  In continuation to earlier works where the problem of joint information
embedding and lossless compression (of the composite signal) was studied in the
absence \cite{MM03} and in the presence \cite{MM04} of attacks, here we
consider the additional ingredient of protecting the secrecy of the watermark
against an unauthorized party, which has no access to a secret key shared by
the legitimate parties. In other words, we study the problem of joint coding
for three objectives: information embedding, compression, and encryption.Our
main result is a coding theorem that provides a single--letter characterization
of the best achievable tradeoffs among the following parameters: the distortion
between the composite signal and the covertext, the distortion in
reconstructing the watermark by the legitimate receiver, the compressibility of
the composite signal (with and without the key), and the equivocation of the
watermark, as well as its reconstructed version, given the composite signal. In
the attack--free case, if the key is independent of the covertext, this coding
theorem gives rise to a {\it threefold} separation principle that tells that
asymptotically, for long block codes, no optimality is lost by first applying a
rate--distortion code to the watermark source, then encrypting the compressed
codeword, and finally, embedding it into the covertext using the embedding
scheme of \cite{MM03}. In the more general case, however, this separation
principle is no longer valid, as the key plays an additional role of side
information used by the embedding unit.
