Producing Quality Pseudorandomness with a Generalized Gauss Continued-Fraction Map

TL;DR

This paper explores the use of generalized Gauss continued-fraction maps to generate high-quality pseudorandomness, outperforming standard generators in statistical tests, and suggests their potential for cryptographic applications.

Contribution

It introduces the use of $r$-continued-fraction maps for pseudorandom generation, demonstrating their superior statistical quality over common generators like Mersenne Twister.

Findings

Generated pseudorandom output outperforms standard generators in statistical tests.

$r$-continued-fraction maps show promise as a basis for novel pseudorandom generators.

Practical motivation for further study of these maps' properties.

Abstract

Well-known chaotic maps, such as the logistic and tent maps, have been used to generate cryptographically secure pseudorandomness, yet we know of no efforts which attempt to use the Gauss continued-fraction map, a known chaotic map, as a starting point for producing quality pseudorandom output. In this paper, we consider the family of $r$-continued-fraction maps, which generalize the Gauss map, and use them to generate pseudorandom output which outperforms many standard generators, such as the Mersenne Twister, in statistical quality, as ascertained by use of the Dieharder, PractRand, and TestU01 suites. In this way, we demonstrate the potential viability of these maps as a starting point for novel generators, and provide practical motivation for further study of the properties of both the exact and finite-precision $r$-continued fraction maps.