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2010, Volume 4, Issue 2: 261-279. Doi: 10.3934/amc.2010.4.261
This issue Previous Article Fast ideal cubing in imaginary quadratic number and function fields Next Article Relations between arithmetic geometry and public key cryptography

Efficient reduction of large divisors on hyperelliptic curves

  • 1.

    Fakultät für Mathematik, Ruhr-Universität Bochum and Horst Gösrtz Institut für IT-Sicherheit, Universitätsstraße 150, D-44780 Bochum

  • 2.

    Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4

  • 3.

    Department of Mathematics & Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4

Received:  May 31, 2009
Revised:  February 28, 2010
Published:  April 2010
Abstract Related Papers Cited by
    Abstract
  • We present an algorithm for reducing a divisor on a hyperelliptic curve of arbitrary genus over any finite field. Our method is an adaptation of a procedure for reducing ideals in quadratic number fields due to Jacobson, Sawilla and Williams, and shares common elements with both the Cantor and the NUCOMP algorithms for divisor arithmetic. Our technique is especially suitable for the rapid reduction of a divisor with very large Mumford coefficients, obtained for example through an efficient tupling technique. Results of numerical experiments are presented, showing that our algorithm is superior to the standard reduction algorithm in many cases.
    Mathematics Subject Classification: Primary: 11R58, 14H45; Secondary: 14G50.

    Citation:
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