We present lower bounds for the static cryptographic data structure problem of single-server
private information retrieval (PIR). PIR considers the setting where a server holds a …

The task of function inversion is central to cryptanalysis: breaking block ciphers, forging
signatures, and cracking password hashes are all special cases of the function-inversion …

We show that static data structure lower bounds in the group (linear) model imply semi-
explicit lower bounds on matrix rigidity. In particular, we prove that an explicit lower bound of …

The conjectured hardness of Boolean matrix-vector multiplication has been used with great
success to prove conditional lower bounds for numerous important data structure problems …

Hillclimbing is an essential part of optimization. An important benchmark for hillclimbing
algorithms on functions f:{0, 1} n→ ℝ are (strictly) montone functions, on which a surprising …

Let f:{0, 1} n→{0, 1} m be a function computable by a circuit with unbounded fan-in, arbitrary
gates, w wires and depth d. With a very simple argument we show that the m-query problem …

We show that for every small AC ^0 circuit C:{0,1\}^ℓ→{0,1\}^m there exists a multiset S of
2^mm^Ω(1) restrictions that preserve the output distribution of C and, moreover, polarize min …

We present a simple and provably optimal non-adaptive cell probe data structure for the
static dictionary problem. Our data structure supports storing a set of n key-value pairs from …

Abstract Recently, Dvir, Golovnev, and Weinstein have shown that sufficiently strong lower
bounds for linear data structures would imply new bounds for rigid matrices. However, their …

We prove new cell-probe lower bounds for dynamic data structures that maintain a subset of
{1, 2,..., n}, and compute various statistics of the set. The data structure is said to handle …