Canonical noise distributions and private hypothesis tests

f-DP has recently been proposed as a generalization of differential privacy allowing lossless analysis composition, post-processing, and amplification via subsampling. In the setting f-DP, we propose concept canonical noise distribution (CND), first mechanism designed for an arbitrary guarantee. The notion CND captures whether additive perfectly matches guarantee given f. We prove that always exists, give construction produces any show private hypothesis tests are intimately related to CNDs, release p-values at no additional cost, well uniformly most powerful (UMP) binary data, within general framework. apply our techniques problem difference-of-proportions testing, construct UMP unbiased (UMPU) “semiprivate” test which upper bounds performance test. Using this benchmark, based on inversion characteristic functions, allows optimal inference two population parameters is nearly semiprivate UMPU. When specialized case (ϵ,0)-DP, empirically more than (ϵ/ 2)-DP accurate type I errors classic normal approximation