On the Existence of Perfect Stegosystems

Abstract

There are several steganography techniques (e.g. linguistic or least significant bit embedding) that provide security but no robustness against an active adversary. On the other hand it is rather well known that the spread-spectrum based technique is robust against an active adversary but it seems to be insecure against a statistical detection of stegosignal. We prove in this paper that actually this is not the case and that there exists an stegosystem that is asymptotically both secure to statistical detection and robust against a jamming of stegosignal by an active adversary. We call such stegosystems quasiperfect whereas we call them perfect if in addition the data rate of secret information is asymptotically constant. We prove that perfect stegosystems do not exist for both blind and informed decoders. Some examples using the simplex and the Reed-Muller codes jointly with stegosystems are given.