The idea with homomorphic encryption is that you can have the host perform computation against the cyphertext without decrypting it. They've gotten this to work, but it's still much too slow to be of practical value. It'll get faster naturally though, even if they don't actually refine the algorithms.
From what I can gather from this link they are just concentrating on encrypting the data stored in something like S3, and having an application that you've developed handle the decryption/encryption.
Actually, there are many cloud-hosted services that aren't HTTP services and could use such a framework as well. With plenty of power for homomorphic encryption.
From what I can gather from this link they are just concentrating on encrypting the data stored in something like S3, and having an application that you've developed handle the decryption/encryption.