A basic goal in complexity theory is to understand the communication complexity of number-on-the-forehead problems $f\colon(\{0,1\}^n)^{k}\to\{0,1\}$ with $k\gg\log n$ parties. We study the problems of inner product and set disjointness and determine their randomized communication complexity for every $k\geq\log n$, showing in both cases that $\Theta(1+\lceil\log n\rceil/\log\lceil1+k/\log n\rceil)$ bits are ... more >>>

In this work, we consider the natural goal of designing secret sharing schemes that ensure security against a powerful adaptive adversary who may learn some ``leaked'' information about all the shares. We say that a secret sharing scheme is $p$-party leakage-resilient, if the secret remains statistically hidden even after an ... more >>>