Does Cut-Choose technique for yao garbled circuit provide statistical security? Yao Garbled circuit is 2 parties secure computation protocol between Semi honest adversaries. However, the cut-and-choose mechanism complies semi-honest garbled circuits into the one secure against malicious adversaries. Specifically, it provides statistical security against malicious garbler (circuit creator). 

My question is as cut-and-choose provides statistical security, can garbler be "unbounded"?
Cut-and-choose is not a specific protocol that we can analyze, but a general technique whose details can be realized in many ways.

The basic idea of cut-and-choose is to generate many garbled circuits, open some of them to test for correctness, and evaluate the rest. The goal is to ensure that most (or, in some protocols, at least one) circuits used for evaluation are correct. If this condition holds, even of those "correct" circuits were generated by a corrupt garbler, there is no problem. Furthermore, the analysis of how many circuits to generate/open doesn't consider the running time of the corrupt garbler. It is a purely statistical argument. So this central idea of garbled circuits is naturally safe in the presence of an unbounded garbler.

But there are other parts of a "cut-and-choose protocol": 


The garbler must provide garbled inputs to the receiver, using oblivious transfer (OT). Naturally the OT protocol must be secure against an unbounded sender, and this is possible.
The protocol must prevent the garbler from using inconsistent inputs across different garbled circuits. Different protocols vary widely in how they realize these properties. I believe that some are secure against an unbounded garbler, and probably others are not.
The protocol must prevent the garbler from causing the receiver to abort with input-dependent probability. Again, whether this is safe against an unbounded garbler depends on how the mechanism is realized. I think that some techniques are safe and others are not.