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Title:
Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors
Authors: Steven D. Galbraith, Michael Harrison, 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.
ePrint: https://eprint.iacr.org/2008/265
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