Secure Wiki

Hi, I am a newbie on here and am really looking for a specific
solution. I want to put up a site that allows the following levels of
access
i) Core pages are readable by all
ii) Other pages restricted to readable by sub sets of site members
iii) Site members can edit designated 'open' pages
iv) Site members can creat their own content and then set the security
level on it to universally readable, readable by members, universally
editable, editable by members, and the same for sub-sets of members (I
would need to maintain 'root' access to all user created content)

Basically it strikes me that a wiki tied into some sort of ldap with
page level authentication would do it but ... rather than design this
form scratch I was wondering if there was wiki software out there that
provided this type of functionality. Any one got any ideas?

The site will have low levels of membersship, no more than 20, so
setting up access for pages can be done on an individual user level,
but an ability to create groups of users would be advantageous.

I can clarify with specific examples if this is unclear.