Abstract
High-quality random number generators (RNGs) are essential in many fields. To overcome the drawbacks in instability of the true RNGs and periodicity of the pseudo-RNGs, based on an analog–digital hybrid chaotic entropy source, an aperiodic hybrid RNG is proposed. The hybrid source is a nondegenerate chaotic system that consists of a delay-coupled digital chaotic map and the analog anticontrol. The anticontrol strategy that considers practical implementation is rarely studied. In this paper, the construction strategy and anticontrol mechanism are well designed and can be regarded as a general methodology to realize multi-dimensional chaotic systems without performance degradation. The proposed system presents good chaotic behaviors in the digital world and has great advantages when realized on hardware platforms. The detailed software simulation and hardware implementation are both presented to verify the effectiveness of the scheme. Due to the excellent properties of the chaotic source, without complicated post-processing, the proposed hybrid RNG can generate high-quality true random bits steadily at relatively low precision and shows robustness to the parameter fluctuation, therefore it is suitable for cryptography and other potential applications.
Similar content being viewed by others
Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
Bakiri, M., Guyeux, C., Couchot, J.F., Oudjida, A.K.: Survey on hardware implementation of random number generators on fpga: theory and experimental analyses. Comput. Sci. Rev. 27, 135–153 (2018)
Yalcin, M.E., Suykens, J.A.K., Vandewalle, J.: True random bit generation from a double-scroll attractor. IEEE Trans. Circuits Syst. I-Regul. Pap. 51(7), 1395–1404 (2004)
Sunar, B., Martin, W.J., Stinson, D.R.: A provably secure true random number generator with built-in tolerance to active attacks. IEEE Trans. Comput. 56(1), 109–119 (2007)
Murillo-Escobar, M.A., Cruz-Hernandez, C., Cardoza-Avendano, L., Mendez-Ramirez, R.: A novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dyn. 87(1), 407–425 (2017)
Karakaya, B., Gülten, A., Frasca, M.: A true random bit generator based on a memristive chaotic circuit: analysis, design and fpga implementation. Chaos Solitons Fractals 119, 143–149 (2019)
Jiang, H., Belkin, D., Savel’ev, S.E., Lin, S., Wang, Z., Li, Y., Joshi, S., Midya, R., Li, C., Rao, M., Barnell, M., Wu, Q., Yang, J.J., Xia, Q.: A novel true random number generator based on a stochastic diffusive memristor. Nat. Commun. 8 (2017)
Fukushima, A., Seki, T., Yakushiji, K., Kubota, H., Imamura, H., Yuasa, S., Ando, K.: Spin dice: a scalable truly random number generator based on spintronics. Appl. Phys. Express 7(8), 083001 (2014)
François, M., Grosges, T., Barchiesi, D., Erra, R.: Pseudo-random number generator based on mixing of three chaotic maps. Commun. Nonlinear Sci. Numer. Simul. 19(4), 887–895 (2014)
Wang, Y., Liu, Z., Ma, J., He, H.: A pseudorandom number generator based on piecewise logistic map. Nonlinear Dyn. 83(4), 2373–2391 (2016)
La Fraga, L.G.D., Torresperez, E., Tlelocuautle, E., Mancillaslopez, C.: Hardware implementation of pseudo-random number generators based on chaotic maps. Nonlinear Dyn. 90(3), 1661–1670 (2017)
İsmail Koyuncu, Turan Özcerit, A.: The design and realization of a new high speed fpga-based chaotic true random number generator. Comput. Electr. Eng. 58, 203–214 (2017)
Nguyen, N.T., Bui, T., Gagnon, G., Giard, P., Kaddoum, G.: Designing a pseudorandom bit generator with a novel five-dimensional-hyperchaotic system. IEEE Trans. Ind. Electron. 69(6), 6101–6110 (2022)
Lv, X., Liao, X., Yang, B.: A novel pseudo-random number generator from coupled map lattice with time-varying delay. Nonlinear Dyn. 94(1), 325–341 (2018)
Sahari, M.L., Boukemara, I.: A pseudo-random numbers generator based on a novel 3d chaotic map with an application to color image encryption. Nonlinear Dyn. 94(1), 723–744 (2018)
Hua, Z., Zhou, Y.: One-dimensional nonlinear model for producing chaos. IEEE Trans. Circuits Syst. I-Regul. Pap. 65(1), 235–246 (2018)
Pareschi, F., Setti, G., Rovatti, R.: Implementation and testing of high-speed cmos true random number generators based on chaotic systems. IEEE Trans. Circuits Syst. I-Regul. Pap. 57(12), 3124–3137 (2010)
Nguyen, N., Kaddoum, G., Pareschi, F., Rovatti, R., Setti, G.: A fully cmos true random number generator based on hidden attractor hyperchaotic system. Nonlinear Dyn. 102(4), 2887–2904 (2020)
Li, P., Wang, Y.C., Zhang, J.Z.: All-optical fast random number generator. Opt. Express 18(19), 20360–20369 (2010)
Dantas, W., Rodrigues, L.R., Ujevic, S., Gusso, A.: Using nanoresonators with robust chaos as hardware random number generators. Chaos 30(4), 043126 (2020)
Li, C., Feng, B., Li, S., Kurths, J., Chen, G.: Dynamic analysis of digital chaotic maps via state-mapping networks. IEEE Trans. Circuits Syst. I-Regul. Pap. 66(6), 2322–2335 (2019)
Tutueva, A.V., Karimov, T.I., Moysis, L., Nepomuceno, E.G., Volos, C., Butusov, D.N.: Improving chaos-based pseudo-random generators in finite-precision arithmetic. Nonlinear Dyn. 104(1), 727–737 (2021)
Hua, Z., Zhou, Y., Huang, H.: Cosine-transform-based chaotic system for image encryption. Inf. Sci. 480, 403–419 (2019)
Cong, L., Xiaofu, W., Songgeng, S.: A general efficient method for chaotic signal estimation. IEEE Trans. Signal Process. 47(5), 1424–1428 (1999)
Chen, S., Lü, J.: Parameters identification and synchronization of chaotic systems based upon adaptive control. Phys. Lett. A 299(4), 353–358 (2002)
Ming, H., Hu, H., Zheng, J.: Analysis of a new coupled hyperchaotic model and its topological types. Nonlinear Dyn. 105(2), 1937–1952 (2021)
Wernecke, H., Sándor, B., Gros, C.: Chaos in time delay systems, an educational review. Phys. Rep.-Rev. Sec. Phys. Lett. 824, 1–40 (2019). Chaos in time delay systems, an educational review
Liu, L., Miao, S.: Delay-introducing method to improve the dynamical degradation of a digital chaotic map. Inf. Sci. 396, 1–13 (2017)
Černák, J.: Digital generators of chaos. Phys. Lett. A 214(3), 151–160 (1996)
Li, S., Chen, G., Mou, X.: On the dynamical degradation of digital piecewise linear chaotic maps. Int. J. Bifurc. Chaos 15(10), 3119–3151 (2005)
Persohn, K., Povinelli, R.: Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation. Chaos Solitons Fractals 45(3), 238–245 (2012)
Wheeler, D.D., Matthews, R.: Supercomputer investigations of a chaotic encryption algorithm. Cryptologia 15(2), 140–152 (1991)
Heidaribateni, G., Mcgillem, C.D.: A chaotic direct-sequence spread-spectrum communication system. IEEE Trans. Commun. 42(234), 1524–1527 (1994)
Nagaraj, N., Shastry, M.C., Vaidya, P.G.: Increasing average period lengths by switching of robust chaos maps in finite precision. Eur. Phys. J.-Spec. Top. 165(1), 73–83 (2008)
Hu, H., Xu, Y., Zhu, Z.: A method of improving the properties of digital chaotic system. Chaos Solitons Fractals 38(2), 439–446 (2008)
Li, C., Chen, Y., Chang, T., Deng, L., To, K.: Period extension and randomness enhancement using high-throughput reseeding-mixing prng. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 20(2), 385–389 (2012)
Chen, G., Lai, D.: Feedback anticontrol of discrete chaos. Int. J. Bifurc. Chaos 8(07), 1585–1590 (1998)
Zheng, J., Hu, H., Xia, X.: Applications of symbolic dynamics in counteracting the dynamical degradation of digital chaos. Nonlinear Dyn. 94(2), 1535–1546 (2018)
Bassham III, L.E., Rukhin, A.L., Soto, J., et al.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. Tech. rep., Nat. Inst. Standards Technol., Special Publication 800-22 Revision 1a (2010)
Barker, E., Kelsey, J., McKay, K.A., Baish, M.L., Boyle, M., et al.: Recommendation for the entropy sources used for random bit generation. NIST Special Publication p. 102 (2018)
L’ecuyer, P., Simard, R.: Testu01: Ac library for empirical testing of random number generators. ACM Trans. Math. Softw. 33(4), 1–40 (2007)
Collet, P., Eckmann, J.P.: Iterated Maps on the Interval as Dynamical Systems. Springer, Berlin (2009)
Wolf, A., Swift, J., Swinney, H., Vastano, J.: Determining lyapunov exponents from a time series. Phys. D 16(15), 285–317 (1985)
Kapitaniak, T., Leonov, G.: Multistability: uncovering hidden attractors. Eur. Phys. J.-Spec. Top. 224(8), 1405–1408 (2015)
Banerjee, S., Yorke, J.A., Grebogi, C.: Robust chaos. Phys. Rev. Lett. 80, 3049–3052 (1998)
Salcedo, A., Alvarez, J.: Oscillations in first-order, continuous-time systems via time-delay feedback. Complexity (2018)
Pincus, S.M.: Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. U. S. A. 88(6), 2297–2301 (1991)
Bandt, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88(17), 174102 (2002)
Wang, Y., Liu, Z., Zhang, L.Y., Pareschi, F., Setti, G., Chen, G.: From chaos to pseudorandomness: a case study on the 2-d coupled map lattice. IEEE T. Cybern. pp. 1–11 (2021)
Hong, Z., Xieting, L.: Generating chaotic secure sequences with desired statistical properties and high security. Int. J. Bifurc. Chaos 7(01), 205–213 (1997)
Lempel, A., Ziv, J.: On the complexity of finite sequences. IEEE Trans. Inform. Theory 22(1), 75–81 (1976)
Funding
This work was supported by the National Key R &D Program of China [Grant Number 2017YFB0802000]; and the Key R &D Program of Hubei Province [Grant Number 2020BAB104].
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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 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.
About this article
Cite this article
Ming, H., Hu, H., Lv, F. et al. A high-performance hybrid random number generator based on a nondegenerate coupled chaos and its practical implementation. Nonlinear Dyn 111, 847–869 (2023). https://doi.org/10.1007/s11071-022-07838-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-022-07838-0