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

An optimization technique on pseudorandom generators based on chaotic iterations

International audienceInternet communication systems involving cryptography and data hiding often require billions of random numbers. In addition to the speed of the algorithm, the quality of the pseudo-random number generator and the ease of its implementation are common practical aspects. In this work we will discuss how to improve the quality of random numbers independently from their generation algorithm. We propose an additional implementation technique in order to take advantage of some chaotic properties. The statistical quality of our solution stems from some well-defined discrete chaotic iterations that satisfy the reputed Devaney's definition of chaos, namely the chaotic iterations technique. Pursuing recent researches published in the previous International Conference on Evolving Internet (Internet 09, 10, and 11), three methods to build pseudorandom generators by using chaotic iterations are recalled. Using standard criteria named NIST and DieHARD (some famous batteries of tests), we will show that the proposed technique can improve the statistical properties of a large variety of defective pseudorandom generators, and that the issues raised by statistical tests decrease when the power of chaotic iterations increase

Discrete Particle Swarm Optimization for Flexible Flow Line Scheduling

Previous research on scheduling flexible flow lines (FFL) to minimize makespan has utilized approaches such as branch and bound, integer programming, or heuristics. Metaheuristic methods have attracted increasing interest for solving scheduling problems in the past few years. Particle swarm optimization (PSO) is a population-based metaheuristic method which finds a solution based on the analogy of sharing useful information among individuals. In the previous literature different PSO algorithms have been introduced for various applications. In this research we study some of the PSO algorithms, continuous and discrete, to identify a strong PSO algorithm in scheduling flexible flow line to minimize the makespan. Then the effectiveness of this PSO algorithm in FFL scheduling is compared to genetic algorithms. Experimental results suggest that discrete particle swarm performs better in scheduling of flexible flow line with makespan criteria compared to continuous particle swarm. Moreover, combining discrete particle swarm with a local search improves the performance of the algorithm significantly and makes it competitive with the genetic algorithm (GA)

Orbital structure of the GJ876 extrasolar planetary system, based on the latest Keck and HARPS radial velocity data

We use full available array of radial velocity data, including recently published HARPS and Keck observatory sets, to characterize the orbital configuration of the planetary system orbiting GJ876. First, we propose and describe in detail a fast method to fit perturbed orbital configuration, based on the integration of the sensitivity equations inferred by the equations of the original $N$-body problem. Further, we find that it is unsatisfactory to treat the available radial velocity data for GJ876 in the traditional white noise model, because the actual noise appears autocorrelated (and demonstrates non-white frequency spectrum). The time scale of this correlation is about a few days, and the contribution of the correlated noise is about 2 m/s (i.e., similar to the level of internal errors in the Keck data). We propose a variation of the maximum-likelihood algorithm to estimate the orbital configuration of the system, taking into account the red noise effects. We show, in particular, that the non-zero orbital eccentricity of the innermost planet \emph{d}, obtained in previous studies, is likely a result of misinterpreted red noise in the data. In addition to offsets in some orbital parameters, the red noise also makes the fit uncertainties systematically underestimated (while they are treated in the traditional white noise model). Also, we show that the orbital eccentricity of the outermost planet is actually ill-determined, although bounded by $\sim 0.2$. Finally, we investigate possible orbital non-coplanarity of the system, and limit the mutual inclination between the planets \emph{b} and \emph{c} orbits by $5^\circ-15^\circ$, depending on the angular position of the mutual orbital nodes.Comment: 36 pages, 11 figures, 3 tables; Accepted to Celestial Mechanics and Dynamical Astronom

Optimal Tuning of PD controllers using Modified Artificial Bee Colony Algorithm

This paper presents an investigation of PD controller tuning using a modified artificial bee colony algorithm (MABC). The main purpose of this work is to apply and investigates the performance of MABC in tuning the PD controller of single link manipulator system (SLMS) in comparison with the original ABC. The objective of the MABC algorithm is to minimize the error by using mean square error (MSE) as an objective function. The proposed algorithm has also been tested in three benchmark functions with different dimensions to checked the robustness of the algorithm in different problems surface. The result shows that the MABC able to tune the controller to their best optimum value