text: Differential privacy is a notion that has emerged in the community of statistical databases, as a response to the problem of protecting the privacy of the database's participants when performing statistical queries. The idea is that a randomized query satisfies differential privacy if the likelihood of obtaining a certain answer for a database x is not too different from the likelihood of obtaining the same answer on adjacent databases, i.e. databases which differ from x for only one individual. Information flow is an area of Security concerned with the problem of controlling the leakage of confidential information in programs and protocols. Nowadays, one of the most established approaches to quantify and to reason about leakage is based on the Renyi min entropy version of information theory. In this paper, we analyze critically the notion of differential privacy in light of the conceptual framework provided by the Renyi min information theory. We show that there is a close relation between differential privacy and leakage, due to the graph symmetries induced by the adjacency relation. Furthermore, we consider the utility of the randomized answer, which measures its expected degree of accuracy. We focus on certain kinds of utility functions called "binary", which have a close correspondence with the Renyi min mutual information. Again, it turns out that there can be a tight correspondence between differential privacy and utility, depending on the symmetries induced by the adjacency relation and by the query. Depending on these symmetries we can also build an optimal-utility randomization mechanism while preserving the required level of differential privacy. Our main contribution is a study of the kind of structures that can be induced by the adjacency relation and the query, and how to use them to derive bounds on the leakage and achieve the optimal utility.
  @cite_4: Two kinds of integrity measures—contamination and suppression—are introduced. Contamination measures how much untrusted information reaches trusted outputs; it is the dual of information-flow confidentiality. Suppression measures how much information is lost from outputs; it does not have a confidentiality dual. Two forms of suppression are considered: programs and channels. Program suppression measures how much information about the correct output of a program is lost because of attacker influence and implementation errors. Channel suppression measures how much information about inputs to a noisy channel is missing from channel outputs. The relationship between quantitative integrity, confidentiality, and database privacy is examined.
summary: Clarkson and Schneider also considered differential privacy as a case study of their proposal for quantification of integrity @cite_4 . There, the authors analyze database privacy conditions from the literature (such as differential privacy, @math -anonymity, and @math -diversity) using their framework for utility quantification. In particular, they study the relationship between differential privacy and a notion of leakage (which is different from ours - in particular their definition is based on Shannon entropy) and they provide a tight bound on leakage.