Gaussian Differential Privacy on Riemannian Manifolds. (arXiv:2311.10101v1 [cs.CR])

We develop an advanced approach for extending Gaussian Differential Privacy
(GDP) to general Riemannian manifolds. The concept of GDP stands out as a
prominent privacy definition that strongly warrants extension to manifold
settings, due to its central limit properties. By harnessing the power of the
renowned Bishop-Gromov theorem in geometric analysis, we propose a Riemannian
Gaussian distribution that integrates the Riemannian distance, allowing us to
achieve GDP in Riemannian manifolds with bounded Ricci curvature. To the best
of our knowledge, …

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