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May  2010, 4(2): 141-154. doi: 10.3934/amc.2010.4.141

Improvements in the computation of ideal class groups of imaginary quadratic number fields

Jean-François Biasse 1,

1. 

LIX - École Polytechnique, 91128 Palaiseau, France

Received  May 2009 Revised  February 2010 Published  May 2010

We investigate improvements to the algorithm for the computation of ideal class groups described by Jacobson in the imaginary quadratic case. These improvements rely on the large prime strategy and a new method for performing the linear algebra phase. We achieve a significant speed-up and are able to compute ideal class groups with discriminants of 110 decimal digits in less than a week.
Keywords: Hermite normal form., Ideal class group, index calculus, Gaussian elimination, large prime variant.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Jean-François Biasse. Improvements in the computation of ideal class groups of imaginary quadratic number fields. Advances in Mathematics of Communications, 2010, 4 (2) : 141-154. doi: 10.3934/amc.2010.4.141
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