Paper 2002/121
Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae
Tanja Lange
Abstract
We extend the explicit formulae for arithmetic on genus two curves of Takahashi and Miyamoto,Doi,Matsuo,Chao,and Tsuji to fields of even characteristic and to arbitrary equation of the curve and slightly improve them. These formulae can be evaluated faster than the more general Cantor algorithm and allow to obtain faster arithmetic on a hyperelliptic genus 2 curve than on elliptic curves. We give timings for implementations using various libraries for the field arithmetic.
Note: Corrected NTL timings and mistake on p.4. More recent version at http://www.rub.de/itsc/tanja/preprints.html
Metadata
- Available format(s)
-
PDF
PS
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- elliptic curve cryptosystemimplementationnumber theoryhyperellitptic curve cryptosystemarithmeticexplicit formulae
- Contact author(s)
- lange @ itsc ruhr-uni-bochum de
- History
- 2003-12-15: last of 7 revisions
- 2002-08-17: received
- See all versions
- Short URL
- https://ia.cr/2002/121
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2002/121,
author = {Tanja Lange},
title = {Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae},
howpublished = {Cryptology {ePrint} Archive, Paper 2002/121},
year = {2002},
url = {https://eprint.iacr.org/2002/121}
}
