Master server design

So far so clear

What about when some client wants to connect to the game server.

Suppose client has already got the ip:port of the game server from the master server and now wants to make a connection to game server.

Should I also give the client a temporary access token to use when connecting a game server? So the game server can also safely authenticate who is being connected, either doing itself by using the shared public-key or by asking from the master server.