LIPIcs.STACS.2008.1323.pdf
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Factoring Polynomials over Finite Fields using Balance Test
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25th International Symposium on Theoretical Aspects of Computer Science (STACS 2008)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
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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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
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.
Subject Classification
Keywords
- Algebraic Algorithms
- polynomial factorization
- finite fields
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