We propose steganographic systems for the case when covertexts (containers)
are generated by a finite-memory source with possibly unknown statistics. The
probability distributions of covertexts with and without hidden information are
the same; this means that the proposed stegosystems are perfectly secure, i.e.
an observer cannot determine whether hidden information is being transmitted.
The speed of transmission of hidden information can be made arbitrary close to
the theoretical limit - the Shannon entropy of the source of covertexts. An
interesting feature of the suggested stegosystems is that they do not require
any (secret or public) key.
At the same time, we outline some principled computational limitations on
steganography. We show that there are such sources of covertexts, that any
stegosystem that has linear (in the length of the covertext) speed of
transmission of hidden text must have an exponential Kolmogorov complexity.
This shows, in particular, that some assumptions on the sources of covertext
are necessary