Do you support the crawling and indexing of https or secure server content?

Yes. The Google Mini can crawl and index secure content including content protected by basic authentication, NTLM authentication and LDAP authentication. You can prevent users from seeing search results for documents that they are not authorized to access by using HTTP Basic authorization, NTLM authorization or creating collections for different user groups.

If you want to implement more robust user-level secure search for your information, you should consider the Google Search Appliance at http://www.google.com/enterprise/gsa/index.html.