The JOSE standard introduces a signature (JWS) and encrypted data (JWE) which describe a data bundle, either signed or encrypted. However I cannot find a "request of signature" or "request of encryption" (it's possible to use JWE as request for decryption).
I would like to ask a remote end, as a proof of shared secret ownership, "sign me these bytes using this algorithm and this key" for which the response is a JWS as well as "encrypt these bytes using this key" for which the response is a JWE.
I'm trying to not reinvent the wheel here and while reading the JOSE spec I couldn't find anything like that that could be of use. It seems like such a common type of request that I wonder why/how it could be left out.