We propose a numerical accountant for evaluating the tight $(\varepsilon,\delta)$-privacy loss for algorithms with discrete one-dimensional output. The method is based on the privacy loss distribution formalism and it is able to exploit the recently introduced Fast Fourier Transform based accounting technique. We carry out a complete error analysis of the method in terms of the moment bounds for the numerical estimate of the privacy loss distribution. We demonstrate the performance on the binomial mechanism and show that our approach allows decreasing noise variance up to an order of magnitude at equal privacy compared to existing bounds in the literature. We also give a novel approach for evaluating $(\varepsilon,\delta)$-upper bound for the subsampled Gaussian mechanism. This completes the previously proposed analysis by giving a strict upper bound for $(\varepsilon,\delta)$. We also illustrate how to compute tight bounds for the exponential mechanism applied to counting queries.

提出一种基于隐私损失分布的数值账本方法，用于准确隐私计算，尤其是对子采样高斯机制的严格上下界隐私参数的计算，并给出幂系数约束下的隐私损失分布的误差分析，应用于计数查询的指数机制的计算也满足严格下界隐私参数。

使用FFT的离散值机制和子采样高斯机制的严格差分隐私