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Abstract: . A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented. To factor a polynomial of degree n over F q , the number of arithmetic operations in F q is O((n 2 +n log q) \Delta (log n) 2 loglog n). The main technical innovation is a new way to compute Frobenius and trace maps in the ring of polynomials modulo the polynomial to be factored. Subject classifications. 68Q40; 11Y16, 12Y05. 1. Introduction We consider the problem of factoring a... (Update)
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...f d such that f d is the product of all the irreducible factors of degree d. See, e.g. Knuth [10, pp. 429 431] and more recently [1,2,3,7,11]. Further references can be found in Shparlinski [12,Chapter 1] If a given polynomial f in IF q [X] has k irreducible factors of...
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BibTeX entry: (Update)
Joachim von zur Gathen & Victor Shoup (1992). Computing Frobenius maps and factoring polynomials. computational complexity 2, 187-224. http://citeseer.ist.psu.edu/vonzurgathen92computing.html More
@inproceedings{ gathen92computing,
author = "Joachim von zur Gathen and Victor Shoup",
title = "Computing {Frobenius} maps and factoring polynomials",
pages = "97--105",
year = "1992",
url = "citeseer.ist.psu.edu/vonzurgathen92computing.html" }
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6 A fast deterministic algorithm for factoring polynomials ove.. - Shoup - 1991
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1 Calcul des racines d-i`emes dans un corps fini (context) - Mignotte, Schnorr - 1988
1 Subgroup refinement algorithms for root finding in GF (context) - Menezes, van Oorschot et al. - 1992
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