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Journal of Mathematical Cryptology

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Fast genus 2 arithmetic based on Theta functions

P. Gaudry1

1LIX, Ecole polytechnique and LORIA, projet SPACES, France. Email:

Citation Information: Journal of Mathematical Cryptology JMC. Volume 1, Issue 3, Pages 243–265, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: 10.1515/JMC.2007.012, August 2007

Publication History

Published Online:
2007-08-13

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.

Key Words: Hyperelliptic curve cryptography,; explicit formulae,; Kummer surface,; theta functions.

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