Given F, which is a Pseudo Random Permutation, I need to prove that the following function f is not a OWF:

f(x, y) = Fx(y)

My first thought would be to create an adversary which tries and compute Fx-1(y) with different values for x, but I'm not sure it would be PPT. How can I solve this?

  • $\begingroup$ If you truncate the permutation then it cannot be inverted. $\endgroup$ – cypherfox Mar 22 '18 at 14:46

Any $x$ is fine. Since $F$ is a PRP, for any key $x$ and output string $z$ there is an input string $y$ such that $F_x(y) = z$.

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