Swift - Signing JWT with private key

Question

I'm trying to do something like https://jwt.io/ does: {header}.{payload}.{privateKey}

I have a header, a payload, and a private key ( ----BEGIN PRIVATE KEY--- CODE ----END PRIVATE KEY---- ).

I know header and payload, we need to encrypt it as base64, like this:

let token = [header.toBase64(), payload.toBase64()].joined(separator: ".")

BUT, what about the private key? How can I generate this last part of this JWT using that BEGIN PRIVATE KEY file/string ?

I want to do that without external libs, can I?