A topological chaos framework for hash functions

TL;DR

This paper introduces a novel method for creating hash functions using discrete chaotic iterations and topological chaos, providing mathematical proofs and tools to evaluate their properties.

Contribution

It establishes a theoretical framework linking chaotic iterations to topological chaos for hash function design, with practical measurement tools.

Findings

Discrete chaotic iterations are a particular case of topological chaos.

Tools from topological chaos can evaluate hash function properties.

An example demonstrates the practical creation of hash functions.

Abstract

This paper presents a new procedure of generating hash functions which can be evaluated using some mathematical tools. This procedure is based on discrete chaotic iterations. First, it is mathematically proven, that these discrete chaotic iterations can be considered as a \linebreak particular case of topological chaos. Then, the process of generating hash function based on the \linebreak topological chaos is detailed. Finally it is shown how some tools coming from the domain of \linebreak topological chaos can be used to measure quantitatively and qualitatively some desirable properties for hash functions. An illustration example is detailed in order to show how one can create hash functions using our theoretical study. Key-words : Discrete chaotic iterations. Topological chaos. Hash function