Journal of Mathematical Cryptology
Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran
Editorial Board Member: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti
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Fast genus 2 arithmetic based on Theta functions
1LIX, Ecole polytechnique and LORIA, projet SPACES, France. Email: (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
- Published Online:
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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