The Double-Base Number System and its Application to Elliptic Curve Cryptography

We describe an algorithm for point multiplication on generic elliptic curves, based on a representation of the scalar as a sum of mixed powers of 2 and 3. The sparseness of this so-called double-base number system, combined with some efficient point tripling formulae, lead to efficient point multiplication algorithms for curves defined over both prime and binary fields. Side-channel resistance is provided thanks to side-channel atomicity.

Mots clés

Domaines

Cryptographie et sécurité [cs.CR]

Fichier principal

dbns_ecc_mathcomp_2008.pdf (372.02 Ko)

Origine	Fichiers produits par l'(les) auteur(s)
Licence	Autorisation HAL

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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00341742

Soumis le : vendredi 18 mars 2022-09:43:50

Dernière modification le : jeudi 12 février 2026-03:25:52

Archivage à long terme le : dimanche 19 juin 2022-18:29:55

Dates et versions

lirmm-00341742 , version 1 (18-03-2022)

Licence

Autorisation HAL

Identifiants

HAL Id : lirmm-00341742 , version 1
DOI : 10.1090/S0025-5718-07-02048-0

Citer

Vassil Dimitrov, Laurent Imbert, Pradeep Mishra. The Double-Base Number System and its Application to Elliptic Curve Cryptography. Mathematics of Computation, 2008, 77 (262), pp.1075-1104. ⟨10.1090/S0025-5718-07-02048-0⟩. ⟨lirmm-00341742⟩