{"paper":{"title":"Fingerprinting Codes and the Price of Approximate Differential Privacy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Jonathan Ullman, Mark Bun, Salil Vadhan","submitted_at":"2013-11-13T15:09:48Z","abstract_excerpt":"We show new lower bounds on the sample complexity of $(\\varepsilon, \\delta)$-differentially private algorithms that accurately answer large sets of counting queries. A counting query on a database $D \\in (\\{0,1\\}^d)^n$ has the form \"What fraction of the individual records in the database satisfy the property $q$?\" We show that in order to answer an arbitrary set $\\mathcal{Q}$ of $\\gg nd$ counting queries on $D$ to within error $\\pm \\alpha$ it is necessary that $$ n \\geq \\tilde{\\Omega}\\Bigg(\\frac{\\sqrt{d} \\log |\\mathcal{Q}|}{\\alpha^2 \\varepsilon} \\Bigg). $$ This bound is optimal up to poly-loga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3158","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}