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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2002/121}},
      url = {https://eprint.iacr.org/2002/121}
}
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