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The Capacity of a Stegosystem for the Noisy Attack Channel

We consider a scenario where an attacker is able to receive a stegosignal only over a noisy channel under the condition that he (or she) may even know the cover message (CM). We propose to use a spread-spectrum-signal-based stegosystem (SG) and prove that the capacity of such SG is zero for any fixed security level. Moreover, we show that the code rate satisfies a square root law due to Ker et al. (in reality this law can be found in an earlier paper (2005) by the authors of the current paper). We get the same result for a conventional SG where the CM is modeled by a Gaussian correlated sequence with a correlation matrix unknown for the SG designer. We speculate that for any conventional SG with noiseless attack channel but for a practical CM model, the capacity should also be zero.