Assuming the existence of one-way functions, we show that there is no polynomial-time, differentially private algorithm A that takes a database D\in ({0,1}^d)^n and outputs a ``synthetic database'' D' all of whose two-way marginals are approximately equal to those of D. (A two-way marginal is the fraction of database rows x\in {0,1}^d with a given pair of values in a given pair of columns.) This answers a question of Barak et al. (PODS `07), who gave an algorithm running in time poly(n,2^d). Our proof combines a construction of hard-to-sanitize databases based on digital signatures (by Dwork et al., STOC `09) with PCP-based Levin-reductions from NP search problems to finding approximate solutions to CSPs.

%B Proceedings of the 8th IACR Theory of Cryptography Conference (TCC `11) %S Lecture Notes on Computer Science %7 Lecture Notes on Computer Science %I Springer-Verlag %C Providence, RI %V 5978 %P 572–587 %8 28–30 March %G eng %U http://link.springer.com/chapter/10.1007%2F978-3-642-19571-6_24