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Practical improvements to class group and regulator computation of real quadratic fields

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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https://hal.inria.fr/inria-00477896
Contributor : Jean-François Biasse <>
Submitted on : Friday, April 30, 2010 - 2:02:38 PM
Last modification on : Thursday, March 5, 2020 - 6:26:36 PM
Long-term archiving on: : Thursday, September 30, 2010 - 4:16:35 PM

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  • HAL Id : inria-00477896, version 1
  • ARXIV : 1005.0205

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Jean-François Biasse, Jacobson Michael. Practical improvements to class group and regulator computation of real quadratic fields. Lecture Notes in Computer Science, Springer, 2010. ⟨inria-00477896⟩

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