[davidw]

Here's a hypothetical use case for homomorphic encryption, although I think it needs to do a lot more than the linked example if it's actually going to work in this case:

There's a bunch of data on a server, including, say, encrypted names. Users accessing the server have a key to decrypt those names, but they also need to be able to search for and sort names. Decrypting all the names and searching/sorting would be one option, but with enough names, it becomes very, very slow. Another option is having a big index that you decrypt for searching/sorting. This is kind of unwieldy as well, even if it's faster than decrypting everything piece by piece.

Perhaps the right homomorphic encryption techniques could also be used, although you'd have to account for substring searching in the case of names: finding "David" searching for "Dav".