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Laplace Transform Interpretation of Differential Privacy

Authors Rishav Chourasia , Uzair Javaid , Biplab Sikdar

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  • Security and privacy
Keywords
  • Differential Privacy
  • Composition Theorem
  • Laplace Transform

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.FORC.2025.11

Author Details

Rishav Chourasia
  • School of Computing, National University of Singapore, 13 Computing Drive, Singapore
Uzair Javaid
  • Betterdata, PIXEL at One North, 10 Central Exchange Green, Singapore
Biplab Sikdar
  • Department of ECE, 4 Engineering Drive 3, National University of Singapore, Singapore

Funding

This work was supported in part by the Asian Institute of Digital Finance (AIDF) under grant A-0003504-09-00.

Acknowledgements

We thank Bao Ergute for feedback on earlier versions of this paper.

References

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