A new randomness test solving problems of Discrete Fourier Transform Test

TL;DR

This paper introduces a new randomness test based on the variance of the power spectrum, providing a theoretical reference distribution and demonstrating improved detection power over the traditional DFTT.

Contribution

It proposes a novel randomness test with a derivable theoretical distribution, addressing a key limitation of the existing DFTT.

Findings

The new test has stronger detection power than DFTT.

The reference distribution of the test statistic can be theoretically derived.

Experiments confirm improved periodic feature detection.

Abstract

Discrete Fourier Transform Test (DFTT), which is a randomness test included in NIST SP800-22, has a problem. It is that theoretical reference distribution of the test statistic has not been derived. In this paper, we propose a new test using variance of power spectrum as the test statistic, whose reference distribution can be theoretically derived. The purpose of DFTT is to detect periodic features and that of the proposed test is the same. We make some experiments and show that the proposed test has stronger detection power than DFTT.