https://hal-lirmm.ccsd.cnrs.fr/lirmm-00125442Doche, ChristopheChristopheDocheACAC - Centre for Advanced Computing - Algorithms and Cryptography - Macquarie UniversityImbert, LaurentLaurentImbertARITH - Arithmétique informatique - LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier - UM - Université de Montpellier - CNRS - Centre National de la Recherche ScientifiqueExtended Double-Base Number System with Applications to Elliptic Curve CryptographyHAL CCSD2006Double-base number systemElliptic curve cryptography[INFO.INFO-CR] Computer Science [cs]/Cryptography and Security [cs.CR]Imbert, Laurent2007-01-19 15:09:102022-09-06 16:53:322007-01-29 19:46:31enConference papershttps://hal-lirmm.ccsd.cnrs.fr/lirmm-00125442/document10.1007/11941378_24application/pdf1We investigate the impact of larger digit sets on the length of Double-Base Number system (DBNS) expansions. We present a new representation system called extended DBNS whose expansions can be extremely sparse. When compared with double-base chains, the average length of extended DBNS expansions of integers of size in the range 200– 500 bits is approximately reduced by 20% using one precomputed point, 30% using two, and 38% using four. We also discuss a new approach to approximate an integer n by d2^a3^b where d belongs to a given digit set. This method, which requires some precomputations as well, leads to realistic DBNS implementations. Finally, a left-to-right scalar multiplication relying on extended DBNS is given. On an elliptic curve where operations are performed in Jacobian coordinates, improvements of up to 13% overall can be expected with this approach when compared to window NAF methods using the same number of precomputed points. In this context, it is therefore the fastest method known to date to compute a scalar multiplication on a generic elliptic curve.