Factoring Polynomials over Finite Fields using Balance Test

Saha, Chandan

doi:10.4230/LIPIcs.STACS.2008.1323

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Factoring Polynomials over Finite Fields using Balance Test

Author Chandan Saha

Part of: Volume: 25th International Symposium on Theoretical Aspects of Computer Science (STACS 2008)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution-NoDerivs 3.0 Unported license
Publication Date: 2008-02-06

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DOI: 10.4230/LIPIcs.STACS.2008.1323
URN: urn:nbn:de:0030-drops-13233

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Keywords

Algebraic Algorithms
polynomial factorization
finite fields

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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.

Cite As Get BibTex

Chandan Saha. Factoring Polynomials over Finite Fields using Balance Test. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 609-620, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008) https://doi.org/10.4230/LIPIcs.STACS.2008.1323

Author Details

Chandan Saha

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