We investigate the derandomized version of the classical line-point low-degree test in the high-error regime in the bivariate setting and reveal some unexpected behavior. The classical line-point low-degree test takes an $m$-variate function $f$ over a finite field $\mathbb{F}_q$, queries it along a random line and accepts if the restriction ... more >>>

We revisit a classical result of Coppersmith and Shparlinski [CS00] showing bounds on how well polynomials can approximate the discrete log function. They showed that for any univariate polynomial $f(X) \in \mathbb{F}_p[X]$ with $\deg(f) \leq D$, we have:
$$ |\{ x \in \mathbb{F}_p^\times \mid f(x) = dlog(x) \}| \leq \sqrt{2 ... more >>>

We study the problem of constructing highly nonlinear vectorial maps $F: \mathbb{F}_2^n \to \mathbb{F}_2^m$.
Concretely, we want an $F$ and an $A = A(m,n)>0$ as small as possible, so that for every affine map $L: \mathbb{F}_2^n \to \mathbb{F}_2^m$ (of the form $L(x) = Mx + b$) we have:
$$
agree(F,L) ... more >>>

In this paper, we construct new t-server Private Information Retrieval (PIR) schemes with communication complexity subpolynomial in the previously best known, for all but finitely many t. Our results are
based on combining derivatives (in the spirit of Woodruff-Yekhanin) with the Matching Vector
based PIRs of Yekhanin and Efremenko. Previously ... more >>>