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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [21 references]  Display  Hide  Download

https://hal.inria.fr/inria-00477896
Contributor : Jean-François Biasse <>
Submitted on : Friday, April 30, 2010 - 2:02:38 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:27 PM
Long-term archiving on: Thursday, September 30, 2010 - 4:16:35 PM

Files

ANTS.pdf
Files produced by the author(s)

Identifiers

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

Collections

Citation

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⟩

Share

Metrics

Record views

582

Files downloads

342