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

  • Jean-François Biasse
  • Michael J. JacobsonJr.
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)


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.


Prime Ideal Class Group Gaussian Elimination Relation Matrix Ideal Class Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jean-François Biasse
    • 1
  • Michael J. JacobsonJr.
    • 2
  1. 1.École PolytechniquePalaiseauFrance
  2. 2.Department of Computer ScienceUniversity of CalgaryCalgaryCanada

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