Let $H$ be a hash function that is both hiding and puzzle friendly. Consider $G(z) = H(z) \Vert z_l$ where $z_l$ is the last bit of $z$. Show that $G$ is puzzle frielndly but not hiding.
This question is from this book, page 50). I'm stuck at proving $G$ as non-hiding.
A hash function is hiding if: when a secret value $r$ is chosen from a probability distribution that has a high min-entropy, then given $H(r \Vert x)$ it is infeasible to find $x$.
Now for given function $G$, we have:
$G(r \Vert z) = H(r \Vert z) \Vert z_l$
I don't see how $G$ fails to be hiding. If we are given $G$'s output, we just know about one fixed bit of the input. $H(r \Vert z)$ (the part of the output excluding the last bit) still makes it infeasible to determine $z$ since $H$ is hiding. How can one bit of input prevent $G$ from hiding?