Another approach taken by researchers for carrying out computations over encrypted data is Instance Hiding.
In brief, If a user wants to outsource the computation of a function for a particular input x (instance). She transforms the input x to an encrypted input y (thus hides it) in such a way that the server cannot infer x from y and sends to the server. The server computes the function on y and returns the result. (References below).
This is also called Encrypting Problem Instances. The functions that allow such transformations are called encryptable functions. These techniques argue that encryptabality is property of a function and not all functions can be encryptable.
If this is the case, it may contradict some results of Fully Homomorphic Encryption. FHE tries to evaluate functions on encrypted inputs much generically.
Edit : in FHE, We transform the inputs (encrypt) them to cipher text which is then fed to say a function "add" carried out by server. Here add is generic function, does this mean add is encryptable function ?
I guess the catch is making assumptions on transformations
What is the catch here ? anybody ?
Refer :Abadi, Martin, Joan Feigenbaum, and Joe Kilian. "On hiding information from an oracle." Proceedings of the nineteenth annual ACM symposium on Theory of computing. ACM, 1987.