  Chaotic iterations, a tool formerly used in distributed computing, has
recently revealed various interesting properties of disorder leading to its use
in the computer science security field. In this paper, a comprehensive study of
its topological behavior is proposed. It is stated that, in addition to being
chaotic as defined in the Devaney's formulation, this tool possesses the
property of topological mixing. Additionally, its level of sensibility,
expansivity, and topological entropy are evaluated. All of these properties
lead to a complete unpredictable behavior for the chaotic iterations. As it
only manipulates binary digits or integers, we show that it is possible to use
it to produce truly chaotic computer programs. As an application example, a
truly chaotic hash function is proposed in two versions. In the second version,
an artificial neural network is used, which can be stated as chaotic according
to Devaney.
