Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

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

4 Issues per year

CiteScore 2016: 0.74

SCImago Journal Rank (SJR) 2015: 0.313
Source Normalized Impact per Paper (SNIP) 2015: 0.749

Mathematical Citation Quotient (MCQ) 2015: 0.24

See all formats and pricing
In This Section

Fast genus 2 arithmetic based on Theta functions

P. Gaudry
  • LIX, Ecole polytechnique and LORIA, projet SPACES, France. Email:
Published Online: 2007-08-13 | DOI: https://doi.org/10.1515/JMC.2007.012

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.

About the article

Published Online: 2007-08-13

Published in Print: 2007-08-21

Citation Information: Journal of Mathematical Cryptology JMC, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/JMC.2007.012. Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Joppe W. Bos, Craig Costello, Huseyin Hisil, and Kristin Lauter
Journal of Cryptology, 2016, Volume 29, Number 1, Page 28
Daniel J. Bernstein and Tanja Lange
LMS Journal of Computation and Mathematics, 2014, Volume 17, Number A, Page 181
David Lubicz and Damien Robert
Compositio Mathematica, 2012, Volume 148, Number 05, Page 1483
Pierrick Gaudry and David Lubicz
Finite Fields and Their Applications, 2009, Volume 15, Number 2, Page 246
Sylvain Duquesne
Mathematics in Computer Science, 2010, Volume 3, Number 2, Page 173
Jan Steffen Müller
LMS Journal of Computation and Mathematics, 2010, Volume 13, Page 47

Comments (0)

Please log in or register to comment.
Log in