ECCC-Report TR05-008https://eccc.weizmann.ac.il/report/2005/008Comments and Revisions published for TR05-008en-usTue, 18 Jan 2005 19:45:25 +0200
Paper TR05-008
| Recognizing permutation functions in polynomial time. |
Neeraj Kayal
https://eccc.weizmann.ac.il/report/2005/008Let $\mathbb{F}_q$ 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.
Tue, 18 Jan 2005 19:45:25 +0200https://eccc.weizmann.ac.il/report/2005/008