I've lately found about digital signatures with message recovery.
I was wondering, in what degree do these signatures provide confidentiality of the message (if they do at all) ? I've briefly read a couple of papers but they don't mention confidentiality as a security service provided and I wander why.
My theory is that since the message is recovered from the signature, after the verification is done, and for the verification to be done a key is needed, this means that whoever does not have the key (ignoring it is public), cannot recover the message.
Am I correct, from a mathematical point of view? I'd like a cryptographer to comment if possible, or someone who knows the mathematics behind digital signatures with message recovery.