Paper 2006/257

Efficient Divisor Class Halving on Genus Two Curves

Peter Birkner


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.

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Published elsewhere. Full version
hyperelliptic curvedivisor classhalvingbinary field
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peter @ mat dtu dk
2006-08-03: revised
2006-08-02: received
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      author = {Peter Birkner},
      title = {Efficient Divisor Class Halving on Genus Two Curves},
      howpublished = {Cryptology ePrint Archive, Paper 2006/257},
      year = {2006},
      note = {\url{}},
      url = {}
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