@conference {UllmanVa11,
title = {PCPs and the Hardness of Generating Synthetic Data},
booktitle = {Proceedings of the 8th IACR Theory of Cryptography Conference (TCC {\textquoteleft}11)},
series = {Lecture Notes on Computer Science},
volume = {5978},
year = {2011},
note = {Full version posted as {\em ECCC} TR10-017.},
month = {28{\textendash}30 March},
pages = {572{\textendash}587},
publisher = {Springer-Verlag},
organization = {Springer-Verlag},
edition = {Lecture Notes on Computer Science},
address = {Providence, RI},
abstract = {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 {\textquoteleft}{\textquoteleft}synthetic database{\textquoteright}{\textquoteright} D{\textquoteright} 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 {\textquoteleft}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 {\textquoteleft}09) with PCP-based Levin-reductions from NP search problems to finding approximate solutions to CSPs.},
url = {http://link.springer.com/chapter/10.1007\%2F978-3-642-19571-6_24},
author = {Jon Ullman and Salil Vadhan},
editor = {Yuval Ishai}
}