TY - CHAP

T1 - Fast elliptic curve arithmetic and improved weil pairing evaluation

AU - Eisenträger, Kirsten

AU - Lauter, Kristin

AU - Montgomery, Peter L.

PY - 2003

Y1 - 2003

N2 - We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8% to 8.5% over the best known general methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P+Q from given points P, Q on the curve. We give applications to simultaneous multiple scalar multiplication and to the Elliptic Curve Method of factorization. We show how this improvement together with another idea can speed the computation of the Weil and Tate pairings by up to 7.8%.

AB - We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8% to 8.5% over the best known general methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P+Q from given points P, Q on the curve. We give applications to simultaneous multiple scalar multiplication and to the Elliptic Curve Method of factorization. We show how this improvement together with another idea can speed the computation of the Weil and Tate pairings by up to 7.8%.

UR - http://www.scopus.com/inward/record.url?scp=35248862491&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248862491&partnerID=8YFLogxK

U2 - 10.1007/3-540-36563-x_24

DO - 10.1007/3-540-36563-x_24

M3 - Chapter

AN - SCOPUS:35248862491

SN - 3540008470

SN - 9783540008477

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

SP - 343

EP - 354

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

A2 - Joye, Marc

PB - Springer Verlag

ER -