On the Evaluation Criteria for Random Number Generators Using Monte Carlo Integration Algorithm

Book Publisher International (a part of SCIENCEDOMAIN International), pp. 126–150

Abstract

Among all the manifestations of chaos in various scientific fields, deriving Random Number Generators by the use of chaotic systems is widely investigated. Although the fundamental premise of the chaos theory states determinism in the resulting series, with the extreme sensitivity and dependence on the initial conditions of the system, one could address the problem of randomness in the realms of chaos theory. In this study, we present 8 defined mathematical schemes applying to the experimental data extracted from capacitors’ voltages of the classical configuration of Chua’s circuit. Each of the 8 suggested schemes operate as functions aiming for the generation of randomly distributed values and are eventually compared with the commercially common timer-based random generators. The Monte Carlo Integration Algorithm, the evaluator method of the research, indicates the spectral distributed data and then the ranking of the schemes has been proceeded through a visualization of the supposed algorithm. As the geometrical domain in the Monte Carlo Integration has defined in such a way that the most randomly scattered data set would result in a closer estimation of the number Pi, the suggested scheme, Frequency indicator, is evaluated as the highest-ranked scheme in that regard, with the estimated numerical value of 3.1424 for Pi.

Authors 4

1. Aidin Momtaz

   Isfahan University of Technology

   Affiliation as printed

   Department of Physics, Isfahan University of Technology, Isfahan, Iran

2. Ehsan Qoreishi

   Isfahan University of Technology

   Affiliation as printed

   Department of Physics, Isfahan University of Technology, Isfahan, Iran

3. Sarah Amini

   K. N. Toosi University of Technology

   Affiliation as printed

   Department of Computer Engineering, K. N. Toosi University of Technology, Tehran, Iran

4. Sanaz Haddadian

   Paderborn University

   Affiliation as printed

   System and Circuit Technology Group, Heinz Nixdorf Institute, University of Paderborn, Paderborn, Germany