Rainbow Differential Privacy
Ziqi Zhou, Onur G\"unl\"u, Rafael G. L. D'Oliveira, Muriel M\'edard,, Parastoo Sadeghi, and Rafael F. Schaefer

TL;DR
This paper generalizes a framework for designing differentially private mechanisms from binary to multi-valued functions, introducing rainbow partitions and providing closed-form solutions for ternary functions.
Contribution
It extends the graph coloring approach for DP mechanisms to multi-valued functions and derives closed-form solutions for ternary cases.
Findings
Unique optimal DP mechanisms can be characterized by boundary conditions.
The framework can be extended to higher-dimensional query spaces.
Closed-form expressions are provided for ternary functions.
Abstract
We extend a previous framework for designing differentially private (DP) mechanisms via randomized graph colorings that was restricted to binary functions, corresponding to colorings in a graph, to multi-valued functions. As before, datasets are nodes in the graph and any two neighboring datasets are connected by an edge. In our setting, we assume that each dataset has a preferential ordering for the possible outputs of the mechanism, each of which we refer to as a rainbow. Different rainbows partition the graph of datasets into different regions. We show that if the DP mechanism is pre-specified at the boundary of such regions and behaves identically for all same-rainbow boundary datasets, at most one optimal such mechanism can exist and the problem can be solved by means of a morphism to a line graph. We then show closed form expressions for the line graph in the case of ternary…
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Taxonomy
TopicsPrivacy-Preserving Technologies in Data · Cryptography and Data Security · Blockchain Technology Applications and Security
