Experimental Validation of a Chaotic Jerk Circuit Based True Random Number Generator

Year 2022, Volume: 4 Issue: 2, 64 - 70, 30.07.2022

R. Chase Harrison Benjamin K. Rhea Ariel Oldag Robert N. Dean Edmon Perkins

https://doi.org/10.51537/chaos.1112243

Cited By: 4

Abstract

A method for true random number generation by directly sampling a high frequency chaotic jerk circuit is explored. A method for determination of the maximum Lyapunov exponent, and thus the maximum bit rate for true random number generation, of the jerk system of interest is shown. The system is tested over a wide range of sampling parameters in order to simulate possible hardware configurations. The system is then implemented in high speed electronics on a small printed circuit board to verify its performance over the chosen parameters. The resulting circuit is well suited for random number generation due to its high dynamic complexity, long term aperiodicity, and extreme sensitivity to initial conditions. This system passes the Dieharder RNG test suite at 3.125 Mbps.

Keywords

Random number generation, Dieharder, Chaotic circuits, Chaos theory, Nonlinear dynamics, Jerk oscillator

References

• Akhshani, A., A. Akhavan, A. Mobaraki, S.-C. Lim, and Z. Hassan, 2014 Pseudo random number generator based on quantum chaotic map. Communications in Nonlinear Science and Numerical Simulation 19: 101–111.
• Balachandran, B., E. Perkins, and T. Fitzgerald, 2015 Response localization in micro-scale oscillator arrays: influence of cubic coupling nonlinearities. International Journal of Dynamics and Control 3: 183–188.
• Bassham III, L. E., A. L. Rukhin, J. Soto, J. R. Nechvatal, M. E. Smid, et al., 2010 Sp 800-22 rev. 1a. a statistical test suite for random and pseudorandom number generators for cryptographic applications. National Institute of Standards & Technology.
• Blaszczyk, M. and R. A. Guinee, 2008 A true random binary sequence generator based on chaotic circuit. In IET Irish Signals and Systems Conference (ISSC 2008), pp. 294–299.
• Brown, R. G., D. Eddelbuettel, and D. Bauer, 2013 Dieharder: A random number test suite. Open Source software library, under development, URL http://www. phy. duke. edu/˜ rgb/General/dieharder. php .
• Cicek, I., A. E. Pusane, and G. Dundar, 2014 A novel design method for discrete time chaos based true random number generators. INTEGRATION, the VLSI journal 47: 38–47.
• Ergun, S. and S. Ozoguz, 2007 A chaos-modulated dual oscillatorbased truly random number generator. In Circuits and Systems, 2007. ISCAS 2007. IEEE International Symposium on, pp. 2482– 2485, IEEE.
• Guinee, R. A. and M. Blaszczyk, 2009 A novel true random binary sequence generator based on a chaotic double scroll oscillator combination with a pseudo random generator for cryptographic applications. In Internet Technology and Secured Transactions, 2009. ICITST 2009. International Conference for, pp. 1–6, IEEE.
• Han, M. and Y. Kim, 2017 Unpredictable 16 bits LFSR-based true random number generator. In SoC Design Conference (ISOCC), 2017 International, pp. 284–285, IEEE.
• Harrison, R. C., B. K. Rhea, A. N. Ramsey, R. N. Dean, and J. E. Perkins, 2019 A true random number generator based on a chaotic jerk system. In 2019 SoutheastCon, pp. 1–5, IEEE.
• Harrison, R. C., B. K. Rhea, F. T. Werner, and R. Dean, 2017 A compact and low power realization of a high frequency chaotic oscillator. Additional Conferences (Device Packaging, HiTEC, HiTEN, & CICMT) 2017: 4.
• Harrison, R. C., B. K. Rhea, F. T. Werner, and R. N. Dean, 2016 A 4 MHz chaotic oscillator based on a jerk system. In International Conference on Applications in Nonlinear Dynamics, pp. 41–51, Springer.
• Kengne, J., R. L. T. Mogue, T. F. Fozin, and A. N. K. Telem, 2019 Effects of symmetric and asymmetric nonlinearity on the dynamics of a novel chaotic jerk circuit: Coexisting multiple attractors, period doubling reversals, crisis, and offset boosting. Chaos, Solitons & Fractals 121: 63–84.
• Lepik, Ü. and H. Hein, 2005 On response of nonlinear oscillators with random frequency of excitation. Journal of sound and vibration 288: 275–292.
• Li, C.-Y., T.-Y. Chang, and C.-C. Huang, 2010 A nonlinear PRNG using digitized logistic map with self-reseeding method. In VLSI Design Automation and Test (VLSI-DAT), 2010 International Symposium on, pp. 108–111, IEEE.
• Li, X., M. R. E. U. Shougat, T. Mollik, A. N. Beal, R. N. Dean, et al., 2021 Stochastic effects on a hopf adaptive frequency oscillator. Journal of Applied Physics 129: 224901.
• Njitacke, Z., L. K. Kengne, et al., 2017 Antimonotonicity, chaos and multiple coexisting attractors in a simple hybrid diode-based jerk circuit. Chaos, Solitons & Fractals 105: 77–91.
• Pareschi, F., G. Scotti, L. Giancane, R. Rovatti, G. Setti, et al., 2009 Power analysis of a chaos-based random number generator for cryptographic security. In Circuits and Systems, 2009. ISCAS 2009. IEEE International Symposium on, pp. 2858–2861, IEEE.
• Pareschi, F., G. Setti, and R. Rovatti, 2010 Statistical testing of a chaos based CMOS true-random number generator. Journal of Circuits, Systems, and Computers 19: 897–910.
• Perkins, E., 2017 Effects of noise on the frequency response of the monostable duffing oscillator. Physics Letters A 381: 1009–1013.
• Perkins, E. and B. Balachandran, 2012 Noise-enhanced response of nonlinear oscillators. Procedia Iutam 5: 59–68.
• Perkins, E. and B. Balachandran, 2015 Effects of phase lag on the information rate of a bistable duffing oscillator. Physics Letters A 379: 308–313.
• Perkins, E. and T. Fitzgerald, 2018 Continuation method on cumulant neglect equations. Journal of Computational and Nonlinear Dynamics 13.
• Perkins, E., M. Kimura, T. Hikihara, and B. Balachandran, 2016 Effects of noise on symmetric intrinsic localized modes. Nonlinear Dynamics 85: 333–341.
• Saito, T. and H. Fujita, 1981 Chaos in a manifold piecewise linear system. Electronics and Communications in Japan (Part I: Communications) 64: 9–17.
• Sprott, J. C., 2000 Simple chaotic systems and circuits. American Journal of Physics 68: 758–763.
• Sprott, J. C., 2010 Elegant chaos: algebraically simple chaotic flows. World Scientific.
• Sundaresan, S., R. Doss, S. Piramuthu, andW. Zhou, 2015 Secure tag search in RFID systems using mobile readers. IEEE Transactions on Dependable and Secure Computing 12: 230–242.
• Tavas, V., A. S. Demirkol, S. Ozoguz, A. Zeki, and A. Toker, 2010 An ADC based random bit generator based on a double scroll chaotic circuit. Journal of Circuits, Systems, and Computers 19: 1621–1639
• Valtierra, J. L., E. Tlelo-Cuautle, and Á. Rodríguez-Vázquez, 2017 A switched-capacitor skew-tent map implementation for random number generation. International Journal of Circuit Theory and Applications 45: 305–315.
• Volos, C. K., 2013 Image encryption scheme based on coupled chaotic systems. Journal of Applied Mathematics and Bioinformatics 3: 123.
• Wolf, A., J. B. Swift, H. L. Swinney, and J. A. Vastano, 1985 Determining lyapunov exponents from a time series. Physica D: Nonlinear Phenomena 16: 285–317.
• Yalçin, M. E., 2007 Multi-scroll and hypercube attractors from a general jerk circuit using josephson junctions. Chaos, Solitons & Fractals 34: 1659–1666.