Subquadratic Computation of Vector Generating Polynomials and Improvement of the Block Wiedemann Algorithm

This paper describes a new algorithm for computing linear generators (vector generating polynomials) for matrix sequences, running in subquadratic time. This algorithm applies in particular to the sequential stage of Coppersmith’s block Wiedemann algorithm. Experiments showed that our method can be...

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Bibliographic Details
Published inJournal of symbolic computation Vol. 33; no. 5; pp. 757 - 775
Main Author Thomé, Emmanuel
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.05.2002
Elsevier
Subjects
Computer Science
Cryptography and Security
Distributed, Parallel, and Cluster Computing
Symbolic Computation
Online AccessGet full text
ISSN0747-7171
1095-855X
1095-855X
DOI10.1006/jsco.2002.0533

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Summary:This paper describes a new algorithm for computing linear generators (vector generating polynomials) for matrix sequences, running in subquadratic time. This algorithm applies in particular to the sequential stage of Coppersmith’s block Wiedemann algorithm. Experiments showed that our method can be substituted in place of the quadratic one proposed by Coppersmith, yielding important speedups even for realistic matrix sizes. The base fields we were interested in were finite fields of large characteristic. As an example, we have been able to compute a linear generator for a sequence of 4 × 4 matrices of length 242 304 defined over F 2607−1 in less than 2 days on one 667 MHz alpha ev67 CPU.
ISSN:0747-7171
1095-855X
1095-855X
DOI:10.1006/jsco.2002.0533