng. 2017, 8424139 (2017)

    Google Scholar 

  27. Zhang, F., Chen, R., Chen, X.: Analysis of a generalized Lorenz-Stenflo equation. Complexity 2017, 7520590 (2017)

    MATH  Google Scholar 

  28. Butusov, D.N., Karimov, T.I., Lizunova, I.A., Soldatkina, A.A., Popova, E.N.: Synchronization of analog and discrete rössler chaotic systems. In: IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (EIConRus), pp. 265–270. IEEE (2017)

    Google Scholar 

  29. Liao, T.-L., Chen, H.-C., Peng, C.-Y., Hou, Y.-Y.: Chaos-based secure communications in biomedical information application. Electronics 10(3), 359 (2021)

    Article  Google Scholar 

  30. Wei, Z.: Dynamical behaviors of a chaotic system with no equilibria. Phys. Lett. A 376(2), 102–108 (2011)

    Article  MathSciNet  Google Scholar 

  31. Baruah, B., Saikia, M.: An FPGA implementation of chaos based image encryption and its performance analysis. IJCSN Int. J. Comput. Sci. Netw. 5(5), 712–720 (2016)

    Google Scholar 

  32. Lopez-Hernandez, J., Diaz-Mendez, A., Vazquez-Medina, R., Alejos-Palomares, R.: Analog current-mode implementation of a logistic-map based chaos generator. In: 52nd IEEE International Midwest Symposium on Circuits and Systems, pp. 812–814. IEEE (2009)

    Google Scholar 

  33. Farfan-Pelaez, A., Del-Moral-Hernández, E., Navarro, J., Van Noije, W.: A CMOS implementation of the sine-circle map. In: 48th Midwest Symposium on Circuits and Systems, pp. 1502–1505. IEEE (2005)

    Google Scholar 

  34. Callegari, S., Setti, G., Langlois, P.J.: A CMOS tailed tent map for the generation of uniformly distributed chaotic sequences. In: IEEE International Symposium on Circuits and Systems (ISCAS), vol. 2, pp. 781–784. IEEE (1997)

    Google Scholar 

  35. Dudek, P., Juncu, V.: Compact discrete-time chaos generator circuit. Electron. Lett. 39(20), 1431–1432 (2003)

    Article  Google Scholar 

  36. Juncu, V., Rafiei-Naeini, M., Dudek, P.: Integrated circuit implementation of a compact discrete-time chaos generator. Analog Integr. Circ. Sig. Process 46(3), 275–280 (2006)

    Article  Google Scholar 

  37. Kia, B., Mobley, K., Ditto, W.L.: An integrated circuit design for a dynamics-based reconfigurable logic block. IEEE Trans. Circuits Syst. II Express Briefs 64(6), 715–719 (2017)

    Article  Google Scholar 

  38. Zhou, Y., Hua, Z., Pun, C.-M., Chen, C.P.: Cascade chaotic system with applications. IEEE Trans. Cybern. 45(9), 2001–2012 (2014)

    Article  Google Scholar 

  39. Al-Shameri, W.F.H.: Dynamical properties of the hénon mapping. Int. J. Math. Anal. 6(49), 2419–2430 (2012)

    MathSciNet  MATH  Google Scholar 

  40. Hua, Z., Zhou, Y.: Dynamic parameter-control chaotic system. IEEE Trans. Cybern. 46(12), 3330–3341 (2015)

    Article  Google Scholar 

  41. Rieger, R., Demosthenous, A., Taylor, J.: A 230-nW 10-s time constant CMOS integrator for an adaptive nerve signal amplifier. IEEE J. Solid-State Circ. 39(11), 1968–1975 (2004)

    Article  Google Scholar 

  42. Carbajal-Gomez, V.H., Tlelo-Cuautle, E., Muñoz-Pacheco, J.M., de la Fraga, L.G., Sanchez-Lopez, C., Fernandez-Fernandez, F.V.: Optimization and CMOS design of chaotic oscillators robust to PVT variations. Integration 65, 32–42 (2019)

    Article  Google Scholar 

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Acknowledgement

The simulations on this paper are done using Cadence virtuoso, supplied by Cadence university program to California State University Long Beach. This work is supported by the National Science Foundation under award No. 2131156.

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Authors and Affiliations

  1. College of Engineering, California State University Long Beach, Long Beach, USA

    Ava Hedayatipour, Ravi Monani, Amin Rezaei, Mehrdad Aliasgari & Hossein Sayadi

Authors
  1. Ava Hedayatipour
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  2. Ravi Monani
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  3. Amin Rezaei
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  4. Mehrdad Aliasgari
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  5. Hossein Sayadi
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Corresponding author

Correspondence to Ava Hedayatipour .

Editor information

Editors and Affiliations

  1. University of Colorado, Colorado Springs, CO, USA

    Sang-Yoon Chang

  2. IBM Almaden Research Center, San Jose, CA, USA

    Luis Bathen

  3. San Jose State University, San Jose, CA, USA

    Fabio Di Troia

  4. San Jose State University, San Jose, CA, USA

    Thomas H. Austin

  5. National Institute of Standards and Technology, Gaithersburg, MD, USA

    Alex J. Nelson

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Hedayatipour, A., Monani, R., Rezaei, A., Aliasgari, M., Sayadi, H. (2022). A Comprehensive Analysis of Chaos-Based Secure Systems. In: Chang, SY., Bathen, L., Di Troia, F., Austin, T.H., Nelson, A.J. (eds) Silicon Valley Cybersecurity Conference. SVCC 2021. Communications in Computer and Information Science, vol 1536. Springer, Cham. https://doi.org/10.1007/978-3-030-96057-5_7

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  • DOI: https://doi.org/10.1007/978-3-030-96057-5_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-96056-8

  • Online ISBN: 978-3-030-96057-5

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