Fast genus 2 arithmetic based on Theta functions

Fast genus 2 arithmetic based on Theta functions

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 la...

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Veröffentlicht in:Journal of mathematical cryptology 2007-08, Vol.1 (3), p.243-265
1. Verfasser: Gaudry, P.
Format: Artikel
Sprache:eng
Schlagworte:
Computer Science
Cryptography and Security
explicit formulae
Hyperelliptic curve cryptography
Kummer surface
theta functions
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Beschreibung
Zusammenfassung: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.
ISSN:1862-2976
1862-2984
DOI:10.1515/JMC.2007.012