FHE (Fully Homomorphic Encryption) is a cryptographic encryption schema in which it is possible to perform arithmetic operations on the ciphered text without deciphering it.
Though there is no really efficient crypto-system with this property at this time, several proofs of concepts show that this kind of cryptography does actually exist. And, that, maybe one day, we might find an efficient crypto-system with the FHE properties.
For now, the usage of FHE is mainly directed towards "Cloud Computing" where one want to delegate a costly computation to a remote computer without spreading his data away. So, the principle is just to send out encrypted data and the Cloud will apply a given computation on the data and send back the encrypted answer without having knowledge of what is inside.
The link with code obfuscation is quite obvious as if we can perfectly obfuscate data, then we can also perfectly obfuscate the algorithm by coding it into a universal Turing machine. But, the Devil is always in the details. A recent paper  presents a way to use the FHE for obfuscation, but in a too stronger way (in my humble opinion).
My question is the following: Suppose we have an efficient FHE schema, suppose also that our goal is to slow down the analysis of a program (and not totally prevent it). Then, what would be the most efficient usage of the FHE in obfuscation ?