# Worst case one way function

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?

• This is probably just me not understanding the notation, but represents $f^{-1}$ all possible values if somebody does try to reverse the function? – Maarten Bodewes Jun 21 '15 at 17:12
• Yeah, actually A is an advetsary who tries to find a pre-image for y (where y=f(x)) – A.Soleimani Jun 22 '15 at 11:06
• 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/… – Daniel Apon Jun 23 '15 at 4:24
• 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? – A.Soleimani Jun 23 '15 at 16:43