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International Conference on Coding and Cryptology

IWCC 2011: Coding and Cryptology pp 238–245Cite as

Arithmetic of Split Kummer Surfaces: Montgomery Endomorphism of Edwards Products

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6639))

Abstract

Let E be an elliptic curve, \(\mathcal{K}_1\) its Kummer curve E/{±1}, E 2 its square product, and \(\mathcal{K}_2\) the split Kummer surface E 2/{±1}. The addition law on E 2 gives a large endomorphism ring, which induce endomorphisms of \(\mathcal{K}_2\). With a view to the practical applications to scalar multiplication on \(\mathcal{K}_1\), we study the explicit arithmetic of \(\mathcal{K}_2\).

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References

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Author information

Authors and Affiliations

  1. Institut de Mathématiques de Luminy, Université de la Méditerranée, 163, avenue de Luminy, Case 907, 13288, Marseille Cedex 9, France

    David Kohel

Authors
  1. David Kohel
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Editor information

Editors and Affiliations

  1. School of Physical and Mathematical Sciences, Division of Mathematical Sciences, Nanyang Technological University, 637371, Singapore

    Yeow Meng Chee , San Ling , Huaxiong Wang  & Chaoping Xing , ,  & 

  2. College of Information Engineering, Qingdao University, 266071, Shandong, P.R. China

    Zhenbo Guo

  3. Qingdao University, 266071, Shandong, P.R. China

    Fengjing Shao

  4. School of Mathematical Sciences, Yangzhou University, 225002, Jiangsu, P.R. China

    Yuansheng Tang

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© 2011 Springer-Verlag Berlin Heidelberg

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Kohel, D. (2011). Arithmetic of Split Kummer Surfaces: Montgomery Endomorphism of Edwards Products. In: Chee, Y.M., et al. Coding and Cryptology. IWCC 2011. Lecture Notes in Computer Science, vol 6639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20901-7_15

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  • DOI: https://doi.org/10.1007/978-3-642-20901-7_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20900-0

  • Online ISBN: 978-3-642-20901-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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