How to formally prove that random guess is the best attack How to formally argue that there exists no efficient $A$ who can come up with a $e$ such that $$\begin{align}x&amp;=PRF(e,0) \land \\ y &amp;= PRF(e,1) \land \\ x &amp;= H(y)\end{align}$$ where $H$ is a secure hash function and $|x|=|y|=\ell$?
Note that it's easy to argue that if $A$ just guesses randomly, the success probability for each guess is negligible (something like $\frac{1}{2^{\ell}}$). But how to argue there is no better algorithm than guessing?
But how to argue there is no better algorithm than guessing?

Show that, if there is a better algorithm than guessing, you can distinguish the PRF from random.