The Noisy Max mechanism and its variations are fundamental private selection algorithms that are used to select items from a set of candidates (such as the most common diseases in a population), while controlling the privacy leakage in the underlying data. A recently proposed extension, Noisy Top-k with Gap, provides numerical information about how much better the selected items are compared to the non-selected items (e.g., how much more common are the selected diseases). This extra information comes at no privacy cost but crucially relies on infinite precision for the privacy guarantees. In this paper, we provide a finite-precision secure implementation of this algorithm that takes advantage of integer arithmetic.

翻译：带噪最大值机制及其变体是基础的私有选择算法，用于从候选集合中（如人群中最常见疾病）筛选项目，同时控制底层数据的隐私泄露。近期提出的扩展算法——带间隔的Top-k带噪最大值，可提供被选项目相较于未选项目的数值优势信息（例如所选疾病的常见程度差异）。该额外信息无需额外隐私成本，但其隐私保障严格依赖于无限精度计算。本文提出一种利用整数运算的有限精度安全实现方案。