The Black-Box Niederreiter Algorithm and its Implementation Over the Binary Field

Fleischmann, Peter and Holder, Markus Chr. and Roelse, Peter (2003) The Black-Box Niederreiter Algorithm and its Implementation Over the Binary Field. Mathematics of Computation, 72 (244). pp. 1887-1899. ISSN 0025-5718 . (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1090/S0025-5718-03-01494-7

Abstract

The most time-consuming part of the Niederreiter algorithm for factoring univariate polynomials over finite fields is the computation of elements of the nullspace of a certain matrix. This paper describes the so-called "black-box" Niederreiter algorithm, in which these elements are found by using a method developed by Wiedemann. The main advantages over an approach based on Gaussian elimination are that the matrix does not have to be stored in memory and that the computational complexity of this approach is lower. The black-box Niederreiter algorithm for factoring polynomials over the binary field was implemented in the C programming language, and benchmarks for factoring high-degree polynomials over this field are presented. These benchmarks include timings for both a sequential implementation and a parallel implementation running on a small cluster of workstations. In addition, the Wan algorithm, which was recently introduced, is described, and connections between (implementation aspects of) Wan's and Niederreiter's algorithm are given.

Item Type: Article
Uncontrolled keywords: Finite fields, polynomial factorization, implicit linear algebra
Subjects: Q Science
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Peter Fleischmann
Date Deposited: 10 Sep 2008 09:33
Last Modified: 19 Jun 2014 11:34
Resource URI: http://kar.kent.ac.uk/id/eprint/8957 (The current URI for this page, for reference purposes)
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