Information Leakage Envelopes

2026-05-20

AI Summary

Existing privacy metrics struggle to simultaneously ensure post-processing robustness and provide an upper bound on the failure probability of information leakage exceeding a given threshold. This work proposes the Pointwise Maximal Leakage (PML) envelope, which for the first time satisfies both of these critical properties, and uncovers its structural characteristics, including monotonicity. Through information-theoretic analysis, extremal mechanism modeling, and evaluation of randomized response mechanisms, we establish general upper and lower bounds for the PML envelope. Furthermore, in the high-privacy regime, we precisely characterize concrete mechanisms under this framework, thereby demonstrating both the theoretical rigor and practical applicability of the proposed measure.

Abstract

We study privacy guarantees in the framework of pointwise maximal leakage (PML) that satisfy two requirements: they are robust under post-processing and upper bound the failure probability, i.e., the probability that the information leakage exceeds a given threshold. We first examine two candidate definitions inspired by (approximate) differential privacy and show that neither one satisfies both requirements simultaneously. We then introduce the notion of the PML envelope, which quantifies the largest amount of information leakage about a secret after arbitrary post-processing of a mechanism's output. By construction, the PML envelope satisfies both requirements. We discuss basic structural properties of the envelope, such as monotonicity, and derive general upper and lower bounds. We further analyze the envelope for two widely used privacy mechanisms: the PML-extremal mechanisms in the high-privacy regime and randomized response. Overall, this work establishes the PML envelope as a natural and operationally meaningful definition for providing privacy guarantees that are preserved under arbitrary downstream transformations.

Problem

• privacy guarantees
• pointwise maximal leakage
• post-processing robustness
• failure probability
• information leakage

Innovation

• pointwise maximal leakage
• PML envelope
• post-processing robustness
• privacy guarantees
• randomized response