> If they use the Magic Wormhole default settings the files/messages will travel over the internet, using a third party rendezvous server.
I am very, very sure this is incorrect. The rendezvous indeed happens over the internet with their default handshake server, but the transfer itself should run in LAN.
Yes, thank you for the correction. Sloppy wording on my part. What I meant was the rendezvous happens over the internet.
Perhaps Magic Wormhole has an option to forward traffic (if so, IMHO that's not peer-to-peer) but I only meant the process of setting peer-to-peer connections requires packets to travel over the internet and, by default, to a third party server.
Yes, the "setup" messages via the Mailbox Server will be over the internet to a third-party server.
All the contents of these messages are end-to-end encrypted so you reveal which two IP addresses are communicating, but not the contents of those communications. (If you don't want to reveal that, use the Tor options).
The "bulk transfer" connection should be over the LAN only if both devices are on the same network. In any case, all of these messages are also end-to-end encrypted as well.
I am very, very sure this is incorrect. The rendezvous indeed happens over the internet with their default handshake server, but the transfer itself should run in LAN.