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Reasons for the asymptotic approach

tl flag

While reading Katz & Lindell's textbook (2nd edition) I stumbled over the chapter about the asymptotic approach. In the first part there is explained, why the concrete approach is not good. Then the asymptotic approach is introduced. A negligible success probability is defined over a function, that is asymptotically smaller than any inverse polynomial function.

My question: Why was it defined over functions with this property? Why weren't e.g. logarithmic functions or functions with different properties to polynomials? Is it because only exponential functions grow faster than polynomials?

kelalaka avatar
in flag
If you are polynomially bounded, then if your success probbaility is worse than any polynomial then, you had gained almost nothing with your polynomial effort.
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