Introducing the truly chaotic finite state machines and their applications in security field

TL;DR

This paper presents truly chaotic finite state machines, explores their mathematical foundations, and demonstrates their potential applications in security, particularly in hash functions, highlighting their chaotic behavior with slight input changes.

Contribution

It introduces a new class of chaotic finite state machines and formalizes their behavior using chaotic iterations, expanding the understanding of chaos in computational models.

Findings

Finite state machines can exhibit chaotic behavior with small input changes

Mathematical formalization using chaotic iterations

Application example in hash functions

Abstract

The truly chaotic finite machines introduced by authors in previous research papers are presented here. A state of the art in this discipline, encompassing all previous mathematical investigations, is provided, explaining how finite state machines can behave chaotically regarding the slight alteration of their inputs. This behavior is explained using Turing machines and formalized thanks to a special family of discrete dynamical systems called chaotic iterations. An illustrative example is finally given in the field of hash functions.