  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.
