Random number generation with a chaotic electromechanical resonator

Abstract

Chaos enables the emergence of randomness in deterministic physical systems. Therefore it can be exploited for the conception of true random number generators (RNG) mandatory in classical cryptography applications. Meanwhile, nanomechanical oscillators, at the core of many on-board functionalities such as sensing, reveal as excellent candidates to behave chaotically. This is made possible thanks to intrinsic mechanical nonlinearities emerging at the nanoscale. Here we present a platform gathering a nanomechanical oscillator and its integrated capacitive actuation. Using a modulation of the resonant force induced by the electrodes, we demonstrate chaotic dynamics and study how it depends on the dissipation of the system. The randomness of a binary sequence generated from a chaotic time trace is evaluated and discussed such that the generic parameters enabling successful random number generation can be established. This demonstration makes use of concepts which are sufficiently general to be applied to the next generation of nano-electro-optomechanical systems.

FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points

“…with K > 0 and α z = 2E x + 2E y + E z exponentially stabilizes the new chaotic jerk systems (18) and ( 19) for all initial states in R 3 .…”

“…Mechanical dynamical systems have several applications in chaos theory [1][2][3][4]. For instance, Reis and Savi [1] studied quasi-periodic and spatiotemporal chaotic responses in a conservative Duffing-type mechanical system with cubic nonlinearity.…”

“…Using Lyapunov stability theory and power spectrum analysis, Cai et al [2] studied the periodic motion and chaos in the dynamics of a van der Pol (VDP) oscillator. Madiot et al [3] demonstrated dissipative chaotic motion in an electromechanical resonator. Balamurali et al [4] investigated the generation of multi-scroll chaos in coupled Rayleigh-Duffing oscillators.…”

“…To represent the jerk system in a set of 3-D equations, (1) presents a system of ordinary differential equations (ODE), for which one can use the phase variables given in ( 2), so that one can rewrite the jerk differential equations as described by (3), where F(x, y, z) represents the nonlinear dynamics that the system uses to drive different chaotic behaviors.…”

“…Rajagopal et al [14] proposed a new dissipative chaotic jerk system with two quadratic nonlinearities, discussed its dynamic properties, and provided a circuit realization of the new jerk system. Chaotic jerk systems have applications in many areas, such as oscillators [3,15], microcontrollers [16], circuits [17,18], memristors [19,20], encryption [21], etc.…”