We present an optimal ``worst-case exact to average-case approximate'' reduction for matrix multiplication over a finite field of prime order $p$. Any efficient algorithm that correctly computes, in expectation, at least $(\frac{1}{p} + \varepsilon)$-fraction of entries of the multiplication $A \cdot B$ of a pair $(A, B)$ of uniformly ... more >>>

We propose a simple variant of the INW pseudo-random generator, where blocks have varying lengths, and prove it gives the same parameters as the more complicated construction of Armoni's PRG. This shows there is no need for the specialized PRGs of Nisan and Zuckerman and Armoni, and they can be ... more >>>

We prove that hashing $n$ balls into $n$ bins via a random matrix over $GF(2)$ yields expected maximum load $O(\log n / \log \log n)$. This matches the expected maximum load of a fully random function and resolves an open question posed by Alon, Dietzfelbinger, Miltersen, Petrank, and Tardos (STOC ... more >>>