Grey-box steganography

In steganography secret messages are encoded into unsuspicious covertexts such that an adversary cannot distinguish the resulting stegotexts from original covertexts. To accomplish their respective tasks, encoder and adversary need information about the covertext distribution. In previous investigations, the knowledge about the covertext channel was highly unbalanced: while the adversary was granted full knowledge, the encoder could only query a black-box sampling oracle. In such a situation, the only general steganographic technique known is rejection sampling. But this method requires exponential sampling complexity with respect to the number of message bits per covertext document. The other extreme, a white-box setting, where the encoder knows the covertext distribution perfectly, resp. the distribution is efficiently computable, is also unrealistic in practice. To resolve these deficiencies and to get a finer-grained security analysis, we propose a new model, called grey-box steganography. Here, the encoder starts with at least some partial knowledge about the type of covertext channel. Using the sampling oracle, he first uses machine learning techniques to learn the covertext distribution and then tries to actively construct a suitable stegotext-either by modifying a covertext or by creating a new one. We illustrate our concept with three examples of concept classes of different complexity: channels that can be described by monomials, by decision trees and by DNF-formulae. Their learning complexity ranges from easily learnable up to (probably) difficult to learn. A generic construction is given showing that besides the learning complexity, the efficiency of grey-box steganography depends on the complexity of the membership test, and suitable modification procedures. For the concept classes considered we present efficient algorithms for changing a covertext into a stegotext. (C) 2012 Elsevier B.V. All rights reserved.