Paper 2006/257

Efficient Divisor Class Halving on Genus Two Curves

Peter Birkner

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.

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. Full version
Keywords
hyperelliptic curvedivisor classhalvingbinary field
Contact author(s)
peter @ mat dtu dk
History
2006-08-03: revised
2006-08-02: received
See all versions
Short URL
https://ia.cr/2006/257
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2006/257,
      author = {Peter Birkner},
      title = {Efficient Divisor Class Halving on Genus Two Curves},
      howpublished = {Cryptology ePrint Archive, Paper 2006/257},
      year = {2006},
      note = {\url{https://eprint.iacr.org/2006/257}},
      url = {https://eprint.iacr.org/2006/257}
}
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