论文标题
用于离散值机制的紧密差异隐私以及使用FFT的下采样高斯机制
Tight Differential Privacy for Discrete-Valued Mechanisms and for the Subsampled Gaussian Mechanism Using FFT
论文作者
论文摘要
我们提出了一个数字会计师，用于评估具有离散一维输出的算法的紧密$（\ varepsilon，δ）$ - 隐私损失。该方法基于隐私损失分配形式主义，它使用了最近引入的快速基于傅立叶变换的会计技术。我们根据隐私损失分布的力矩界限对方法进行了错误分析，这会导致真实$（\ varepsilon，δ）$ - 值的严格下限和上限。作为一种应用，我们提出了一种新颖的方法，可以准确地对上采样的高斯机制进行隐私会计。这通过为隐私参数提供严格的下限和上限来完成先前提出的分析。我们证明了会计师在二项式机制上的性能，并表明我们的方法允许与文献中现有界限相比，在同样隐私处将噪声方差降低到75％。我们还说明了如何计算用于计数查询的指数机制的紧密界限。
We propose a numerical accountant for evaluating the tight $(\varepsilon,δ)$-privacy loss for algorithms with discrete one dimensional output. The method is based on the privacy loss distribution formalism and it uses the recently introduced fast Fourier transform based accounting technique. We carry out an error analysis of the method in terms of moment bounds of the privacy loss distribution which leads to rigorous lower and upper bounds for the true $(\varepsilon,δ)$-values. As an application, we present a novel approach to accurate privacy accounting of the subsampled Gaussian mechanism. This completes the previously proposed analysis by giving strict lower and upper bounds for the privacy parameters. We demonstrate the performance of the accountant on the binomial mechanism and show that our approach allows decreasing noise variance up to 75 percent at equal privacy compared to existing bounds in the literature. We also illustrate how to compute tight bounds for the exponential mechanism applied to counting queries.
