Upper and Lower Bounds on Black-Box Steganography

by Nenad Dedić, Gene Itkis, Leonid Reyzin, and Scott Russell

We study the limitations of steganography when the sender is not using any properties of the underlying channel beyond its entropy and the ability to sample from it. On the negative side, we show that the number of samples the sender must obtain from the channel is exponential in the rate of the stegosystem. On the positive side, we present the first secret-key stegosystem that essentially matches this lower bound regardless of the entropy of the underlying channel. Furthermore, for high-entropy channels, we present the first secret-key stegosystem that matches this lower bound statelessly (i.e., without requiring synchronized state between sender and receiver).

Extended abstract of this work appeared in Second Theory of Cryptography Conference, TCC 2005, Joe Kilian, editor, volume 3378 of Lecture Notes in Computer Science, pp. 227-244, Springer-Verlag, 2005. The version posted above appears in the Journal of Cryptology, 22(3), pp. 365-394, July 2009, © by the authors.