Statistic Maximal Leakage

TL;DR

This paper introduces statistic maximal leakage, a privacy measure that quantifies information leakage about a specific secret, extending maximal leakage to focus on known secrets and analyzing its properties and mechanisms.

Contribution

It defines and analyzes statistic maximal leakage, demonstrating its properties, efficient computation for certain mechanisms, and comparing privacy-utility tradeoffs.

Findings

Quantization mechanism outperforms in privacy-utility tradeoffs.

Statistic maximal leakage satisfies composition and post-processing.

Efficient computation for deterministic mechanisms.

Abstract

We introduce a privacy measure called statistic maximal leakage that quantifies how much a privacy mechanism leaks about a specific secret, relative to the adversary's prior information about that secret. Statistic maximal leakage is an extension of the well-known maximal leakage. Unlike maximal leakage, which protects an arbitrary, unknown secret, statistic maximal leakage protects a single, known secret. We show that statistic maximal leakage satisfies composition and post-processing properties. Additionally, we show how to efficiently compute it in the special case of deterministic data release mechanisms. We analyze two important mechanisms under statistic maximal leakage: the quantization mechanism and randomized response. We show theoretically and empirically that the quantization mechanism achieves better privacy-utility tradeoffs in the settings we study.