A non-interactive zero-knowledge proof of faithful execution

Intriguing concept, but I have some doubts about its security, considering there isn't any kind of security proof at all. I'm not really an expert in zero knowledge proofs, but what I've been taught about them raises some questions here...

For starters, notice that a hash function as a commitment scheme is neither information-theoretically hiding, nor information-theoretically blinding [1], unlike e.g. a simple Pedersen commit. Another problem is that the XOR in the example table needs to be exactly one bit -- it is non-trivial to show that this actually works. Thirdly and perhaps chiefly, it is unclear why this would actually produce a zero knowledge proof, since the same inputs will produce the same circuits and the same output. Thus, I think we can build a distinguisher better than guessing to decide whether two inputs are the same given the same output (and all other inputs being equal).

Maybe these aren't a definitive end point, but they sure as hell require merit investigation.

[1] for more info on these ideas, try these: http://www.win.tue.nl/~berry/2WC13/LectureNotes.pdf (chapter 3) http://en.wikipedia.org/wiki/Commitment_scheme#Defining_the_...