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 collaboratively discovering the minimum value (\(\min _i x_i\)) 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 stegosystems 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.
KeywordsSteganography Communication protocols EREW PRAM