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In the definition below, what exactly does it mean for the adversary (not even sure that's the correct term?) to equal one?

$$ \underset{K}{Pr} \left [A^{F_k(\cdot)} = 1 \right ] $$

Source (Page 22/35?)

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    $\begingroup$ Asymptotic security definitions ARGHHH $\endgroup$ – CodesInChaos Feb 19 '13 at 17:15
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This represents the probability over all $K$ that $A$ given an oracle access to $F_K(\cdot)$ outputs 1. You usually compare that to the probability of A ouptputting 1 while having oracle access to a random function and the difference tells you how well $A$ does at telling $F_K$ from random

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