Arithmetic of special curves

Christophe Doche, Tanja Lange

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Citations (Scopus)


In this chapter we present the arithmetic for special choices of curves that offer advantages in the computation of scalar multiples. The first example is given by Koblitz curves. There the improvement results from a clever use of the Frobenius endomorphism. The use of endomorphisms on special curves over prime fields is the topic of the following section. An approach similar to Koblitz curves but for large characteristic is the key to trace zero varieties, which we present in the last section.

Original languageEnglish
Title of host publicationHandbook of elliptic and hyperelliptic curve cryptography
Place of PublicationBoca Raton, Florida, USA
PublisherCRC Press, Taylor & Francis Group
Number of pages33
ISBN (Electronic)9781420034981
ISBN (Print)9781584885184
Publication statusPublished - 2006

Publication series

NameDiscrete mathematics and its applications


  • Koblitz curves
  • scalar multiples
  • endomorphism
  • special curves
  • trace zero varieties


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