Using nanoresonators with robust chaos as hardware random number generators.

In this paper, we investigate theoretically the potential of a nanoelectromechanical suspended beam resonator excited by two-external frequencies as a hardware random number generator. This system exhibits robust chaos, which is usually required for practical applications of chaos. Taking advantage of the robust chaotic oscillations, we consider the beam position as a possible random variable and perform tests to check its randomness. The beam position collected at fixed time intervals is used to create a set of values that is a candidate for a random sequence of numbers. To determine how close to a random sequence this set is, we perform several known statistical tests of randomness. The performance of the random sequence in the simulation of two relevant physical problems, the random walk and the Ising model, is also investigated. An excellent overall performance of the system as a random number generator is obtained.

[1]  M. Roukes,et al.  Nonlinear dynamics and chaos in two coupled nanomechanical resonators , 2008, 0811.0870.

[2]  O. Gottlieb,et al.  Nonlinear damping in a micromechanical oscillator , 2009, 0911.0833.

[3]  W. San-Um,et al.  A 0.18-μm CMOS high-data-rate true random bit generator through ΔΣ modulation of chaotic jerk circuit signals. , 2018, Chaos.

[4]  A. Akhavan,et al.  A novel algorithm for image encryption based on mixture of chaotic maps , 2008 .

[5]  Philip Holmes,et al.  A magnetoelastic strange attractor , 1979 .

[6]  S. Brush.  History of the Lenz-Ising Model , 1967 .

[7]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[8]  Stephan Mertens,et al.  Pseudo Random Coins Show More Heads Than Tails , 2003 .

[9]  L. Kocarev.  Chaos-based cryptography: a brief overview , 2001 .

[10]  André Gusso,et al.  Analysis of the Chaotic Dynamics of MEMS/NEMS Doubly Clamped Beam Resonators with Two-Sided Electrodes , 2018, Int. J. Bifurc. Chaos.

[11]  M. Feigenbaum.  Quantitative universality for a class of nonlinear transformations , 1978 .

[12]  Steven W. Shaw,et al.  Chaotic vibrations of a beam with non-linear boundary conditions , 1983 .

[13]  L. Onsager.  Crystal statistics. I. A two-dimensional model with an order-disorder transition , 1944 .

[14]  Phatak,et al.  Logistic map: A possible random-number generator. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  Markus Rohe,et al.  Obtaining True-Random Binary Numbers from a Weak Radioactive Source , 2005, ICCSA.

[16]  Soo-Chang Pei,et al.  Evidence of the correlation between positive Lyapunov exponents and good chaotic random number sequences , 2004, Comput. Phys. Commun..

[17]  G. F. Newell,et al.  On the Theory of the Ising Model of Ferromagnetism , 1953 .

[18]  Kenichi Arai,et al.  A compact chaotic laser device with a two-dimensional external cavity structure , 2014 .

[19]  W G Dantas,et al.  Prediction of robust chaos in micro and nanoresonators under two-frequency excitation. , 2019, Chaos.

[20]  André Gusso,et al.  Analysis of the chaotic regime of MEMS/NEMS fixed–fixed beam resonators using an improved 1DOF model , 2015 .

[21]  Timon Rabczuk,et al.  A review on nanomechanical resonators and their applications in sensors and molecular transportation , 2015 .

[22]  André Gusso,et al.  Nonlinear dynamics and chaos in micro/nanoelectromechanical beam resonators actuated by two-sided electrodes , 2019, Chaos, Solitons & Fractals.

[23]  H. H. Nien,et al.  Digital color image encoding and decoding using a novel chaotic random generator , 2007 .

[24]  Alan M. Ferrenberg,et al.  Monte Carlo simulations: Hidden errors from "good" random number generators. , 1992, Physical review letters.

[25]  Joseph Rudnick,et al.  Elements of the random walk , 2004 .

[26]  Arantxa Uranga,et al.  CMOS-MEMS resonators , 2015 .

[27]  Nonlinear damping in suspended beam micro- and nanoresonators due to surface loss , 2020 .

[28]  Kurt Binder,et al.  A Guide to Monte Carlo Simulations in Statistical Physics: Frontmatter , 2009 .

[29]  G. Marsaglia,et al.  Some Difficult-to-pass Tests of Randomness , 2022 .

[30]  G. Vineyard.  The Number of Distinct Sites Visited in a Random Walk on a Lattice , 1963 .

[31]  Shaohua Zhang,et al.  Random Number Generation with Cosmic Photons. , 2016, Physical review letters.

[32]  A. Gusso.  Nonlinear damping in doubly clamped beam resonators due to the attachment loss induced by the geometric nonlinearity , 2016 .

[33]  L. E. Guerrero,et al.  Chaos-induced true randomness , 2002 .