Paper 2002/147

Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves

Tanja Lange

Abstract

We investigate formulae to double and add in the ideal class group of a hyperelliptic genus 2 curve avoiding inversions. To that aim we introduce a further coordinate in the representation of a class in which we collect the common denominator of the usual 4 coordinates. The analysis shows that this is practical and advantageous whenever inversions are expensive compared to multiplications like for example on smart cards.

Note: An updated, enlarged, and corrected paper has been submitted and can be found on the author's homepage http://www.ruhr-uni-bochum.de/itsc/tanja