Cryptology ePrint Archive: Report 2008/265
Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors
Steven D. Galbraith and Michael Harrison and David J. Mireles Morales
Abstract: We discuss arithmetic in the Jacobian of a
hyperelliptic curve $C$ of genus $g$. The traditional approach is to
fix a point $P_\infty \in C$ and represent divisor classes in the
form $E - d(P_\infty)$ where $E$ is effective and $0 \le d \le g$.
We propose a different representation which is balanced at infinity.
The resulting arithmetic is more efficient than previous approaches
when there are 2 points at infinity.
This is a corrected and extended version of the article presented in ANTS 2008. We include an appendix with explicit formulae to compute a very efficient `baby step' in genus 2 hyperelliptic curves given by an imaginary model.
Category / Keywords: foundations / hyperelliptic curves, real models, efficient arithmetic
Publication Info: Extended and corrected version of the ANTS 2008 article.
Date: received 11 Jun 2008
Contact author: david mireles at gmail com
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Version: 20080618:121813 (All versions of this report)
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