It is possible to convert a pre-image resistant function $f:\{0,1\}^{n}\rightarrow \{0,1\}^{n}$ to a second-preimage resistant function? I am thinking to use a pseudo-random generator and construct that second pre-image resistant function in this way:
$$F(x)=f(x)+\text{PRNG}(x).$$
What kind of tests I need to make to verify this function is second-preimage resistant?
