Adversarial Classification under Gaussian Mechanism: Calibrating the Attack to Sensitivity

Ayse Unsal; Melek Onen

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arXiv · 2201.09751

Adversarial Classification under Gaussian Mechanism: Calibrating the Attack to Sensitivity

Ayse Unsal·Melek Onen

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Abstract

This work studies anomaly detection under differential privacy (DP) with Gaussian perturbation using both statistical and information-theoretic tools. In our setting, the adversary aims to modify the content of a statistical dataset by inserting additional data without being detected by using the DP guarantee to her own benefit. To this end, we characterize information-theoretic and statistical thresholds for the first and second-order statistics of the adversary's attack, which balances the privacy budget and the impact of the attack in order to remain undetected. Additionally, we introduce a new privacy metric based on Chernoff information for classifying adversaries under differential privacy as a stronger alternative to $(\epsilon, \delta)-$ and Kullback-Leibler DP for the Gaussian mechanism. Analytical results are supported by numerical evaluations.

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Ayse Unsal, Melek Onen. 2022-01-24. Adversarial Classification under Gaussian Mechanism: Calibrating the Attack to Sensitivity. https://arxiv.org/abs/2201.09751

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