Efficient scalar multiplication for elliptic curves over binary fields
Haihua Gu, Dawu Gu, Ya Liu · Wuhan University Journal of Natural Sciences · 2008
Scalar multiplication [n]P is the kernel and the most time-consuming operation in elliptic curve cryptosystems. In order to improve scalar multiplication, in this paper, we propose a tripling algorithm using Lopez and Dahab projective coordinates, in which there are 3 field multiplications and 3 field squarings less than that in the Jacobian projective tripling algorithm. Furthermore, we map P to ϕ −1 (P), and compute [n]ϕ −1 (P) on elliptic curve E ε , which is faster than computing [n]P on E, where ϕ ε is an isomorphism. Finally we calculate ϕ ε ([n]ϕ −1 (P)) = [n]P. Combined with our efficient point tripling formula, this method leads scalar multiplication using double bases to achieve about 23% improvement, compared with Jacobian projective coordinates.