Paper 2022/066

A remark on the Discrete Fourier Transform statistical test

Anghel Florin and Asandoaiei David and Tabacaru Robert

Abstract

The study of randomness has always been a topic of significant relevance, and the importance of this topic in cryptography is undeniable. In this paper, we are going to provide a short introduction regarding pseudo-random number generators, their applications in cryptography and an analysis of the Discrete Fourier Transform statistical test. Our contribution is that of compiling the results of multiple runs on several popular pseudo-random number generators, and a Python implementation for computing the probability of a type II error. We intend to underline the weak points of the Discrete Fourier Transform test by showcasing results on large amounts of data, and showcase how testing bigger sequences of bits can help reduce the probability of type II errors.