# Efficient arithmetic on elliptic curves in characteristic 2

Abstract : We present normal forms for elliptic curves over a field of characteristic 2 analogous to Edwards normal form, and determine bases of addition laws, which provide strikingly simple expressions for the group law. We deduce efficient algorithms for point addition and scalar multiplication on these forms. The resulting algorithms apply to any elliptic curve over a field of characteristic 2 with a 4-torsion point, via an isomorphism with one of the normal forms. We deduce algorithms for duplication in time $2M + 5S + 2m_c$ and for addition of points in time $7M + 2S$, where $M$ is the cost of multiplication, $S$ the cost of squaring , and $m_c$ the cost of multiplication by a constant. By a study of the Kummer curves $\mathcal{K} = E/\{\pm1]\}$, we develop an algorithm for scalar multiplication with point recovery which computes the multiple of a point P with $4M + 4S + 2m_c + m_t$ per bit where $m_t$ is multiplication by a constant that depends on $P$.
Type de document :
Communication dans un congrès
Progress in Cryptology - INDOCRYPT 2012, Dec 2012, Kolkata, India. Lecture Notes in Computer Science, 7668, pp.378-398, 2012, 〈10.1007/978-3-642-34931-7_22〉
Domaine :

Littérature citée [19 références]

https://hal.archives-ouvertes.fr/hal-01257333
Contributeur : David Kohel <>
Soumis le : lundi 18 janvier 2016 - 14:00:03
Dernière modification le : vendredi 4 mars 2016 - 11:24:09
Document(s) archivé(s) le : mardi 19 avril 2016 - 10:20:45

### Fichier

indocrypt.pdf
Fichiers produits par l'(les) auteur(s)

### Citation

David Kohel. Efficient arithmetic on elliptic curves in characteristic 2. Progress in Cryptology - INDOCRYPT 2012, Dec 2012, Kolkata, India. Lecture Notes in Computer Science, 7668, pp.378-398, 2012, 〈10.1007/978-3-642-34931-7_22〉. 〈hal-01257333〉

Consultations de
la notice

## 137

Téléchargements du document