Let \mathbb{F}_q be a finite field and f(x) \in \mathbb{F}_q(x) be a rational function over \mathbb{F}_q.
The decision problem {\bf PermFunction} consists of deciding whether f(x) induces a permutation on
the elements of \mathbb{F}_q. That is, we want to decide whether the corresponding map
f : \mathbb{F}_q \mapsto \mathbb{F}_q defined by a \mapsto f(a) is a bijective mapping or not.
This problem was known to be in \mathcal{ZPP} but not known to be in
\mathcal{P}. We resolve the complexity of {\bf PermFunction} by giving a deterministic polynomial-time
algorithm for this problem.