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DOI: 10.4230/LIPIcs.FORC.2025.11

Laplace Transform Interpretation of Differential Privacy

Authors: Rishav Chourasia, Uzair Javaid, and Biplab Sikdar

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract

We introduce a set of useful expressions of Differential Privacy (DP) notions in terms of Laplace transformations. The underlying bare-form expressions for these transforms appear in several works on analyzing DP, either as an integral or an expectation. We show that recognizing these expressions as Laplace transformations unlocks a new way to reason about DP properties by exploiting the duality between time and frequency domains. Leveraging our interpretation, we connect the (q, ρ(q))-Rényi DP curve and the (ε, δ(ε))-DP curve as being the Laplace and inverse-Laplace transforms of one another. Using our Laplace transform-based analysis, we also prove an adaptive composition theorem for (ε, δ)-DP guarantees that is exactly-tight (i.e., matches even in constants) for all values of ε. Additionally, we resolve an issue regarding symmetry of f-DP on subsampling that prevented equivalence across all functional DP notions.

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Rishav Chourasia, Uzair Javaid, and Biplab Sikdar. Laplace Transform Interpretation of Differential Privacy. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chourasia_et_al:LIPIcs.FORC.2025.11,
  author =	{Chourasia, Rishav and Javaid, Uzair and Sikdar, Biplab},
  title =	{{Laplace Transform Interpretation of Differential Privacy}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{11:1--11:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.11},
  URN =		{urn:nbn:de:0030-drops-231387},
  doi =		{10.4230/LIPIcs.FORC.2025.11},
  annote =	{Keywords: Differential Privacy, Composition Theorem, Laplace Transform}
}

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Laplace Transform Interpretation of Differential Privacy

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