[hcrypt]

The attacker can do whatever she wants. You can't prevent her from doing anything. But maybe you can elaborate on what you mean with "each power of two". When trying to compare with zero (what zero?), keep in mind we're talking about a probabilistic cryptosystem. The machine is just an application of the underlying scheme, so it's not the machine that provides the atomic functions.

To be precise, the state of the machine includes the flags, the PC and memory. It's easy to implement a simple stack pattern in circuits but you don't need it in order to implement arbitrary functions.

We already published the solution for encrypted memory access and encrypted program flow control (without unfolding) but halting is an issue you (at least to my knowledge) cannot solve under the assumptions we made.