I have heard of token-based authentication, but the problem is that most of it requires trusting the server. What I need is something else.
Alice, with my game, wants to connect to Bob's server, which is designed for my game. Alice can get a token from my official (trusted) server. She also needs to authenticate on Bob's server to prove she is really Alice. But if she sends the token to Bob directly, Bob can exploit her token.
So, what is the way for Alice to show to Bob's server that she is registered as Alice on my server without leaking exploitable data? The connection is unencrypted UDP (if you know how to properly encrypt UDP, than tell me), not https or even http.
Edit: from a comment talking about PKI and an answer mentioning Singning Certificates, I decided I'd use something like RSA and RSA certificates for authentication.