Fast genus 2 arithmetic based on Theta functions

Pierrick Gaudry 1, 2
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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.
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Contributor : Pierrick Gaudry <>
Submitted on : Thursday, November 10, 2005 - 11:01:12 AM
Last modification on : Wednesday, March 27, 2019 - 4:41:29 PM
Long-term archiving on: Friday, April 2, 2010 - 6:53:44 PM


  • HAL Id : inria-00000625, version 1


Pierrick Gaudry. Fast genus 2 arithmetic based on Theta functions. 2005. ⟨inria-00000625v1⟩



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