Differential privacy: an information-theoretic approach to preserve privacy in datasets

In large datasets, anonymization may be not enough to preserve privacy. In recent years to tackle privacy preservation in datasets, it has been proposed a mathematical approach called differential privacy, which is the topic of this thesis. We start by giving some simple examples and illustrate necessary conditions that allow privacy. We then define differential privacy and we study basic mechanisms, i.e. randomized response and the Laplace method, to preserve privacy when releasing public datasets. We then move to analyse weaker notions of privacy that still provide privacy protection. In this context we introduce the Renyi divergence. The latter allows us to study the Gaussian mechanism. In conclusion we study the exponential mechanism, which preserves more general sets of properties.