Sidebar section for registered users only

We have a site set with some public and some private content. We can restrict the private content to two or three specific categories.

What I need to do is, in the sidebar, list out only the public-access categories in the regular categories section. Then lower down in the sidebar I want another section for subscribed users that shows the link for logging in (I’ve got this one thing working), and once the user is logged in, they should then see the links to categories that are for members-only.

So how do we go about serving up a subset of content to only usergroup X or higher?