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According to the attached reference, does it mean that the adversary computes $PPT(initial~input)$, $PPT(z)$ and $PPT(f_i(x',y'))$?

For example, suppose the corrupted party, in the malicious model, has inputs $x,z$ and it wants to compute $x \land y$, then the adversary's output will be:

$PPT(x)$, $PPT(z)$ and $PPT(x \land y))$. Am I right?

Note: PPT is a probabilistic polynomial-time algorithm

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It means that the adversary can perform whatever (PPT) computation it wants based on all the information it has (namely, the corrupted party's input, the adversary's auxiliary input, and the value received from the trusted party) and output the result of that computation.

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  • $\begingroup$ Is my example correct? $\endgroup$
    – Amirhossein Adavoudi
    Sep 2, 2018 at 4:04
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    $\begingroup$ What is $y$ in your example? If the adversary has only $x$ and $z$, how can it compute $x\wedge y$? $\endgroup$
    – fkraiem
    Sep 2, 2018 at 4:06
  • $\begingroup$ The honest party sends y to the corrupted party. $\endgroup$
    – Amirhossein Adavoudi
    Sep 2, 2018 at 4:09
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    $\begingroup$ We are here in the ideal world; the parties do not communicate with each other directly, only through the trusted party. $\endgroup$
    – fkraiem
    Sep 2, 2018 at 4:11
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    $\begingroup$ Not really. What you describe is one possibility, but there are others. The adversary can for example output $x\wedge y\wedge z$. $\endgroup$
    – fkraiem
    Sep 2, 2018 at 4:18

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