I am sorry if this is a naive question but is there any justification for the way that s is computed in the DSA signature algorithm:
$$ s = k^{-1} * (rx + m) $$
This looks to me like a very arbitrary combination of $k$, $r$, $x$ and $m$. Is this just one particular way that's found to work or does it actually have some kind of structure/reason behind it that I am missing?
