# American Institute of Mathematical Sciences

May  2010, 4(2): 237-260. doi: 10.3934/amc.2010.4.237

## Fast ideal cubing in imaginary quadratic number and function fields

 1 CNRS, PIMS, Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4, Canada 2 Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4, Canada, Canada

Received  June 2009 Revised  January 2010 Published  May 2010

We present algorithms for computing the cube of an ideal in an imaginary quadratic number field or function field. In addition to a version that computes a non-reduced output, we present a variation based on Shanks' NUCOMP algorithm that computes a reduced output and keeps the sizes of the intermediate operands small. Extensive numerical results are included demonstrating that in many cases our formulas, when combined with double base chains using binary and ternary exponents, lead to faster exponentiation.
Citation: Laurent Imbert, Michael J. Jacobson, Jr., Arthur Schmidt. Fast ideal cubing in imaginary quadratic number and function fields. Advances in Mathematics of Communications, 2010, 4 (2) : 237-260. doi: 10.3934/amc.2010.4.237
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