Robust coin flipping

Abstract

Alice seeks an information-theoretically secure source of private random data. Unfortunately, she lacks a personal source and must use remote sources controlled by other parties. Alice wants to simulate a coin flip of specified bias α, as a function of data she receives from p sources; she seeks privacy from any coalition of r of them. We show: If p/2≥ r < p, the bias can be any rational number and nothing else; if 0< r