We study the pointwise maximal leakage (PML) envelope of the Gaussian mechanism, which characterizes the smallest information leakage bound that holds with high probability under arbitrary post-processing. For the Gaussian mechanism with a Gaussian secret, we derive a closed-form expression for the deterministic PML envelope for sufficiently small failure probabilities. We then extend this result to general unbounded secrets by identifying a sufficient condition under which the envelope coincides with the Gaussian case. In particular, we show that strongly log-concave priors satisfy this condition via an application of the Brascamp-Lieb inequality.

翻译：本文研究高斯机制的点态最大泄露（PML）包络，该包络刻画了在任意后处理下以高概率成立的最小信息泄露界。对于具有高斯秘密的高斯机制，我们针对足够小的失效概率导出了确定性PML包络的闭式表达式。随后，通过识别一个充分条件——在该条件下包络与高斯情形一致，我们将此结果推广至一般无界秘密。特别地，我们借助Brascamp-Lieb不等式的应用，证明了强对数凹先验满足该条件。