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

12/18/2020
by   Staal A. Vinterbo, et al.
0

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

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/23/2022

Differential privacy for symmetric log-concave mechanisms

Adding random noise to database query results is an important tool for a...
research
08/28/2019

Rényi Differential Privacy of the Sampled Gaussian Mechanism

The Sampled Gaussian Mechanism (SGM)---a composition of subsampling and ...
research
01/31/2023

Gaussian Noise is Nearly Instance Optimal for Private Unbiased Mean Estimation

We investigate unbiased high-dimensional mean estimators in differential...
research
03/31/2020

The Discrete Gaussian for Differential Privacy

We show how to efficiently provide differentially private answers to cou...
research
09/26/2018

Optimal Noise-Adding Mechanism in Additive Differential Privacy

We derive the optimal (0, δ)-differentially private query-output indepen...
research
03/15/2021

A Central Limit Theorem for Differentially Private Query Answering

Perhaps the single most important use case for differential privacy is t...
research
12/21/2019

Closed Form Variances for Variational Auto-Encoders

We propose a reformulation of Variational Auto-Encoders eliminating half...

Please sign up or login with your details

Forgot password? Click here to reset