# Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds

@article{Bun2016ConcentratedDP, title={Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds}, author={Mark Bun and Thomas Steinke}, journal={ArXiv}, year={2016}, volume={abs/1605.02065} }

"Concentrated differential privacy" was recently introduced by Dwork and Rothblum as a relaxation of differential privacy, which permits sharper analyses of many privacy-preserving computations. We present an alternative formulation of the concept of concentrated differential privacy in terms of the Renyi divergence between the distributions obtained by running an algorithm on neighboring inputs. With this reformulation in hand, we prove sharper quantitative results, establish lower bounds, and…

## 431 Citations

Rényi Differential Privacy

- Computer Science2017 IEEE 30th Computer Security Foundations Symposium (CSF)
- 2017

This work argues that the useful analytical tool can be used as a privacy definition, compactly and accurately representing guarantees on the tails of the privacy loss, and demonstrates that the new definition shares many important properties with the standard definition of differential privacy.

Reasoning about Divergences for Relaxations of Differential Privacy

- Computer ScienceArXiv
- 2017

We develop a semantics framework for verifying recent relaxations of differential privacy: R\'enyi differential privacy and zero-concentrated differential privacy. Both notions require a bound on a…

Approximate Span Liftings: Compositional Semantics for Relaxations of Differential Privacy

- Computer Science2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2019

We develop new abstractions for reasoning about three relaxations of differential privacy: $R$ényi differential privacy, zero-concentrated differential privacy, and truncated concentrated…

Gaussian differential privacy

- Computer ScienceJournal of the Royal Statistical Society: Series B (Statistical Methodology)
- 2022

The privacy guarantees of any hypothesis testing based definition of privacy (including the original differential privacy definition) converges to GDP in the limit under composition and a Berry–Esseen style version of the central limit theorem is proved, which gives a computationally inexpensive tool for tractably analysing the exact composition of private algorithms.

Sharp Composition Bounds for Gaussian Differential Privacy via Edgeworth Expansion

- Computer Science, MathematicsICML
- 2020

This work introduces a family of analytical and sharp privacy bounds under composition using the Edgeworth expansion in the framework of the recently proposed f-differential privacy to address a fundamental question in differential privacy regarding how the overall privacy bound degrades under composition.

Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences

- Computer ScienceNeurIPS
- 2018

This paper presents a general method that recovers and improves prior analyses, yields lower bounds and derives new instances of privacy amplification by subsampling, which leverages a characterization of differential privacy as a divergence which emerged in the program verification community.

Composable and versatile privacy via truncated CDP

- Computer ScienceSTOC
- 2018

This new definition of truncated concentrated differential privacy provides robust and efficient composition guarantees, supports powerful algorithmic techniques such as privacy amplification via sub-sampling, and enables more accurate statistical analyses.

PrivacyBuDe: Privacy Buckets Demo Tight Differential Privacy Guarantees made Simple

- Computer ScienceCCS
- 2018

This work provides an easy-to-use interface for computing state-of-the-art differential privacy guarantees by simply accessing a website and guaranteeing the scale parameter of the noise, the sensitivity, and the number of compositions for the widely used Laplace mechanism and the similarly popular Gauss mechanism.

Local Differential Privacy Is Equivalent to Contraction of $E_\gamma$-Divergence

- Computer Science
- 2021

This work shows that LDP constraints can be equivalently cast in terms of the contraction coefficient of the Eγ-divergence, and uses this equivalent formula to express LDP guarantees of privacy mechanisms in Terms of contraction coefficients of arbitrary f -divergences.

Privacy Loss Classes: The Central Limit Theorem in Differential Privacy

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2018

This paper shows 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) and derives several relevant insights.

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