Creating a password-protected RSS feed

I’d like to create a private RSS feed, that is, a password-protected RSS feed. This is for a private site that is entirely password protected using the Registered Only plugin (written by Carthik Sharma, based on work done by Ryan Boren).
This has nothing to do with using the per-post password protection.
I’ve read surveys of aggregators that support HTTPS authentication. But I’m not really a RSS aggregated content reader, even less an expert in the ways of tweaking RSS feeds. What I’d like to know is what I need to do in order to create a feed that is published, but the entire contents of it are password-protected.