RSA-SHA256 Signing for JSON Web Token

I am interested in using the HTTP connector in PP9.5 to connect to a REST API that can accept JSON Web Tokens (JWT) for initial authentication. I have started building a test protocol, but I am running into a snag trying to figure out how to create the signature for the JWT Assertion. The service only supports digital signatures generated using RSASSA-PKCS-v1_5 using SHA-256, SHA-384, or SHA-512 hash algorithm.

Has anyone else implemented a method of signing strings using this algorithm?