Analysis of Random Number Generators Based on Fibonacci-Galois Ring Oscillators

Abstract

This paper presents the analysis of random number generators(RNGs) based on regular sampling of irregular waveform method where the irregular signal is obtained from the oscillations of combined Fibonacci and Galois ring oscillators. As the proposed random number generator is made up of logic gates only, it is implemented on a FPGA (field-programmable gate array). The regular waveform generated by the digital clock manager of the FPGA is used for sampling the irregular signal and the resulting bit stream is uploaded to a computer where it is subjected to standard statistical test. The polynomials defining the Fibonacci and Galois ring oscillators are varied to assess the relationship between the polynomial and the randomness of the output bit stream. It is demonstrated that for both polynomial functions, by combining enough number of oscillator structures, the output bit streams from each RNG satisfy standard statistical tests without post processing. To the best of our knowledge, this paper presents the first comparative study on the impact of polynomials on random number generators based on Fibonacci and Galois ring oscillators.