TY - JOUR
AU - Gu, Yuzhou
AU - Zhou, Ziqi
AU - Günlü, Onur
AU - D'Oliveira, Rafael G. L.
AU - Sadeghi, Parastoo
AU - Médard, Muriel
AU - Schaefer, Rafael F.
PY - 2024/06/24
Y2 - 2024/07/21
TI - Generalized Rainbow Differential Privacy
JF - Journal of Privacy and Confidentiality
JA - JPC
VL - 14
IS - 2
SE - Articles
DO - 10.29012/jpc.896
UR - https://journalprivacyconfidentiality.org/index.php/jpc/article/view/896
SP -
AB - <p>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 $(\epsilon,\delta)$-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 $(\epsilon,\delta)$-DP, improving upon previous results that only apply to at most three colors and for $\epsilon$-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.</p>
ER -