Discrete-Time Chaotic-Map Truly Random Number Generators: Design, Implementation, and Variability Analysis of the Zigzag Map

In this paper, we introduce a novel discrete chaotic map named zigzag map that demonstrates excellent chaotic behaviors and can be utilized in Truly Random Number Generators (TRNGs). We comprehensively investigate the map and explore its critical chaotic characteristics and parameters. We further present two circuit implementations for the zigzag map based on the switched current technique as well as the current-mode affine interpolation of the breakpoints. In practice, implementation variations can deteriorate the quality of the output sequence as a result of variation of the chaotic map parameters. In order to quantify the impact of variations on the map performance, we model the variations using a combination of theoretical analysis and Monte-Carlo simulations on the circuits. We demonstrate that even in the presence of the map variations, a TRNG based on the zigzag map passes all of the NIST 800-22 statistical randomness tests using simple post processing of the output data.Comment: To appear in Analog Integrated Circuits and Signal Processing (ALOG

Bifurcations and synchronization using an integrated programmable chaotic circuit

This paper presents a CMOS chip which can act as an autonomous stand-alone unit to generate different real-time chaotic behaviors by changing a few external bias currents. In particular, by changing one of these bias currents, the chip provides different examples of a period-doubling route to chaos. We present experimental orbits and attractors, time waveforms and power spectra measured from the chip. By using two chip units, experiments on synchronization can be carried out as well in real-time. Measurements are presented for the following synchronization schemes: linear coupling, drive-response and inverse system. Experimental statistical characterizations associated to these schemes are also presented. We also outline the possible use of the chip for chaotic encryption of audio signals. Finally, for completeness, the paper includes also a brief description of the chip design procedure and its internal circuitry

Chaotic dynamical systems associated with tilings of RN\R^N

In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of $\R^N$, whose most familiar example is provided by the $N-$dimensional torus \T ^N. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that it admits at least one positive Lyapunov exponent. Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup

Regular and stochastic behavior of Parkinsonian pathological tremor signals

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.Comment: 39 pages, 10 figures, 1 table Physica A, in pres

Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies

In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the descychnronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis. A new fast switching stability criterion here-in gives sufficiency of a fast-switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD

Design considerations for integrated continuous-time chaotic oscillators

This paper presents an optimization procedure to choose the chaotic state equation which is best suited for implementation using Gm-C integrated circuit techniques. The paper also presents an analysis of the most significant hardware nonidealities of Gm-C circuits on the chaotic operation-the basis to design robust integrated circuits with reproducible and easily controllable behavior. The techniques in the paper are illustrated through a circuit fabricated in 2.4-/iin double-poly technology.Comisión Interministerial de Ciencia y Tecnología TIC 96-1392-CO2-