Differential privacy is a notion of privacy that has become very popular in
the database community. Roughly, the idea is that a randomized query mechanism
provides sufficient privacy protection if the ratio between the probabilities
of two different entries to originate a certain answer is bound by e^\epsilon.
In the fields of anonymity and information flow there is a similar concern for
controlling information leakage, i.e. limiting the possibility of inferring the
secret information from the observables. In recent years, researchers have
proposed to quantify the leakage in terms of the information-theoretic notion
of mutual information. There are two main approaches that fall in this
category: One based on Shannon entropy, and one based on R\'enyi's min entropy.
The latter has connection with the so-called Bayes risk, which expresses the
probability of guessing the secret. In this paper, we show how to model the
query system in terms of an information-theoretic channel, and we compare the
notion of differential privacy with that of mutual information. We show that
the notion of differential privacy is strictly stronger, in the sense that it
implies a bound on the mutual information, but not viceversa
