Supervisor

Suitable for

Abstract

Prerequisite: Part A Probability, or a similar course

 

Bag gain is something that happens when a sender wishes to use steganography to spread a secret message across a number of covers: the set of objects sent, some of which contain the hidden payload, is called a bag. Theory predicts that the size of the secret that can be undetectably transmitted should scale with the square root of the size of the bag, but in practice researchers have observed that it grows faster. This is attributed to being able to select only the "best" covers in the bag, where "best" means those in which the presence hidden data is hardest to detect (for example, noisy images).

This is theoretical project that aims to prove theorems about highly abstract versions of the above problem. For example, the "covers" can be simply binary pixels with different Bernoulli probabilities, and the "steganography" can simply flip a bit. The first part of the project would re-prove the classic square-root law when the flipped pixels are selected at random, and the second part would try to prove asymptotic bounds on detectability when the "covers" are selected to carry "steganography" depending on their Bernoulli parameter.