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Implementing the Arithmetic of C3,4 Curves

  • Abdolali Basiri
  • Andreas Enge
  • Jean-Charles Faugère
  • Nicolas Gürel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3076)

Abstract

We provide explicit formulae for realising the group law in Jacobians of superelliptic curves of genus 3 and C 3,4 curves. It is shown that two distinct elements in the Jacobian of a C 3,4 curve can be added with 150 multiplications and 2 inversions in the field of definition of the curve, while an element can be doubled with 174 multiplications and 2 inversions. In superelliptic curves, 10 multiplications are saved.

Keywords

Great Common Divisor Hyperelliptic Curve Euclidian Algorithm Straight Line Program Jacobian Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Abdolali Basiri
    • 1
    • 3
  • Andreas Enge
    • 2
  • Jean-Charles Faugère
    • 1
  • Nicolas Gürel
    • 2
  1. 1.Laboratoire d’Informatique de Paris 6 (CNRS/UMR 7606)Paris Cedex 05France
  2. 2.INRIA Futurs & Laboratoire d’Informatique (CNRS/FRE 2653)Palaiseau CedexFrance
  3. 3.Department of Mathematics and Computer SciencesDamghan University of SciencesDamghanIran

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