Computing Maximal Per-Record Leakage and Leakage-Distortion Functions for Privacy Mechanisms under Entropy-Constrained Adversaries

TL;DR

This paper introduces a computational framework for analyzing and optimizing privacy mechanisms against entropy-constrained adversaries, improving privacy-utility tradeoffs beyond classical differential privacy.

Contribution

It develops efficient algorithms for maximal leakage and leakage-distortion tradeoffs under entropy constraints, with theoretical guarantees and practical validation.

Findings

Algorithms achieve better privacy-utility tradeoffs than classical methods

Theoretical convergence guarantees for the proposed optimization methods

Validated on binary symmetric channels and modular sum queries

Abstract

The exponential growth of data collection necessitates robust privacy protections that preserve data utility. We address information disclosure against adversaries with bounded prior knowledge, modeled by an entropy constraint $H(X) \geq b$. Within this information privacy framework -- which replaces differential privacy's independence assumption with a bounded-knowledge model -- we study three core problems: maximal per-record leakage, the primal leakage-distortion tradeoff (minimizing worst-case leakage under distortion $D$), and the dual distortion minimization (minimizing distortion under leakage constraint $L$). These problems resemble classical information-theoretic ones (channel capacity, rate-distortion) but are more complex due to high dimensionality and the entropy constraint. We develop efficient alternating optimization algorithms that exploit convexity-concavity duality, with theoretical guarantees including local convergence for the primal problem and convergence to a stationary point for the dual. Experiments on binary symmetric channels and modular sum queries validate the algorithms, showing improved privacy-utility tradeoffs over classical differential privacy mechanisms. This work provides a computational framework for auditing privacy risks and designing certified mechanisms under realistic adversary assumptions.