@MISC{Kayal04recognizingpermutation, author = {Neeraj Kayal}, title = {Recognizing permutation functions in polynomial time}, year = {2004} }

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Abstract

Let Fq be a finite field and f(x) ∈ Fq(x) be a rational function over Fq. The decision problem PermFunction consists of deciding whether f(x) induces a permutation on the elements of Fq. That is, we want to decide whether the corresponding map f: Fq ↦ → Fq defined by a ↦ → f(a) is a bijective mapping or not. This problem was known to be in ZPP but not known to be in P. We resolve the complexity of PermFunction by giving a deterministic polynomial-time algorithm for this problem. 1