Differentially Private Verification of Distribution Properties

[2604.10819] Differentially Private Verification of Distribution Properties Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Data Structures and Algorithms arXiv:2604.10819 (cs) [Submitted on 12 Apr 2026 ( v1 ), last revised 14 Aug 2026 (this version, v2)] Title: Differentially Private Verification of Distribution Properties Authors: Elbert Du , Cynthia Dwork , Pranay Tankala , Linjun Zhang View a PDF of the paper titled Differentially Private Verification of Distribution Properties, by Elbert Du and 2 other authors View PDF HTML (experimental) Abstract: A recent line of work initiated by Chiesa and Gur and further developed by Herman and Rothblum investigates the sample and communication complexity of verifying properties of distributions with the assistance of a powerful, knowledgeable, but untrusted prover. In this work, we initiate the study of differentially private distribution property verification. After all, if we do not trust the prover to help us with verification, why should we trust it with our sensitive sample? We map a landscape of differentially private verification of properties of distributions. In the non-private case it is known that one-round private-coin protocols can have substantially lower complexity than public-coin (AM) protocols. In contrast, the possibility for improvement in differentially private interactive proofs depends on the privacy parameter regime and model. Drawing on connections between privacy and replicability and privacy amplification techniques in the literature we show: 1. There exists a reduction from any one-round $(\varepsilon,\delta)$-differentially private private-coin protocol to a differentially private AM protocol for the parameter regime $\varepsilon = O(1/\sqrt{s})$ and $\delta= O(1/s^{5/2})$ with the same privacy and sample and communication complexities. In the local model, this is relaxed to $\varepsilon = O(1/\sqrt{\log s})$ 2. However, when the privacy guarantee is very relaxed ($\varepsilon \in \Omega(\log s)$), private coins indeed reduce sample and communication complexities. We also obtain a computationally efficient Merlin-Arthur proof for privately testing whether samples are drawn from a product distribution and prove that its sample complexity is optimal up to a $polylog N$ factor by reducing uniformity testing to independence testing with Boolean attributes and appealing to known lower bounds on sample complexity for private uniformity testing. Subjects: Data Structures and Algorithms (cs.DS) ; Computational Complexity (cs.CC); Machine Learning (cs.LG) Cite as: arXiv:2604.10819 [cs.DS] (or arXiv:2604.10819v2 [cs.DS] for this version) https://doi.org/10.48550/arXiv.2604.10819 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Elbert Du [ view email ] [v1] Sun, 12 Apr 2026 21:17:43 UTC (49 KB) [v2] Fri, 14 Aug 2026 23:38:49 UTC (64 KB) Full-text links: Access Paper: View a PDF of the paper titled Differentially Private Verification of Distribution Properties, by Elbert Du and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.DS < prev | next > new | recent | 2026-04 Change to browse by: cs cs.CC cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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