We show how to construct a variety of ``trapdoor'' cryptographic tools assuming the worst-case hardness of standard lattice problems (such as approximating the shortest nonzero vector to within small factors). The applications include trapdoor functions with \emph{preimage sampling}, simple and efficient ``hash-and-sign'' digital signature schemes, universally composable oblivious transfer, and ... more >>>

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'' $\hat{D}$ all of whose two-way marginals are approximately equal to those of $D$. (A two-way marginal is the fraction of database rows ... more >>>