Alice sends the garbled circuit for a function to Bob in the offline stage. In the online stage, Alice sends affine transformations for the circuit to Bob. Then, Bob employs the garbled circuit and the affine transformations to re-randomize the circuit, and evaluates the re-randomized circuit on his input (using OT). The adversary chooses the input after seeing the garbled circuit. Is the garbled circuit adaptive?
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$\begingroup$ I have read this paper where garbled circuit is generated in the offline stage. However, in the above scheme, the re-randomized garbled circuit is generated in the online stage. Is the garbled circuit adaptive? $\endgroup$– samualJan 14, 2018 at 11:54
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$\begingroup$ If the garbled circuit is adaptive, I do not know how to define the simulator and how to define a sequence of hybrids where all gates are switch from RealGate to InputDepSimGate and from InputDepSimGate to SimGate. $\endgroup$– samualJan 14, 2018 at 12:00
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Adaptivity essentially refers to giving the adversary the power to choose an input which potentially depends on the garbled circuit, i.e., the input is adaptiveley chosen after seeing the circuit.
So if a GC scheme is proven secure in the model where the adversary outputs $x$ after seeing the garbled circuit, yes. Otherwise, no.
For formal definitions see, e.g., [1]
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