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

2026-01-31

AI Summary

This work addresses privacy-preserving data release under a realistic threat model where the adversary’s prior knowledge is constrained by an entropy lower bound (H(X) ≥ b), thereby relaxing the independence assumption inherent in differential privacy. The authors develop a unified framework for privacy analysis and mechanism design tailored to adversaries with bounded prior knowledge. Focusing on three core objectives—minimizing worst-case leakage under a given distortion budget, minimizing distortion under a leakage constraint, and bounding single-record maximum leakage—they propose an alternating optimization algorithm grounded in convex-concave duality to efficiently compute the leakage-distortion trade-off in high-dimensional spaces. Experiments on binary symmetric channels and modular addition queries demonstrate that the proposed approach achieves superior privacy-utility trade-offs compared to classical differential privacy mechanisms and further enables rigorous privacy risk auditing and mechanism certification.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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.

Problem

• maximal per-record leakage
• leakage-distortion tradeoff
• entropy-constrained adversaries
• information privacy
• privacy mechanisms

Innovation

• entropy-constrained adversary
• leakage-distortion tradeoff
• alternating optimization
• information privacy
• convex-concave duality