Paper 2018/820
Privacy Loss Classes: The Central Limit Theorem in Differential Privacy
David Sommer and Sebastian Meiser and Esfandiar Mohammadi
Abstract
Quantifying the privacy loss of a privacy-preserving mechanism on potentially sensitive data is a complex and well-researched topic; the de-facto standard for privacy measures are $\varepsilon$-differential privacy (DP) and its versatile relaxation $(\varepsilon,\delta)$-approximate differential privacy (ADP). Recently, novel variants of (A)DP focused on giving tighter privacy bounds under continual observation. In this paper we unify many previous works via the \emph{privacy loss distribution} (PLD) of a mechanism. We show that for non-adaptive mechanisms, the privacy loss under sequential composition undergoes a convolution and will converge to a Gauss distribution (the central limit theorem for DP). We derive several relevant insights: we can now characterize mechanisms by their \emph{privacy loss class}, i.e., by the Gauss distribution to which their PLD converges, which allows us to give novel ADP bounds for mechanisms based on their privacy loss class; we derive \emph{exact} analytical guarantees for the approximate randomized response mechanism and an \emph{exact} analytical and closed formula for the Gauss mechanism, that, given $\varepsilon$, calculates $\delta$, s.t., the mechanism is $(\varepsilon, \delta)$-ADP (not an over-approximating bound).
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- differential privacyprivacy loss
- Contact author(s)
- s meiser @ ucl ac uk
- History
- 2020-08-12: last of 3 revisions
- 2018-09-06: received
- See all versions
- Short URL
- https://ia.cr/2018/820
- License
-
CC BY