Basic Differentially Private Mechanisms

Abstract

This chapter presents simple mechanisms for signal filtering under differential privacy constraints, which add white noise directly on the sensitive input signals or at the output of a desired filter. We introduce concrete examples of adjacency relations for individual and collective privacy-sensitive input signals. We then describe the Laplace and Gaussian mechanisms to enforce (formula presented)- or (formula presented)-differential privacy with respect to these adjacency relations, by adding Laplace and Gaussian noise respectively. For these mechanisms, adding noise at the output of the desired filter requires computing the sensitivity of this filter with respect to the signal variations allowed by the chosen adjacency relation.