  The $k$-subset sum problem over finite fields is a classical NP-complete
problem.Motivated by coding theory applications, a more complex problem is the
higher $m$-th moment $k$-subset sum problem over finite fields. We show that
there is a deterministic polynomial time algorithm for the $m$-th moment
$k$-subset sum problem over finite fields for each fixed $m$ when the
evaluation set is the image set of a monomial or Dickson polynomial of any
degree $n$. In the classical case $m=1$, this recovers previous findings.
