I was trying to prove that a given function is not a one way function and I was not sure how to do it because maybe I had unclear what a one way function was (OWF).
The definition that I have for a OWF is the following:
Easy to compute for all inputs: for all PPT A (probabilistic polynomial time algorithms), A(x) = f(x) $\forall x$
But hard to invert:
$$Pr[B(1^k, f(x)) = x' \ s.t. \ f(x) = f(x')] < neg(k)$$
for all probabilistic polynomial time adversaries.
However, the part that I was unclear about is, if EVERY f(x) has to be hard to invert, or if its ok for it to be easy to invert say for only and only two values (say f(x) and f($\neg x$) ). I guess I was a little confused about the "invertibility" part of the definition. Is there a problem if its easy to invert for some inputs?
Thanks in advance!