Non-detectable patterns hidden within sequences of bits

TL;DR

This paper constructs special bit sequences from combinatorial objects with symmetries and demonstrates that standard NIST randomness tests fail to detect these hidden patterns, highlighting limitations in current testing methods.

Contribution

It introduces a novel method for generating sequences with concealed symmetries and shows their undetectability by established NIST tests.

Findings

Sequences exhibit symmetries undetected by NIST tests

Combinatorial methods can produce non-random-looking sequences

Highlights limitations of current randomness testing suites

Abstract

In this paper we construct families of bit sequences using combinatorial methods. Each sequence is derived by con- verting a collection of numbers encoding certain combinatorial nu- merics from objects exhibiting symmetry in various dimensions. Using the algorithms first described in [1] we show that the NIST testing suite described in publication 800-22 does not detect these symmetries hidden within these sequences.