For this application I've mine I feel like I can get away with a 40 bit hash key, which seems awfully low, but see if you can confirm my reasoning (I want a small key because I want a small filename and the key will be converted to a filename):
(Note: only accidental collisions a concern - no security issues.)
A key point here is that the population in question is divided into groups, and a collision is only relevant if it occurs within the same group. A "group" is a directory on a user's system (the contents of files are hashed and a collision is only relevant if it occurs for files within the same directory). So with speculating roughly 100,000 potential users, say 2^17, that corresponds to 2^18 "groups" assuming 2 directories per user on average. So with a 40 bit key I can expect 2^(20+9) files created (among all users) before a collision occurs for some user somewhere. (Or IOW 2^((40+18)/2), due to the "birthday effect".) That's an average 4096 unique files created per user, for 2^17 users, before a single collision occurs for some user somewhere. And then that long again before another collision occurs somewhere (right?)
