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Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors

Authors:
Steven D. Galbraith
Michael Harrison
David J. Mireles Morales
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URL: http://eprint.iacr.org/2008/265
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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.
BibTeX
@misc{eprint-2008-17942,
  title={Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors},
  booktitle={IACR Eprint archive},
  keywords={foundations / hyperelliptic curves, real models, efficient arithmetic},
  url={http://eprint.iacr.org/2008/265},
  note={Extended and corrected version of the ANTS 2008 article. david.mireles@gmail.com 14041 received 11 Jun 2008},
  author={Steven D. Galbraith and Michael Harrison and David J.  Mireles Morales},
  year=2008
}