Goodness-of-fit and Randomness Tests For The Sun’s Emissions True Random Number Generator Süleyman Gökhun Tanyer Department of Electrical and Electronics Engineering Faculty of Engineering, Başkent University Eskisehir yolu 20. km., Etimesgut, 06810 Ankara, Turkey E-mail: gokhun.tanyer@gmail.com, gokhuntanyer@baskent.edu.tr Kumru Didem Atalay Education in Medicine Faculty of Medicine Başkent University, Bahcelievler, Ankara, Turkey Sıtkı Çağdaş İnam Department of Electrical and Electronics Engineering Faculty of Engineering, Başkent University Eskisehir yolu 20. km., Etimesgut, 06810 Ankara, Turkey Abstract—Random number generators (RNGs) are one of the key tools necessary for statistical analysis and optimization methods such as Monte Carlo, particle swarm optimization (PSO) and the genetic algorithm. Various pseudo and true RNGs are available today, and they provide sufficient randomness. Unfortunately, they generate data that do not always represent the required distribution accurately, especially when the data length is small. This could possibly threaten the ‘repeatability’ of an academic study. A novel true RNG (TRNG) using the method of uniform sampling (MUS) is recently proposed. In this work, the Sun’s RF emissions MUS-TRNG is comparatively tested with well known pseudo and true RNGs. It is observed that both randomness and very high goodness-of-fit qualities are possible. Keywords—random number generator, statistical signal processing, probability, test statistics, optimization. I. INTRODUCTION The modeling and simulation analysis of a system is generally motivated by the need to be able to predict its future behavior. Many problems encountered appear too complex to be understood in purely deterministic terms, it is often convenient to treat them statistically. [1]. If the system model inherits some amount of undeterministic behavior, then at least one of the variables should be modeled by a random variable. Then, the simulation requires some sets of observed samples for that random variable. Various statistical analysis problems in mathematics, physics and engineering have led to the development of methods for generating random data for a given distribution. Cumulative distribution function (CDF) and the probability density functions (PDF) are the theoretical asymptotical functions that define those distributions. Unfortunately, those functions are valid only when the number of observed samples converge infinity. In practical simulations however, CPU time and computer memory are some of the limiting factors, and the observed samples need to be tested for their goodness-of-fit and randomness. Various random number generators (RNGs) are available. In this work, the novel method of uniform sampling true RNG utilizing the Sun’s RF emissions [2] is tested for its goodness-of-fit and randomness for different number of observed samples. II. RANDOM NUMBER GENERATORS There are two principal methods used for the generation of random numbers; true and pseudo- RNGs. True RNGs use some sources of natural entropy; radioactive decay, cosmic background radiation, electronic noise etc. Pseudo RNGs use computational algorithms that provide long sequences of random results. These periodic sequences are defined by an initial value, known as a seed or key. For an observer with no prior information, pseudo RNGs are observed to yield sufficiently random sequences when the length of the observed sequence is shorter than its period. For an observer knowing the algorithm and the seed, pseudo RNG numbers are just deterministic computation results. If some algorithm is simple and its sequence is predictable, the generator is often referred to as quasi RNG. Today, it is known that hybrid algorithms could have the advantage of improved statistical qualities. III. THE SUN AS THE SOURCE OF ENTROPY The Sun radiates mainly in and around the visual band of the electromagnetic spectrum. However, due to its proximity, the Sun is also a bright celestial object in many other bands including the RF. Solar radio emission and the physical mechanisms behind this RF radiation have been reviewed by Shibasaki et al. [3]. The Sun can be used as the source of natural entropy to generate true RNG numbers. It is shown that true RNGs generally have good merits of randomness, unfortunately for short lengths of data i.e. 10,000 or less, goodness-of-fit metrics show discrepancies from their theoretical CDF [4]. A. RF Signal Processing In this paper, San Vito Solar Observatory (SVSO) data is used. SVSO is one of the observatories of the Radio Solar Telescope Network [5]. The part of the archival data that is used consists of 1 second binned radio flux from 8 distinct frequency bands obtained from 31 days in January 1990. The data were retrieved from the web page of National Geophysical Data Center (NGDC). Observed frequency bands