License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2008.1323
URN: urn:nbn:de:0030-drops-13233
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1323/
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Saha, Chandan

Factoring Polynomials over Finite Fields using Balance Test

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22011.SahaChandan.Paper.1323.pdf (0.2 MB)

Abstract

We study the problem of factoring univariate polynomials over
finite fields. Under the assumption of the Extended Riemann
Hypothesis (ERH), (Gao, 2001) designed a polynomial time algorithm
that fails to factor only if the input polynomial satisfies a
strong symmetry property, namely square balance. In this paper, we
propose an extension of Gao's algorithm that fails only under an
even stronger symmetry property. We also show that our property
can be used to improve the time complexity of best deterministic
algorithms on most input polynomials. The property also yields a
new randomized polynomial time algorithm.

BibTeX - Entry

@InProceedings{saha:LIPIcs:2008:1323,
  author =	{Chandan Saha},
  title =	{{Factoring Polynomials over Finite Fields using Balance Test}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{609--620},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Susanne Albers and Pascal Weil},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1323},
  URN =		{urn:nbn:de:0030-drops-13233},
  doi =		{10.4230/LIPIcs.STACS.2008.1323},
  annote =	{Keywords: Algebraic Algorithms, polynomial factorization, finite fields}
}

Keywords: Algebraic Algorithms, polynomial factorization, finite fields
Collection: 25th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2008
Date of publication: 06.02.2008

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