FHE for secret operations is very straight forward. You first define a universal circuit— that is a circuit that can compute the result of any circuit (of the size) depending on its inputs. You then have the FHE environment run that universal circuit with the operations you really want specified as an input.
Okay, the issue isn't whether you can obfuscate, but whether you can do it in a stronger sense than "regular" FHE or plain ol binaries or deliberate obfuscation. And what you've described doesn't do that.
The universal FHE circuit still sees the operations "you really want to execute", as it has to implement them in the first place. It's certainly obscured "gee, what do all these ANDs in this structure mean", but that's no different from eg an FHE scheme where you compute the circuit for the specific input size/function pair you want to compute rather than let the untrusted server generate it from knowledge of the algorithm you pass it.
So yeah, it's obfuscated, but no more than you get through regular computing; FHE has added nothing in this respect.
Comments
Okay, the issue isn't whether you can obfuscate, but whether you can do it in a stronger sense than "regular" FHE or plain ol binaries or deliberate obfuscation. And what you've described doesn't do that.
The universal FHE circuit still sees the operations "you really want to execute", as it has to implement them in the first place. It's certainly obscured "gee, what do all these ANDs in this structure mean", but that's no different from eg an FHE scheme where you compute the circuit for the specific input size/function pair you want to compute rather than let the untrusted server generate it from knowledge of the algorithm you pass it.
So yeah, it's obfuscated, but no more than you get through regular computing; FHE has added nothing in this respect.