Factorization in Z[x]: The Searching Phase

John Abbott, Victor Shoup, Paul Zimmermann

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper we describe ideas used to accelerate the Searching Phase of the Berlekamp-Zassenhaus algorithm, the algorithm most widely used for computing factorizations in Z[x]. Our ideas do not alter the theoretical worst-case complexity, but they do have a significant effect in practice: especially in those cases where the cost of the Searching Phase completely dominates the rest of the algorithm. A complete implementation of the ideas in this paper is publicly available in the library NTL. We give timings of this implementation on some difficult factorization problems.

Original languageEnglish (US)
Title of host publicationProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
PublisherACM
Pages1-7
Number of pages7
StatePublished - 2000
EventProceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000) - St Andrews, UK
Duration: Aug 7 2000Aug 9 2000

Other

OtherProceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000)
CitySt Andrews, UK
Period8/7/008/9/00

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Factorization
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ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Abbott, J., Shoup, V., & Zimmermann, P. (2000). Factorization in Z[x]: The Searching Phase. In Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC (pp. 1-7). ACM.

Factorization in Z[x] : The Searching Phase. / Abbott, John; Shoup, Victor; Zimmermann, Paul.

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC. ACM, 2000. p. 1-7.

Research output: Chapter in Book/Report/Conference proceedingChapter

Abbott, J, Shoup, V & Zimmermann, P 2000, Factorization in Z[x]: The Searching Phase. in Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC. ACM, pp. 1-7, Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000), St Andrews, UK, 8/7/00.
Abbott J, Shoup V, Zimmermann P. Factorization in Z[x]: The Searching Phase. In Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC. ACM. 2000. p. 1-7
Abbott, John ; Shoup, Victor ; Zimmermann, Paul. / Factorization in Z[x] : The Searching Phase. Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC. ACM, 2000. pp. 1-7
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