Department of Computer Science
 
Chair V

 
University of Bonn -> Department of Computer Science -> Chair V
CS-Reports 2008 Copyright 2008 University of Bonn, Department of Computer Science, Abt. V
85289

14.04.2008

Schemes for Deterministic Polynomial Factoring
Gábor Ivanyos, Marek Karpinski and Nitin Saxena
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In this work we relate the deterministic complexity of factoring polynomials (over finite fields) to certain combinatorial objects we call m-schemes. We extend the known conditional deterministic subexponential time polynomial factoring algorithm for finite fields to get an underlying m-scheme. We demonstrate how the properties of m-schemes relate to improvements in the deterministic complexity of factoring polynomials over finite fields assuming the generalized Riemann Hypothesis (GRH). In particular, we give the first deterministic polynomial time algorithm (assuming GRH) to find a nontrivial factor of a polynomial of prime degree n where (n-1) is a smooth number.

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University of Bonn -> Department of Computer Science -> Chair V