2026-08-06T03:42:08Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23138 2025-06-03T06:37:37Z ddc:004 open_access

Laplace Transform Interpretation of Differential Privacy Chourasia, Rishav Javaid, Uzair Sikdar, Biplab Differential Privacy Composition Theorem Laplace Transform 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Rishav Chourasia and Uzair Javaid and Biplab Sikdar 2025 Is Part Of LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FORC.2025.11 urn:nbn:de:0030-drops-231387 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.11 eng https://creativecommons.org/licenses/by/4.0/legalcode