LIPIcs.ITCS.2025.27.pdf
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The Randomness Complexity of Differential Privacy
Authors
Clément L. Canonne 
,
Francis E. Su ,
Salil P. Vadhan
-
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Volume:
16th Innovations in Theoretical Computer Science Conference (ITCS 2025)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Innovations in Theoretical Computer Science Conference (ITCS) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2025-02-11
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Acknowledgements
We thank Mark Bun for pointing out the connections to recent work on replicability, and anonymous referees for helpful corrections and comments.
Cite As Get BibTex
Clément L. Canonne, Francis E. Su, and Salil P. Vadhan. The Randomness Complexity of Differential Privacy. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
https://doi.org/10.4230/LIPIcs.ITCS.2025.27
Abstract
We initiate the study of the randomness complexity of differential privacy, i.e., how many random bits an algorithm needs in order to generate accurate differentially private releases. As a test case, we focus on the task of releasing the results of d counting queries, or equivalently all one-way marginals on a d-dimensional dataset with boolean attributes. While standard differentially private mechanisms for this task have randomness complexity that grows linearly with d, we show that, surprisingly, only log₂ d+O(1) random bits (in expectation) suffice to achieve an error that depends polynomially on d (and is independent of the size n of the dataset), and furthermore this is possible with pure, unbounded differential privacy and privacy-loss parameter ε = 1/poly(d). Conversely, we show that at least log₂ d-O(1) random bits are also necessary for nontrivial accuracy, even with approximate, bounded DP, provided the privacy-loss parameters satisfy ε,δ ≤ 1/poly(d). We obtain our results by establishing a close connection between the randomness complexity of differentially private mechanisms and the geometric notion of "deterministic rounding schemes" recently introduced and studied by Vander Woude et al. (2022, 2023).
Subject Classification
ACM Subject Classification
- Theory of computation → Pseudorandomness and derandomization
- Theory of computation → Computational complexity and cryptography
- Security and privacy
- Mathematics of computing
Keywords
- differential privacy
- randomness
- geometry
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References
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