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Implementing Fast Carryless Multiplication

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Mathematical Aspects of Computer and Information Sciences (MACIS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10693))

Abstract

The efficient multiplication of polynomials over the finite field \(\mathbb {F}_2\) is a fundamental problem in computer science with several applications to geometric error correcting codes and algebraic crypto-systems. In this paper we report on a new algorithm that leads to a practical speed-up of about two over previously available implementations. Our current implementation assumes a modern AVX2 and CLMUL enabled processor.

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Author information

Authors and Affiliations

  1. Laboratoire d’informatique de l’École polytechnique LIX, UMR 7161 CNRS, Campus de l’École polytechnique 1, rue Honoré d’Estienne d’Orves Bâtiment Alan Turing, CS35003, 91120, Palaiseau, France

    Joris van der Hoeven, Robin Larrieu & Grégoire Lecerf

Authors
  1. Joris van der Hoeven
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  2. Robin Larrieu
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  3. Grégoire Lecerf
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Corresponding author

Correspondence to Joris van der Hoeven .

Editor information

Editors and Affiliations

  1. University of Paderborn, Paderborn, Germany

    Johannes Blömer

  2. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  3. Johannes Kepler University Linz, Linz, Austria

    Temur Kutsia

  4. SBA Research, Vienna, Austria

    Dimitris E. Simos

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van der Hoeven, J., Larrieu, R., Lecerf, G. (2017). Implementing Fast Carryless Multiplication. In: Blömer, J., Kotsireas, I., Kutsia, T., Simos, D. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2017. Lecture Notes in Computer Science(), vol 10693. Springer, Cham. https://doi.org/10.1007/978-3-319-72453-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-72453-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72452-2

  • Online ISBN: 978-3-319-72453-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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