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 language | English |
|---|---|
| Title of host publication | Handbook of elliptic and hyperelliptic curve cryptography |
| Place of Publication | Boca Raton, Florida, USA |
| Publisher | CRC Press, Taylor & Francis Group |
| Pages | 267-302 |
| Number of pages | 36 |
| ISBN (Electronic) | 9781420034981 |
| ISBN (Print) | 9781584885184 |
| Publication status | Published - 2006 |
Publication series
| Name | Discrete mathematics and its applications |
|---|---|
| Publisher | Chapman & Hall/CRC |
| Volume | 34 |
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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.