Ad multilevel dynamic menubar to arbitary page

Hi

I am using the default twenty-twelve theme and have a menubar like I want on the front page which is public. (Not a tree on the sidebar).
The largest part of the site is for authenticated users and here I have a page where I also want to have this type of menu.

How would I implement this?

Ideally I wan to use the default system and if a plugin is required,
we need it to be very stable – bug tolerance is low ??

Thanks for any kind suggestions.

Eric Smith