Topological chaos and chaotic iterations. Application to Hash functions

TL;DR

This paper develops a new class of chaotic algorithms based on chaotic iterations, linking them to topological chaos, and demonstrates their potential for secure applications like hash functions.

Contribution

It introduces a novel framework connecting chaotic iterations with topological chaos, enabling the design of highly unpredictable algorithms for security purposes.

Findings

Algorithms exhibit topological chaos under certain conditions

Practical implementations produce true chaotic behavior

Applications in information security, such as hash functions

Abstract

This paper introduces a new notion of chaotic algorithms. These algorithms are iterative and are based on so-called chaotic iterations. Contrary to all existing studies on chaotic iterations, we are not interested in stable states of such iterations but in their possible unpredictable behaviors. By establishing a link between chaotic iterations and the notion of Devaney's topological chaos, we give conditions ensuring that these kind of algorithms produce topological chaos. This leads to algorithms that are highly unpredictable. After presenting the theoretical foundations of our approach, we are interested in its practical aspects. We show how the theoretical algorithms give rise to computer programs that produce true topological chaos, then we propose applications in the area of information security.