TY - GEN

T1 - Extended double-base number system with applications to elliptic curve cryptography

AU - Doche, Christophe

AU - Imbert, Laurent

PY - 2006

Y1 - 2006

N2 - We 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 d2a3b 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.

AB - We 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 d2a3b 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.

KW - double-base number system

KW - elliptic curve cryptography

UR - http://www.scopus.com/inward/record.url?scp=84992376874&partnerID=8YFLogxK

M3 - Conference proceeding contribution

SN - 9783540497677

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 336

EP - 348

BT - Progress in cryptology

A2 - Barua, Rana

A2 - Lange, Tanja

PB - Springer, Springer Nature

CY - Berlin

T2 - 7th International Conference on Cryptology in India

Y2 - 11 December 2006 through 13 December 2006

ER -