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Should I normalize adversary's advantage in IND-XXX Game?

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apapapa

The Cryptography made simple (page 207, under Fig 11.12)(Nigel Smart) say that adversary's advantage of IND-PASS Game is $Adv1 = 2\times|Pr[b=b']-\frac{1}{2}|$.
The reason for multiplying by 2 is to normalize advantage from $[0,\frac{1}{2}]$ to $[0,1]$.

But in this paper (page 5, line 9), the advantage of IND-CKA Game is $Adv2 = |Pr[b=b']-\frac{1}{2}|$ which is not normalized and scale is $[0,\frac{1}{2}]$.
And this value is used with the advantage of pseudo random function
$Adv3 = |Pr[A(f)=0]-Pr[A(g)=0]|$
(f is pseudo random function. g is random function)
which scale is $[0,1]$.

Does $Adv2$ need not be normalized to $[0,1]$ for use with $Adv3$?
Or do I usually not need to be aware of normalization of "advantage"?

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kelalaka avatar
in flag
kelalaka
Welcome to Cryptography.SE. We have $\LaTeX$/MathJax enabled on our site. You can also provide the page number of the book. It is free to download that I've given the link.
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bd flag
apapapa
thank you! Added page number. (It is 207 pages in print, but it looks 212 page in Google Chrome)
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Marc Ilunga avatar
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Marc Ilunga
The "value" of the advantage often depends on the context and agreed-upon conventions as long as they express something meaningful. Consequently, the expression for a CPA game may look different than the one for a hash collision game. For a specific game, the scale should not really matter as long as the goal is understood. I would say it is still good to be aware of the different conventions even though they express the same thing.
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