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Practical Improvements to Class Group and Regulator Computation of Real Quadratic Fields

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Algorithmic Number Theory (ANTS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6197))

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Abstract

We present improvements to the index-calculus algorithm for the computation of the ideal class group and regulator of a real quadratic field. Our improvements consist of applying the double large prime strategy, an improved structured Gaussian elimination strategy, and the use of Bernstein’s batch smoothness algorithm. We achieve a significant speed-up and are able to compute the ideal class group structure and the regulator corresponding to a number field with a 110-decimal digit discriminant.

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Author information

Authors and Affiliations

  1. École Polytechnique, 91128, Palaiseau, France

    Jean-François Biasse

  2. Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada, T2N 1N4

    Michael J. Jacobson Jr.

Authors
  1. Jean-François Biasse
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  2. Michael J. Jacobson Jr.
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Editor information

Editors and Affiliations

  1. LIP/ENS-Lyon, 46, allée d’Italie, 69364, Lyon, Cedex 07, France

    Guillaume Hanrot

  2. Laboratoire d’Informatique (CNRS/UMR 7650), École polytechnique, 91128, Palaiseau Cedex, France

    François Morain

  3. INRIA Nancy, project CARAMEL, 615 rue du jardin botanique, 54602, Villers-lès-Nancy Cedex,, France

    Emmanuel Thomé

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Biasse, JF., Jacobson, M.J. (2010). Practical Improvements to Class Group and Regulator Computation of Real Quadratic Fields. In: Hanrot, G., Morain, F., Thomé, E. (eds) Algorithmic Number Theory. ANTS 2010. Lecture Notes in Computer Science, vol 6197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14518-6_8

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  • DOI: https://doi.org/10.1007/978-3-642-14518-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14517-9

  • Online ISBN: 978-3-642-14518-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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