# What does this advantage statement signify?

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?

• Is $b$ a single bit {0 or 1}? Did you mean $=1/2$ not $-1/2$? Jan 20 '16 at 18:39
• 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 Jan 20 '16 at 18:54
• 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". Jan 20 '16 at 22:13
• 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 Jan 20 '16 at 22:14

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 $3/4-1/2 = 1/4$.