If our token is intended to be read by third parties, then an asymmetric signature generation algorithm makes sense. This is because, on top of providing authenticity and integrity, it asymmetric signature generation also provides the property of non-repudiation where the issuer of the JWT cannot deny (or repudiate) that they issued the token.
With an asymmetric signature, only our server would have access to the private key; this provides consumers of the JWT with confidence that the token was issued by our server and nobody else. If we instead use symmetric signature generation, we must securely share the secret with third party consumers so that they can decrypt the token. But it also means the third-parties can use ...
