PCPs and the Hardness of Generating Private Synthetic Data

  title={PCPs and the Hardness of Generating Private Synthetic Data},
  author={Jonathan Ullman and Salil P. Vadhan},
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… 

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