Unified Interpretation of the Gaussian Mechanism for Differential Privacy Through the Sensitivity Index

The Gaussian mechanism (GM) represents a universally employed tool for achieving differential privacy (DP), and large body of work has been devoted to its analysis. We argue that the three prevailing interpretations GM, namely epsilon/delta-DP, f-DP Rényi DP can be expressed by using single parameter psi, which we term sensitivity index. Psi uniquely characterises GM properties encapsulating two fundamental quantities: query magnitude noise perturbation. With strong links ROC curve hypothesis-testing interpretation DP, psi offers practitioner powerful method interpreting, comparing communicating guarantees mechanisms.