Analytic Theory to Differential Privacy

The purpose of this paper is to develop a mathematical analysis theory to solve differential privacy problems. The heart of our approaches is to use analytic tools to characterize the correlations among the outputs of different datasets, which makes it feasible to represent a differentially private mechanism with minimal number of parameters. These results are then used to construct differentially private mechanisms analytically. Furthermore, our approaches are universal to almost all query functions. We believe that the approaches and results of this paper are indispensable complements to the current studies of differential privacy that are ruled by the ad hoc and algorithmic approaches.