PCPs and the Hardness of Generating Synthetic Data

Assuming the existence of one-way functions, we show that there is no polynomial-time, differentially private algorithm A that takes a database D ({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 {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, 2d ). 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.

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Jonathan Ullman, Salil P. Vadhan
• Keywords: Databases, ECCC 2010, One-way Functions, Two-way Marginal