A closed form scale bound for the (ε, δ)-differentially private Gaussian Mechanism valid for all privacy regimes

Abstract

The standard closed form lower bound on for providing (, )-differential privacy by adding zero mean Gaussian noise with variance ^2 is > 2(^-1) ( 5/4^-1 ) for (0,1). We present a similar closed form bound (2)^-1 (az+ + saz) for z=-(4(1-)) and (a,s)=(1,1) if 1/2 and (a,s)=(/4,-1) otherwise. Our bound is valid for all > 0 and is always lower (better). We also present a sufficient condition for (, )-differential privacy when adding noise distributed according to even and log-concave densities supported everywhere.

Tasks

Reproductions