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. We ask the question: 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 \(- \frac{\log(1-c)}{c} -\log(e)\) bits.