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Fast Chinese Remaindering in Practice

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Book cover Mathematical Aspects of Computer and Information Sciences (MACIS 2017)

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

Abstract

The Chinese remainder theorem is a key tool for the design of efficient multi-modular algorithms. In this paper, we study the case when the moduli \(m_1, \ldots , m_{\ell }\) are fixed and can even be chosen by the user. If \(\ell \) is small or moderately large, then we show how to choose gentle moduli that allow for speedier Chinese remaindering. The multiplication of integer matrices is one typical application where we expect practical gains for various common matrix dimensions and bitsizes of the coefficients.

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Author information

Authors and Affiliations

  1. Laboratoire d’informatique, 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

Authors
  1. Joris van der Hoeven
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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. (2017). Fast Chinese Remaindering in Practice. 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_7

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  • DOI: https://doi.org/10.1007/978-3-319-72453-9_7

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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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