Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography /

Date: received 7 Sep 2005

Contact author: gaudry at lix polytechnique fr

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Version: 20050912:121029 (All versions of this report)

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