For a propositional proof system $\mathcal{P}$ and a polynomial-time function $G: \{0, 1\}^n \to \{0, 1\}^N$ ($N > 10n$), we say that $G$ is a *proof complexity generator* against $\mathcal{P}$ if $\mathcal{P}$ cannot efficiently prove the (suitably encoded) statement "$y\not\in\mathrm{Range}(G)$" for every $y \in \{0, 1\}^N$, and $G$ is a ... more >>>

We introduce and study a new model of decision trees that lies at the frontier of provable circuit lower bounds.

We study $\ell$-local decision trees, in which each internal node queries an $\ell$-local function of the input. We show that sufficiently strong lower bounds for $\ell$-local decision trees would imply ... more >>>

Private information retrieval (PIR) inherently requires public-key cryptography. A recent line of work suggests that this barrier can be avoided in secret-key PIR, where the client first preprocesses an N-bit database and retains only a short secret key. This line of work has yielded communication O(N^\epsilon) for any constant \epsilon ... more >>>