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In many Attribute Based Encryption papers I see this line...

The advantage of an adversary A in this game is defined as Pr[b' = b] − 1/2.

Can someone explain what it means to me?

I assume it means that the chances of the guess being correct is equal to 1/2. Is this assumption accurate?

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  • $\begingroup$ Is $b$ a single bit {0 or 1}? Did you mean $=1/2$ not $-1/2$? $\endgroup$
    – mikeazo
    Jan 20, 2016 at 18:39
  • $\begingroup$ yes b is a single bit {0 or 1}. In the papers it appears that was so I am assuming it 1/2 as there is always a space between '-' and 1/2 $\endgroup$
    – chisky
    Jan 20, 2016 at 18:54
  • $\begingroup$ It really means that: you can phrase it as "how good is the adversary in guessing the right answer against a simple guessing with a random coin". $\endgroup$
    – ddddavidee
    Jan 20, 2016 at 22:13
  • $\begingroup$ Acutally it works also in the opposite sense: "how bad is..." because ad adversary that never guess correctly can easily transformed in a good guesser just inverting its answers $\endgroup$
    – ddddavidee
    Jan 20, 2016 at 22:14

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It means exactly what is written, the advantage of the adversary is a quantity which is defined as the difference between the probability that $b = b'$ and $1/2$. For example if the probability that $b = b'$ is $3/4$, then the advantage of the adversary is $3/4-1/2 = 1/4$.

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  • $\begingroup$ Was thinking it was more complicated and thanks alot for pointing it out. I didnt take it literarily and was thinking there was more to the statement. Thank You $\endgroup$
    – chisky
    Jan 20, 2016 at 19:13

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