Efficient Divisor Class Halving on Genus Two Curves

Peter Birkner

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 curve divisor class halving binary 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: 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},
      url = {https://eprint.iacr.org/2006/257}
}