Fast genus 2 arithmetic based on Theta functions

P.  Gaudry

Paper 2005/314 Original: eprint.iacr.org/2005/314 ↗

Fast genus 2 arithmetic based on Theta functions

P. Gaudry

Abstract

In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming from Theta functions for the arithmetic in Jacobians of genus 2 curves. We follow this idea and derive fast formulae for the scalar multiplication in the Kummer surface associated to a genus 2 curve, using a Montgomery ladder. Our formulae can be used to design very efficient genus 2 cryptosystems that should be faster than elliptic curve cryptosystems in some hardware configurations.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2005-09-12: last updated; 2005-09-12: published
Short URL: https://ia.cr/2005/314
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2005/314,
      author = {P.  Gaudry},
      title = {Fast genus 2 arithmetic based on Theta functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2005/314},
      year = {2005},
      url = {https://eprint.iacr.org/2005/314}
}