Information Theoretical Cryptogenography

We consider problems where n people are communicating and a random subset of them is trying to leak information, without making it clear who are leaking the information. We introduce a measure of suspicion and show that the amount of leaked information will always be bounded by the expected increase in suspicion, and that this bound is tight. Suppose a large number of people have some information they want to leak, but they want to ensure that after the communication, an observer will assign probability at most c to the events that each of them is trying to leak the information. How much information can they reliably leak, per person who is leaking? We show that the answer is (-log(1-c)/c - log(e)) bits.