论文标题
$（ε，δ）$的封闭式量表 - 差异化私人高斯机制有效
A closed form scale bound for the $(ε, δ)$-differentially private Gaussian Mechanism valid for all privacy regimes
论文作者
论文摘要
通过添加零平均高斯噪声$（ε，δ）$ - 差异噪声$σ^2 $是$σ>δ\ sqrt {2}（ε^{ - 1}）$ qrt（-1}） （0,1）$。我们提出了类似的封闭形式绑定$σ\geqδ（ε\ sqrt {2}）^{ - 1} \ left（\ sqrt {\ sqrt {az +ε} + s \ s \ s \ sqrt {az} {az} \ right）的$ 1/2 $和$（a，s）=（π/4，-1）$否则。我们的界限对所有$ε> 0 $都是有效的，并且总是较低（更好）。我们还提供了$（ε，δ）$差分隐私的足够条件，当添加根据均匀和对数孔的密度分布的噪声时，各处支持的噪声。
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 $σ> Δ\sqrt {2}(ε^{-1}) \sqrt {\log \left( 5/4δ^{-1} \right)}$ for $ε\in (0,1)$. We present a similar closed form bound $σ\geq Δ(ε\sqrt{2})^{-1} \left(\sqrt{az+ε} + s\sqrt{az}\right)$ for $z=-\log(4δ(1-δ))$ and $(a,s)=(1,1)$ if $δ\leq 1/2$ 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.
