due to the (probabilistic) correlation with public observables. In this talk we will report on one of the most recent
proposals to formalize the notion of the vulnerability of the secrets. This approach offers a rich operational model
of the attacker, based on decision theory, and it turns out that it is characterized by a surprisingly simple set of axioms.
Then, we will discuss the relation with the axiomatic systems defining Shannon and Renyi information theory,
which have been the foundations of the most popular proposal for (quantitative) language-based security so far,
thus providing an axiomatically structured view of the field.