research-article

Fast Polynomial Multiplication over F₂₆₀

Authors:

Joris van der Hoeven,

Grégoire LecerfAuthors Info & Claims

ISSAC '16: Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation

Pages 255 - 262

https://doi.org/10.1145/2930889.2930920

Published: 20 July 2016 Publication History

Abstract

Can post-Schönhage-Strassen multiplication algorithms be competitive in practice for large input sizes? So far, the GMP library still outperforms all implementations of the recent, asymptotically more efficient algorithms for integer multiplication by Fürer, De--Kurur--Saha--Saptharishi, and ourselves. In this paper, we show how central ideas of our recent asymptotically fast algorithms turn out to be of practical interest for multiplication of polynomials over finite fields of characteristic two. Our Mathemagix implementation is based on the automatic generation of assembly codelets. It outperforms existing implementations in large degree, especially for polynomial matrix multiplication over finite fields.

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Cited By

Harvey Dvan der Hoeven J(2022)Polynomial Multiplication over Finite Fields in Time Journal of the ACM10.1145/350558469:2(1-40)Online publication date: 10-Mar-2022
https://dl.acm.org/doi/10.1145/3505584
Harvey Dvan der Hoeven J(2019)Faster integer multiplication using short lattice vectorsThe Open Book Series10.2140/obs.2019.2.2932:1(293-310)Online publication date: 28-Jan-2019
https://doi.org/10.2140/obs.2019.2.293
Covanov SMohajerani DMoreno Maza MWang LDavenport JWang DKauers MBradford R(2019)Big Prime Field FFT on Multi-core ProcessorsProceedings of the 2019 International Symposium on Symbolic and Algebraic Computation10.1145/3326229.3326273(106-113)Online publication date: 8-Jul-2019
https://dl.acm.org/doi/10.1145/3326229.3326273
Show More Cited By

Index Terms

Fast Polynomial Multiplication over F₂₆₀
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
  2. Mathematical software
    1. Mathematical software performance

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cover image ACM Conferences

ISSAC '16: Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation

July 2016

434 pages

ISBN:9781450343800

DOI:10.1145/2930889

General Chairs:
Sergei Abramov
Russian Academy of Sciences, Russia
,
Eugene Zima
Wilfrid Laurier University, Canada
,
Program Chair:
Xiao-Shan Gao
Chinese Academy of Sciences, China

Copyright © 2016 ACM.

Publication rights licensed to ACM. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of a national government. As such, the Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

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SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 20 July 2016

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ISSAC '16: International Symposium on Symbolic and Algebraic Computation

July 20 - 22, 2016

ON, Waterloo, Canada

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Harvey Dvan der Hoeven J(2022)Polynomial Multiplication over Finite Fields in Time Journal of the ACM10.1145/350558469:2(1-40)Online publication date: 10-Mar-2022
https://dl.acm.org/doi/10.1145/3505584
Harvey Dvan der Hoeven J(2019)Faster integer multiplication using short lattice vectorsThe Open Book Series10.2140/obs.2019.2.2932:1(293-310)Online publication date: 28-Jan-2019
https://doi.org/10.2140/obs.2019.2.293
Covanov SMohajerani DMoreno Maza MWang LDavenport JWang DKauers MBradford R(2019)Big Prime Field FFT on Multi-core ProcessorsProceedings of the 2019 International Symposium on Symbolic and Algebraic Computation10.1145/3326229.3326273(106-113)Online publication date: 8-Jul-2019
https://dl.acm.org/doi/10.1145/3326229.3326273
Li WChen MKuo PCheng CYang BKauers MOvchinnikov ASchost É(2018)Frobenius Additive Fast Fourier TransformProceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3208976.3208998(263-270)Online publication date: 11-Jul-2018
https://dl.acm.org/doi/10.1145/3208976.3208998
Larrieu RYap CEl Din M(2017)The Truncated Fourier Transform for Mixed RadicesProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087636(261-268)Online publication date: 23-Jul-2017
https://dl.acm.org/doi/10.1145/3087604.3087636
van der Hoeven JLarrieu RYap CEl Din M(2017)The Frobenius FFTProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087633(437-444)Online publication date: 23-Jul-2017
https://dl.acm.org/doi/10.1145/3087604.3087633
Harvey DHoeven JLecerf G(2017)Faster Polynomial Multiplication over Finite FieldsJournal of the ACM10.1145/300534463:6(1-23)Online publication date: 20-Jan-2017
https://dl.acm.org/doi/10.1145/3005344
van der Hoeven JLarrieu RLecerf G(2017)Implementing Fast Carryless MultiplicationMathematical Aspects of Computer and Information Sciences10.1007/978-3-319-72453-9_9(121-136)Online publication date: 21-Dec-2017
https://doi.org/10.1007/978-3-319-72453-9_9

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