Generalized Rainbow Differential Privacy

Fuente: arXiv
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Autori principali: Gu, Yuzhou, Zhou, Ziqi, Günlü, Onur, D'Oliveira, Rafael G. L., Sadeghi, Parastoo, Médard, Muriel, Schaefer, Rafael F.
Natura: Preprint
Pubblicazione: 2023
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author Gu, Yuzhou
Zhou, Ziqi
Günlü, Onur
D'Oliveira, Rafael G. L.
Sadeghi, Parastoo
Médard, Muriel
Schaefer, Rafael F.
author_facet Gu, Yuzhou
Zhou, Ziqi
Günlü, Onur
D'Oliveira, Rafael G. L.
Sadeghi, Parastoo
Médard, Muriel
Schaefer, Rafael F.
contents We study a new framework for designing differentially private (DP) mechanisms via randomized graph colorings, called rainbow differential privacy. In this framework, datasets are nodes in a graph, and two neighboring datasets are connected by an edge. Each dataset in the graph has a preferential ordering for the possible outputs of the mechanism, and these orderings are called rainbows. Different rainbows partition the graph of connected datasets into different regions. We show that if a DP mechanism at the boundary of such regions is fixed and it behaves identically for all same-rainbow boundary datasets, then a unique optimal $(ε,δ)$-DP mechanism exists (as long as the boundary condition is valid) and can be expressed in closed-form. Our proof technique is based on an interesting relationship between dominance ordering and DP, which applies to any finite number of colors and for $(ε,δ)$-DP, improving upon previous results that only apply to at most three colors and for $ε$-DP. We justify the homogeneous boundary condition assumption by giving an example with non-homogeneous boundary condition, for which there exists no optimal DP mechanism.
format Preprint
id arxiv_https___arxiv_org_abs_2309_05871
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Generalized Rainbow Differential Privacy
Gu, Yuzhou
Zhou, Ziqi
Günlü, Onur
D'Oliveira, Rafael G. L.
Sadeghi, Parastoo
Médard, Muriel
Schaefer, Rafael F.
Cryptography and Security
Information Retrieval
Information Theory
We study a new framework for designing differentially private (DP) mechanisms via randomized graph colorings, called rainbow differential privacy. In this framework, datasets are nodes in a graph, and two neighboring datasets are connected by an edge. Each dataset in the graph has a preferential ordering for the possible outputs of the mechanism, and these orderings are called rainbows. Different rainbows partition the graph of connected datasets into different regions. We show that if a DP mechanism at the boundary of such regions is fixed and it behaves identically for all same-rainbow boundary datasets, then a unique optimal $(ε,δ)$-DP mechanism exists (as long as the boundary condition is valid) and can be expressed in closed-form. Our proof technique is based on an interesting relationship between dominance ordering and DP, which applies to any finite number of colors and for $(ε,δ)$-DP, improving upon previous results that only apply to at most three colors and for $ε$-DP. We justify the homogeneous boundary condition assumption by giving an example with non-homogeneous boundary condition, for which there exists no optimal DP mechanism.
title Generalized Rainbow Differential Privacy
topic Cryptography and Security
Information Retrieval
Information Theory
url https://arxiv.org/abs/2309.05871