I am implementing a REST service which has RESTful authentication using jwt based on suggestions from this and this answers.
In constructing the JWT I have decided to sign it using an rsa public private pair rather than hmac for the obvious benefit of being able to keep my signing key fully private because I don't trust the clients that I will need to share the validation key with.
My question is, since normal https server certificates already use rsa keys, would it be acceptable to use that same key pair to sign a JWT token? One advantage I can see is that I will not have to maintain two certificates and mechanisms for sharing the public key with the client are already well established.
PS In case I sign the JWT with a new specific key pair, what is the best way of sending the public key to the client for use in verifying the token?