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Computer Science > Cryptography and Security

arXiv:2109.10528 (cs)
[Submitted on 22 Sep 2021]

Title:A unified interpretation of the Gaussian mechanism for differential privacy through the sensitivity index

Authors:Georgios Kaissis, Moritz Knolle, Friederike Jungmann, Alexander Ziller, Dmitrii Usynin, Daniel Rueckert
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Abstract:The Gaussian mechanism (GM) represents a universally employed tool for achieving differential privacy (DP), and a large body of work has been devoted to its analysis. We argue that the three prevailing interpretations of the GM, namely $(\varepsilon, \delta)$-DP, f-DP and Rényi DP can be expressed by using a single parameter $\psi$, which we term the sensitivity index. $\psi$ uniquely characterises the GM and its properties by encapsulating its two fundamental quantities: the sensitivity of the query and the magnitude of the noise perturbation. With strong links to the ROC curve and the hypothesis-testing interpretation of DP, $\psi$ offers the practitioner a powerful method for interpreting, comparing and communicating the privacy guarantees of Gaussian mechanisms.
Comments: Under review at PETS 2022
Subjects: Cryptography and Security (cs.CR); Information Theory (cs.IT); Machine Learning (cs.LG)
Cite as: arXiv:2109.10528 [cs.CR]
  (or arXiv:2109.10528v1 [cs.CR] for this version)
  https://doi.org/10.48550/arXiv.2109.10528

Submission history

From: Georgios Kaissis [view email]
[v1] Wed, 22 Sep 2021 06:20:01 UTC (297 KB)
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