Without knowing the actual pointed problem space the generalities of the schema just sounds like a snake game to me.
I can't get past where the veil is dropped for bob to take some ciphertext and operate on it in any meaningful way for him to create some machine that simultaneously can process encrypted data while being completely blinded to what the data is or the insights learned. Any form of ability to process a datum while simultaneously being blinded to it is logically incompatible to me.
Now, could we obfuscated it and lower the chances of an attacker being able to do anything useful with it or knowing what is being processed? Yes...but why muddy the definition of encryption in order to do this?