A Floating-Point Secure Implementation of the Report Noisy Max with Gap Mechanism

TL;DR

This paper presents a finite-precision, secure implementation of the Noisy Top-k with Gap mechanism, enabling private data selection with numerical insights without sacrificing privacy guarantees.

Contribution

It introduces a floating-point secure implementation of the Noisy Top-k with Gap mechanism using integer arithmetic, ensuring privacy in finite-precision environments.

Findings

Provides a secure implementation using integer arithmetic

Maintains privacy guarantees with finite precision

Enables practical use of the Gap mechanism in real systems

Abstract

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.