We prove that the set disjointness problem has randomized communication complexity
$\Omega(\sqrt{n}/2^{k}k)$ in the number-on-the-forehead model with $k$ parties, a quadratic improvement
on the previous bound $\Omega(\sqrt{n}/2^{k})^{1/2}$. Our result remains valid for quantum
protocols, where it is essentially tight. Proving it was an open problem since 1997, ... more >>>

We give a new characterization of NL as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as opposed to its conventional description in terms of deterministic logarithmic-space verifiers. ... more >>>

We show how to efficiently compile any given circuit $C$
into a leakage-resistant circuit $\widehat{C}$ such that any
function on the wires of $\widehat{C}$ that leaks information
during a computation $\widehat{C}(x)$ yields advantage in
computing the product of $|\widehat{C}|^{\Omega(1)}$ elements
of the alternating group $A_u$. In combination with new
compression ... more >>>