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arXiv 2012.10523cs.CRstat.ML
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$(ε, δ)$ -差分私有高斯机制的封闭形式标度

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

Staal A. Vinterbo

摘要:

用于通过添加具有方差$σ^2$的零均值高斯噪声来提供$(ε, δ)$ -差分隐私的$σ$上的标准闭合形式下限是用于$ε\in (0,1)$的$σ> Δ\sqrt {2}(ε^{-1}) \sqrt {\log \left( 5/4δ^{-1} \right)}$。如果$δ\leq 1/2$和$(a,s)=(π/4,-1)$不相同,我们给出了$z=-\log(4δ(1-δ))$和$(a,s)=(1,1)$的类似封闭形式界$σ\geq Δ(ε\sqrt{2})^{-1} \left(\sqrt{az+ε} + s\sqrt{az}\right)$。我们的界对所有$ε> 0$都有效,并且总是更低(更好)。我们还提出了一个充分条件$(ε, δ)$ -差分隐私时,根据均匀分布的噪声和对数凹密度支持无处不在。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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