Stegogames

Abstract

We explore the power of steganographic computation in an game-theoretic setting, where n stegocommunicants are attempting to complete a shared computation, and where a well-resourced censor is attempting to prevent the computation. For example, when collabora-tively discovering the minimum value (mini xi) in a public n-vector X, each stegocommunicant reads a randomly-selected element during each timestep. Each then transmits the index i of the smallest value they have seen to a randomly-selected collaborator. We prove that most stegocommunicants will learn the minimum value in O(log n) time, w.h.p., if at most 10% of their population is censored in any timestep. The censor in our model retains a copy of all intercepted messages, using this information to optimally select the targets of their censorship at the beginning of each timestep. Our model of stegocomputation is relevant to stegosys-tems in which: (1) the stegoencoding is determined by the address of the recipient, (2) the censor does not have sufficient computational resource to stegodecode more than a fixed fraction (nominally 10%) of the messages in flight, and (3) the censor cannot store any messages other than the ones it has stegodecoded.