Twisted Hessian Curves

  • Daniel J. BernsteinEmail author
  • Chitchanok ChuengsatiansupEmail author
  • David KohelEmail author
  • Tanja LangeEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9230)


This paper presents new speed records for arithmetic on a large family of elliptic curves with cofactor 3: specifically, \(8.77\mathbf{M}\) per bit for 256-bit variable-base single-scalar multiplication when curve parameters are chosen properly. This is faster than the best results known for cofactor 1, showing for the first time that points of order 3 are useful for performance and narrowing the gap to the speeds of curves with cofactor 4.


Efficiency Elliptic-curve arithmetic Double-base chains Fast arithmetic Hessian curves Complete addition laws 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenThe Netherlands
  2. 2.Department of Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  3. 3.Institut de Mathématiques de MarseilleAix-Marseille UniversitéMarseille Cedex 09France

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