[Resource Topic] 2005/314: Fast genus 2 arithmetic based on Theta functions

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Fast genus 2 arithmetic based on Theta functions

Authors: P. Gaudry


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

ePrint: https://eprint.iacr.org/2005/314

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