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CORR
2008
Springer

Trading GRH for algebra: algorithms for factoring polynomials and related structures

8 years 6 months ago
Trading GRH for algebra: algorithms for factoring polynomials and related structures
Abstract. In this paper we develop a general technique to eliminate the assumption of the Generalized Riemann Hypothesis (GRH) from various deterministic polynomial factoring algorithms over finite fields. It is the first bona fide progress on that issue for more than 25 years of study of the problem. Our main results are basically of the following form: either we construct a nontrivial factor of a given polynomial or compute a nontrivial automorphism of the factor algebra of the given polynomial. Probably the most notable application of such automorphisms is efficiently finding zero divisors in noncommutative algebras. The proof methods used in this paper exploit virtual roots of unity and lead to efficient actual polynomial factoring algorithms in special cases.
Gábor Ivanyos, Marek Karpinski, Lajos R&oac
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Gábor Ivanyos, Marek Karpinski, Lajos Rónyai, Nitin Saxena
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