Collective Coin-Flipping is a classical problem where n
computationally unbounded processors are trying to generate a random
bit in a setting where only a single broadcast channel is available
for communication. The protocol is said to be b(n)-resilient if any
adversary that can corrupt up to b(n) players, still cannot ... more >>>

We prove that, for every constant $\varepsilon>0$ and every function $f:\Sigma^n\to\{0, 1\}$, there is a coalition of $O(n/\sqrt{\log n})$ coordinates and a target output $b\in\{0, 1\}$ such that, after the remaining coordinates are sampled uniformly and independently, the coalition can choose its values to make the output equal to $b$ ... more >>>