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 -