Tests for Permutation Functions

Authors:
K. Ma;J. Von Zur Gathen
Affiliations:
Department of Computer Science, University of Toronto, Toronto, Ontario M5S 1A4, Canada;Department of Computer Science, University of Toronto, Toronto, Ontario M5S 1A4, Canada
Venue:
Finite Fields and Their Applications
Year:
1995

Citing 15
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Abstract

Let F"q be a finite field with q elements, @? @? F"q(x) a rational function over F"q, and D @? F"q the domain of definition of @?. Consider three notions of ''permutation functions'': @? is a permutation on F"q, or on D, or @? is injective on D. For each of these, a random polynomial-time test is presented. For the image size of an arbitrary rational function, a fully polynomial-time randomized approximation scheme is given.