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

• URL: http://arxiv.org/abs/2602.00689v1
• Date: Sat, 31 Jan 2026 12:23:24 GMT
• Title: Computing Maximal Per-Record Leakage and Leakage-Distortion Functions for Privacy Mechanisms under Entropy-Constrained Adversaries
• Authors: Genqiang Wu, Xiaoying Zhang, Yu Qi, Hao Wang, Jikui Wang, Yeping He,
• Abstract summary: We study three core problems: maximal per-record leakage, the primal leakage-distortion tradeoff, and the dual distortion minimization.<n>We develop efficient alternating optimization algorithms that exploit convexity-concavity duality.<n>This work provides a computational framework for auditing privacy risks and designing certified mechanisms.
• Score: 19.239827561129513
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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