Depending on how big and how many files, you could use Snapdrop. As the name implies, it's like AirDrop but you can use it anywhere
Install Samba on the Ubuntu box, and connect from the Mac.
or..
Set up File Sharing on the Mac, and connect from the Ubuntu box.
Unless you intend to file share across the public internet, either should be secure enough for local LAN use.Thanks. Being that I use the Mac much than the Ubuntu box, which of those approaches would be intrinsically more secure for the Mac? Putting Samba on the Ubuntu box?