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I have difficulties checking whether $f^{-1}(x)$ is a one way function. $x \leq 2^n$ is the sum that we want the set of numbers $a_1,...,a_m$ to be. $m \leq 2^n$. There are $4^n$ different ways to sum up to a number $x$ but I did not get any further in checking if this is a one way function. Can someone help me?

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    $\begingroup$ The question is unclear. What is $f$? Please don't start sentences with mathematical formulas, it's awful. And state your question in the text. Asking "Can someone help me?" is not a good question. $\endgroup$
    – Andrej Bauer
    Commented Jul 5 at 11:51

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The existence of one way functions is an open problem. As is whether the subset sum problem is solvable with a polynomial time algorithm.

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