You referenced the LS220D which I am going to interpret as being LinkStation 220 D – while that model is not listed in the support documentation I am looking at on the Buffalo Technology website, I am going to assume that it also supports acting as a web server.
If that is indeed the case … which from your OP you believe it to be so …
It is very doable to get a SSL cert in this case, but you will need to register a domain first. And that SSL cert will secure the domain that is being hosted, but I do not believe that it will secure the file transfers being handled between your device and their web interface – I would think that they would use encryption built into the hardware for that!