Twisted Edwards Curves

  • Daniel J. Bernstein
  • Peter Birkner
  • Marc Joye
  • Tanja Lange
  • Christiane Peters
Conference paper

DOI: 10.1007/978-3-540-68164-9_26

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5023)
Cite this paper as:
Bernstein D.J., Birkner P., Joye M., Lange T., Peters C. (2008) Twisted Edwards Curves. In: Vaudenay S. (eds) Progress in Cryptology – AFRICACRYPT 2008. AFRICACRYPT 2008. Lecture Notes in Computer Science, vol 5023. Springer, Berlin, Heidelberg

Abstract

This paper introduces “twisted Edwards curves,” a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents fast explicit formulas for twisted Edwards curves in projective and inverted coordinates; and shows that twisted Edwards curves save time for many curves that were already expressible as Edwards curves.

Keywords

Elliptic curves Edwards curves twisted Edwards curves Montgomery curves isogenies 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Daniel J. Bernstein
    • 1
  • Peter Birkner
    • 2
  • Marc Joye
    • 3
  • Tanja Lange
    • 2
  • Christiane Peters
    • 2
  1. 1.Department of Mathematics, Statistics, and Computer Science (M/C 249)University of Illinois at ChicagoChicagoUSA
  2. 2.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenNetherlands
  3. 3.Thomson R&D France, Technology Group, Corporate Research, Security LaboratoryCesson-Sévigné CedexFrance

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