[Resource Topic] 2002/147: Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves

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Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves

Authors: Tanja Lange


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.

ePrint: https://eprint.iacr.org/2002/147

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