Guessing secrets

Abstract

Suppose we are given some fixed (but unknown) subset X of a set Ω, and our object is to learn as much as possible about the elements of X by asking binary questions. Specifically, each question is just a function F : Ω → {0, 1}, and the answer to F is just the value F(Xi) for some Xi ∈ X, (determined, for example, by a potentially malevolent but truthful, adversary). In this paper, we describe various algorithms for solving this problem, and establish upper and lower bounds on the efficiency of such algorithms.