Information Theoretical Cryptogenography
This work addresses the problem of secure and anonymous information leakage in communication systems, with potential applications in cryptography and privacy, but it appears incremental as it builds on existing cryptogenography concepts.
The paper tackles the problem of leaking information by a subset of individuals without revealing their identities, introducing a measure of suspicion and proving that leaked information is bounded by the expected increase in suspicion, with a tight bound. It shows that the maximum reliable information leak per person, given a suspicion probability constraint, is -log(1-c)/c - log(e) bits.
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.