TY - GEN
T1 - Scalar multiplication on Koblitz curves using double bases
AU - Avanzi, Roberto
AU - Sica, Francesco
PY - 2006
Y1 - 2006
N2 - The paper is an examination of double-base decompositions of integers n, namely expansions loosely of the form n = Σi, j ± A iBj for some base {A, B}. This was examined in previous works [5,6], in the case when A, B lie in N. We show here how to extend the results of [5] to Koblitz curves over binary fields. Namely, we obtain a sublinear scalar algorithm to compute, given a generic positive integer n and an elliptic curve point P, the point nP in time O (log n / log lgo n) elliptic curve operations with essentially no storage, thus making the method asymptotically faster than any know scalar multiplication algorithm on Koblitz curves. In view of combinatorial results, this is the best type of estimate with two bases, apart from the value of the constant in the O notation.
AB - The paper is an examination of double-base decompositions of integers n, namely expansions loosely of the form n = Σi, j ± A iBj for some base {A, B}. This was examined in previous works [5,6], in the case when A, B lie in N. We show here how to extend the results of [5] to Koblitz curves over binary fields. Namely, we obtain a sublinear scalar algorithm to compute, given a generic positive integer n and an elliptic curve point P, the point nP in time O (log n / log lgo n) elliptic curve operations with essentially no storage, thus making the method asymptotically faster than any know scalar multiplication algorithm on Koblitz curves. In view of combinatorial results, this is the best type of estimate with two bases, apart from the value of the constant in the O notation.
KW - Double base number systems
KW - Elliptic curves
KW - Koblitz curves
KW - Scalar multiplication
KW - Sublinear algorithms
UR - http://www.scopus.com/inward/record.url?scp=84887303740&partnerID=8YFLogxK
U2 - 10.1007/11958239_9
DO - 10.1007/11958239_9
M3 - Conference contribution
AN - SCOPUS:84887303740
SN - 3540687998
SN - 9783540687993
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 131
EP - 146
BT - Progress in Cryptology, VIETCRYPT 2006 - 1st International Conference on Cryptology in Vietnam, Revised Selected Papers
PB - Springer Verlag
T2 - 1st International Conference on Cryptology in Vietnam, VIETCRYPT 2006
Y2 - 25 September 2006 through 28 September 2006
ER -