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Efficient Divisor Class Halving on Genus Two Curves

Authors:
Peter Birkner
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URL: http://eprint.iacr.org/2006/257
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Abstract: Efficient halving of divisor classes offers the possibility to improve scalar multiplication on hyperelliptic curves and is also a step towards giving hyperelliptic curve cryptosystems all the features that elliptic curve systems have. We present a halving algorithm for divisor classes of genus 2 curves over finite fields of characteristic 2. We derive explicit halving formulae from a doubling algorithm by reversing this process. A family of binary curves, that are not known to be weak, is covered by the proposed algorithm. Compared to previous known halving algorithms, we achieve a noticeable speed-up for this family of curves.
BibTeX
@misc{eprint-2006-21749,
  title={Efficient Divisor Class Halving on Genus Two Curves},
  booktitle={IACR Eprint archive},
  keywords={hyperelliptic curve, divisor class, halving, binary field},
  url={http://eprint.iacr.org/2006/257},
  note={Full version peter@mat.dtu.dk 13363 received 31 Jul 2006, last revised 3 Aug 2006},
  author={Peter Birkner},
  year=2006
}