Analysis of NIST SP800-22 focusing on randomness of each sequence

TL;DR

This paper analyzes the NIST SP800-22 randomness test suite by quantifying dependencies among test items through scalar histograms, providing visual insights and an algorithmic method to identify a minimal set of tests.

Contribution

It introduces a scalar-based approach to visualize dependencies in NIST SP800-22 and proposes an algorithm to derive a minimal test set based on histogram analysis.

Findings

Dependencies among test items are visually demonstrated.

A scalar histogram approach effectively reveals test dependencies.

An algorithm for minimal test set selection is proposed.

Abstract

NIST SP800-22 is a randomness test set applied for a set of sequences. Although SP800-22 widely used, a rational criterion throughout all test items has not been shown. The main reason is that the dependency of test items has not been perfectly clear. In this paper, a certain scalar is computed for each sequence throughout all test items and make the histogram of the scalar. By comparing the histogram and the theoretical distribution under some assumptions, the dependency is visually shown. In addition, an algorithmic method to derive "minimum set" using the histogram is proposed.