Comment by bo1024

It's mind-boggling, but possible. Here's the wikipedia link: http://en.wikipedia.org/wiki/Homomorphic_encryption

The idea is this: I encrypt my data and give it to the cloud. I also encrypt the algorithm I want the cloud to use. In this case, it could be a search algorithm with the search query hardcoded. Right now, it would have to be encoded as a circuit and then encrpyted from there into a different circuit.

The cloud runs my encrypted data through this "transformed" circuit, yielding some encrypted output. The cloud tells me the output. I then decrypt it with my original key.

It's crazy that this works (longstanding open problem solved in 2005 or 06 I think). The name "homomorphic" comes from functions f, like homomorphisms, in which "order doesn't matter":

    f(data) = f(Decrypt(Encrypt(data))) = Decrypt(f(Encrypt(data))).

Hope that makes some sense.