License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2016.47
URN: urn:nbn:de:0030-drops-64609
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6460/
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Guo, Zeyu ; Narayanan, Anand Kumar ; Umans, Chris

Algebraic Problems Equivalent to Beating Exponent 3/2 for Polynomial Factorization over Finite Fields

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LIPIcs-MFCS-2016-47.pdf (0.5 MB)

Abstract

The fastest known algorithm for factoring univariate polynomials over finite fields is the Kedlaya-Umans (fast modular composition) implementation of the Kaltofen-Shoup algorithm. It is randomized and takes ~O(n^{3/2}*log(q)+n*log^2(q)) time to factor polynomials of degree n over the finite field F_q with q elements. A significant open problem is if the 3/2 exponent can be improved. We study a collection of algebraic problems and establish a web of reductions between them. A consequence is that an algorithm for any one of these problems with exponent better than 3/2 would yield an algorithm for polynomial factorization with exponent better than 3/2.

BibTeX - Entry

@InProceedings{guo_et_al:LIPIcs:2016:6460,
  author =	{Zeyu Guo and Anand Kumar Narayanan and Chris Umans},
  title =	{{Algebraic Problems Equivalent to Beating Exponent 3/2 for Polynomial Factorization over Finite Fields}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{47:1--47:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6460},
  URN =		{urn:nbn:de:0030-drops-64609},
  doi =		{10.4230/LIPIcs.MFCS.2016.47},
  annote =	{Keywords: algorithms, complexity, finite fields, polynomials, factorization}
}

Keywords: algorithms, complexity, finite fields, polynomials, factorization
Collection: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue Date: 2016
Date of publication: 19.08.2016

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