Capacity Laws for Steganography in a Crowd

Abstract

A steganographer is not only hiding a payload inside their cover, they are also hiding themselves amongst the non-steganographers. In this paper we study asymptotic rates of growth for steganographic data -- analogous to the classical Square-Root Law -- in the context of a 'crowd' of K actors, one of whom is a steganographer. This converts steganalysis from a binary to a K-class classification problem, and requires some new information-theoretic tools. Intuition suggests that larger K should enable the steganographer to hide a larger payload, since their stego signal is mixed in with larger amounts of cover noise from the other actors. We show that this is indeed the case, in a simple independent-pixel model, with payload growing at O(√(log K)) times the classical Square-Root capacity in the case of homogeneous actors. Further, examining the effects of heterogeneity reveals a subtle dependence on the detector's knowledge about the payload size, and the need for them to use negative as well as positive information to identify the steganographer.