For a matrix H over a field F, its rank-r rigidity, denoted by R_H(r), is the minimum Hamming
distance from H to a matrix of rank at most r over F. A central open challenge in complexity …

We consider the general problem of learning about a matrix through vector-matrix-vector
queries. These queries provide the value of $\boldsymbol {u}^{\mathrm {T}}\boldsymbol …

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 investigate the complexity of explicit construction problems, where the goal is to produce
a particular object possessing some pseudorandom property in time polynomial in the size …

The concept of matrix rigidity was introduced by Valiant (independently by Grigoriev) in the
context of computing linear transformations. A matrix is rigid if it is far (in terms of Hamming …

This paper shows several connections between data structure problems and cryptography
against preprocessing attacks. Our results span data structure upper bounds, cryptographic …

We make the first progress on probabilistic-degree lower bounds and correlation bounds for
polynomials since the papers by Razborov and Smolensky in the 80's. The bounds hold for …

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 …

For a matrix M and a positive integer r, the rank r rigidity of M is the smallest number of
entries of M which one must change to make its rank at most r. There are many known …