True Random-Bit Generation Using a Continuous-Time Chaotic Oscillator Abstract - This paper presents a true random-bit generation through a continuous-time chaotic oscillator, which provides automatically chaotic signals and is fully implemented on 0.18 CMOS standard technology. Chaotic dynamics of the oscillator are exhibited in terms of chaotic strange attractor in phase-space domain. In order to achieve true-random property, a simple designed of post-processing method is utilized. Finally, the quality of randomness is analyzed through 1,000,000 binary sequences which are verified by statistical test methods and NIST standard tests suite. The proposed system has offered a cost-effective and a compact random-bit generator for computer security applications. I. Introduction Due to increasing demand of data storage on the internet, an information security has become a significant issue in both industrial and research fields. During the last decade, data encryption has been the best solution for the information security where searching for an effective key generation has still motivated many researchers. Basically, several key generations have been performed by random number generator (RNG). However, since rapidly advance in computer technology, pure RNG might not be acceptable against an advanced cryptography algorithm. For this reason, true random number generator (TNRG) is widely utilized many applications not only the encryption, but also cryptography as well as some searching algorithm. Thus, extraction of proper randomness source is still a challenging topic in the research area. Recently, chaotic system has been extensively studied due to various fascinating properties such as extremely sensitivity on initial conditions and impossible for prediction. Several chaotic-based TNRG have been proposed using discrete-time chaotic map, for example, logistic map [1], tent map [2] and piecewise-linear chaotic map [3-4]. Such systems provide robust chaotic signals through a one-dimensional chaotic function and are proper as the random sources. On the other hand, implementation on large-scale integrated (LSI) circuits is still challenging. A continuous-time chaotic system has attracted a great attention since a discovery of Chua’s circuit [5], where the chaotic dynamic derives from a set of ordinary-differential equation (ODE). Several oscillators based on such a system have been presented such as Chen’s system oscillator [6] and Van Der Pol oscillator [7]. These circuits truly provide the chaotic behavior, but inappropriate for transistor level due to large value of passive components. Recently presented by Radwan et al. [8] and Güler et al. [9] have suggested the appropriate chaotic oscillator for the LSI design, where the circuit is simply designed based on a Gm-C integrator and a push-pull inverter. Therefore, this paper presents a true random-bit generation which a continuous-time chaotic oscillator is employed as the random signals source. The chaotic behavior of the oscillator is firstly examined through the chaotic attractor, waveform in time and frequency domain (Section 2). Section 3 describes the structural of overall TNRG system. In section 4, the statistical test methods i.e., histogram, autocorrelation and NIST standard test suite are used in order to verify the randomness of bit sequences. II. Double-Score-Like Chaotic Oscillator Typically, the chaotic oscillator can be synthesized based on three-dimensional ODE [10] system which is given by   ) ( x G x x x x             (1) where G(x) and λ are a nonlinear function and adjusting parameter, respectively. Various approaches have been implemented by using a signum function as a nonlinear function, thus, dual supply is required. In this paper, a nonlinear function is consequently replaced by the hyperbolic tangent in order to operate on a single supply. Fig. 1 illustrates the chaotic oscillator comprises three stage of Gm-C integrators, current mirror circuits and approximated hyperbolic tangent portion. As a result, the set of first-order ODE system can be expressed as     ) (tanh 1 2 3 c b ax v v v C g v v C g v v C g v z y x z z y y x             (2) Chatchai Wannaboon Electronic and Photonic System Engineering Kochi University of Technology Tosayamada, Kami-City, Kochi, 782-8502, Japan e-mail : 198007y@gs.kochi-tech.ac.jp Tachibana Masayoshi Electronic and Photonic System Engineering Kochi University of Technology Tosayamada, Kami-City, Kochi, 782-8502, Japan e-mail : tachibana.masayoshi@kochi-tech.ac.jp SASIMI 2016 Proceedings R2-15 - 158 -