Asymptotically optimal perfect steganographic systems

In 1998 C. Cachin proposed an information-theoretic approach to steganography. In particular, in the framework of this approach, so-called perfectly secure stegosystems were defined, where messages that carry and do not carry hidden information are statistically indistinguishable. There was also described a universal steganographic system, for which this property holds only asymptotically, as the message length grows, while encoding and decoding complexity increases exponentially. (By definition, a system is universal if it is also applicable in the case where probabilistic characteristics of messages used to transmit hidden information are not known completely.)
In the present paper we propose a universal steganographic system where messages that carry and do not carry hidden information are statistically indistinguishable, while transmission rate of “hidden” information approaches the limit, the Shannon entropy of the source used to “embed” the hidden information.