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

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

2010-05-03

arxiv.org/abs/1005.0205v1

Lecture notes in computer science (2010)

Mathematics

Number Theory

Scientific paper

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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