In this work we consider the problem of approximating the number of relevant variables in a function given query access to the function. Since obtaining a multiplicative factor approximation is hard in general, we consider several relaxations of the problem. In particular, we consider relaxations in which we have a ... more >>>

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the notion of fractional isomorphism. We show ... more >>>

We put forth several simple candidate pseudorandom functions f_k : {0,1}^n -> {0,1} with security (a.k.a. hardness) 2^n that are inspired by the AES block-cipher by Daemen and Rijmen (2000). The functions are computable more efficiently, and use a shorter key (a.k.a. seed) than previous
constructions. In particular, we ... more >>>