a 3 letter designation would work very well. OPN, PUB, PBT, PFT, PBG, and PVT. or something similar. Open, Public, 3 partially public, and a private.
A second option that would work is a level designation of privacy. that could be from 0-5 or 1-6.
Personally, the open lock always looked like a nun to me. LOL
I definitely like the file idea though.