{"paper":{"title":"On Distributed Differential Privacy and Counting Distinct Elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG","stat.ML"],"primary_cat":"cs.CR","authors_text":"Badih Ghazi, Lijie Chen, Pasin Manurangsi, Ravi Kumar","submitted_at":"2020-09-21T04:13:34Z","abstract_excerpt":"We study the setup where each of $n$ users holds an element from a discrete set, and the goal is to count the number of distinct elements across all users, under the constraint of $(\\epsilon, \\delta)$-differentially privacy:\n  - In the non-interactive local setting, we prove that the additive error of any protocol is $\\Omega(n)$ for any constant $\\epsilon$ and for any $\\delta$ inverse polynomial in $n$.\n  - In the single-message shuffle setting, we prove a lower bound of $\\Omega(n)$ on the error for any constant $\\epsilon$ and for some $\\delta$ inverse quasi-polynomial in $n$. We do so by buil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.09604","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.09604/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}