[mti]

I'm not sure what specific scheme you have in mind, but while FHE for Turing machines does exist, it is really, really hard to instantiate. A construction with some restrictions and requiring a massive amount of preprocessing is given in Goldwasser et al.'s famous paper on reusable garbled circuits, and it already uses succinct functional encryption as a building block; and for the stronger notion of FHE for TM you basically need obfuscation. So thinking about implementing any of this seems somewhat premature to me.