Bun, Mark MarUllman, JonathanVadhan, Salil2017-04-142014Bun, Mark, Jonathan Ullman, and Salil Vadhan. 2014. "Fingerprinting Codes and the Price of Approximate Differential Privacy." In Proceedings of the 46th Annual ACM Symposium on Theory of Computing (STOC '14), New York, NY, May 31-June 3, 2014: 1-10978-1-4503-2710-7http://nrs.harvard.edu/urn-3:HUL.InstRepos:32186909We show new lower bounds on the sample complexity of (ε, δ)-differentially private algorithms that accurately answer large sets of counting queries. A counting query on a database D ∈ ({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 Q of » nd counting queries on D to within error ±α it is necessary that [EQUATION] This bound is optimal up to poly-logarithmic factors, as demonstrated by the Private Multiplicative Weights algorithm (Hardt and Rothblum, FOCS'10). It is also the first to show that the sample complexity required for (ε, δ)-differential privacy is asymptotically larger than what is required merely for accuracy, which is O(log |Q|/α2). In addition, we show that our lower bound holds for the specific case of k-way marginal queries (where |Q| = 2k(d/k)) when α is a constant. Our results rely on the existence of short fingerprinting codes (Boneh and Shaw, CRYPTO'95; Tardos, STOC'03), which we show are closely connected to the sample complexity of differentially private data release. We also give a new method for combining certain types of sample complexity lower bounds into stronger lower bounds.en-USConference Paper2017-04-1410.1145/2591796.2591877