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In Adaptively Secure Garbled Circuits from One-Way Functions, the authors wrote that the adversary may be able to influence the choice of the input $x$ after seeing the garbled circuit, so we need a stronger notion called adaptive security. Why may the adversary be able to influence the choice of the input after seeing the garbled circuit?

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    $\begingroup$ It just depends on how it's used in a protocol. If the garbled circuit is sent in an offline phase, before the inputs are determined, then the corrupted party can make its input depend on the garbled circuit. $\endgroup$ – Yehuda Lindell Jan 2 '18 at 11:58
  • $\begingroup$ We first encrypt the garbled circuit (functional encryption) and send it in an offline phase. Next, the adversary chooses his input (he only can see the encryption of the garbled circuit ) in an online phase, and he decrypts the garbled circuit using the functional encryption scheme and computes a result. In this case , is the garbled circuit secure and adaptive? $\endgroup$ – samual Jan 3 '18 at 2:51
  • $\begingroup$ We encrypt the four ciphertext pairs of every gate in the garbled circuit using the functional encryption scheme. $\endgroup$ – samual Jan 3 '18 at 3:06
  • $\begingroup$ Probably not, unless the functional encryption scheme is equivocal. The answer to all of these things is "try to prove that it's adaptively secure" and then you'll know. $\endgroup$ – Yehuda Lindell Jan 3 '18 at 6:16
  • $\begingroup$ 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? $\endgroup$ – samual Jan 13 '18 at 13:28

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