Arithmetic of elliptic curves

Christophe Doche, Tanja Lange

Research output: Chapter in Book/Report/Conference proceedingChapter

10 Citations (Scopus)

Abstract

Elliptic curves constitute one of the main topics of this book. They have been proposed for applications in cryptography due to their fast group law and because so far no subexponential attack on their discrete logarithm problem (cf. Section 1.5) is known. We deal with security issues in later chapters and concentrate on the group arithmetic here. In an actual implementation this needs to be built on an efficient implementation of finite field arithmetic (cf. Chapter 11).

Original languageEnglish
Title of host publicationHandbook of elliptic and hyperelliptic curve cryptography
Place of PublicationBoca Raton, Florida, USA
PublisherCRC Press, Taylor & Francis Group
Pages267-302
Number of pages36
ISBN (Electronic)9781420034981
ISBN (Print)9781584885184
Publication statusPublished - 2006

Publication series

NameDiscrete mathematics and its applications
PublisherChapman & Hall/CRC
Volume34

    Fingerprint

Keywords

  • elliptic curves
  • efficient implementation
  • odd characteristics
  • even characteristics

Cite this

Doche, C., & Lange, T. (2006). Arithmetic of elliptic curves. In Handbook of elliptic and hyperelliptic curve cryptography (pp. 267-302). (Discrete mathematics and its applications; Vol. 34). Boca Raton, Florida, USA: CRC Press, Taylor & Francis Group.