Topological chaos and chaotic iterations. Application to Hash functions
This work addresses the need for highly unpredictable algorithms in information security, offering a novel theoretical foundation with practical applications.
The paper tackles the problem of designing unpredictable algorithms by linking chaotic iterations to Devaney's topological chaos, resulting in algorithms that produce true topological chaos and are applied to information security.
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.