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the worst-case one way function is defined as follows $$\forall A \exists x : pr(A(f(x))\in f^{-1}(f(x)))\neq 1$$ can you give any example of such function?

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  • $\begingroup$ This is probably just me not understanding the notation, but represents $f^{-1}$ all possible values if somebody does try to reverse the function? $\endgroup$ – Maarten Bodewes Jun 21 '15 at 17:12
  • $\begingroup$ Yeah, actually A is an advetsary who tries to find a pre-image for y (where y=f(x)) $\endgroup$ – A.Soleimani Jun 22 '15 at 11:06
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    $\begingroup$ The more usual notion of an (average-case) one-way function is, naturally, also a worst-case one-way function. See e.g. en.wikipedia.org/wiki/… $\endgroup$ – Daniel Apon Jun 23 '15 at 4:24
  • $\begingroup$ Thanks but I mean a function which is worst-case one way but not weak or strong(average-case) one way. do you have any idea about it? $\endgroup$ – A.Soleimani Jun 23 '15 at 16:43
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Worst-case one-way functions exist if and only if P ≠ NP, therefore, if I were you, I would not expect to get a definitive answer to your question any time soon :).

On the other hand, if you are willing to assume that P ≠ NP, then it is not hard to construct such a function (that is actually exactly a half of the proof of the theorem I stated in the previous paragraph).

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