# New Point Addition Formulae for ECC Applications

Abstract : In this paper we propose a new approach to point scalar multiplication on elliptic curves defined over fields of characteristic greater than 3. It is based on new point addition formulae that suit very well to exponentiation algorithms based on Euclidean addition chains. However finding small chains remains a very difficult problem, so we also develop a specific exponentiation algorithm, based on Zeckendorf representation (i.e. representing the scalar $k$ using Fibonacci numbers instead of powers of 2), which takes advantage of our formulae.
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Communication dans un congrès
Carlet, Claude; Sunar, Berk. WAIFI'07: International Workshop on the Arithmetic of Finite Fields, Jun 2007, Madrid, Springer, 4547, pp.189-201, 2007, LNCS. 〈http://www.waifi.org/〉

Littérature citée [14 références]

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00188957
Contributeur : Nicolas Méloni <>
Soumis le : lundi 19 novembre 2007 - 16:25:46
Dernière modification le : jeudi 11 janvier 2018 - 06:15:40
Document(s) archivé(s) le : lundi 12 avril 2010 - 02:43:43

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• HAL Id : lirmm-00188957, version 1

### Citation

Nicolas Méloni. New Point Addition Formulae for ECC Applications. Carlet, Claude; Sunar, Berk. WAIFI'07: International Workshop on the Arithmetic of Finite Fields, Jun 2007, Madrid, Springer, 4547, pp.189-201, 2007, LNCS. 〈http://www.waifi.org/〉. 〈lirmm-00188957〉

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