φ -NAF_w Decomposition of Scalar Multiplication of ECC
Yong Ding · Jisuanji gongcheng · 2009
For fast computation of scalar multiplication of the elliptic curve over GF(p), with the utilization of the endomorphismφ whose characteristic polynomial is φ 2 + 2 = 0, φ -NAF expansion of the integer k is proposed by Ciet in order to speed up the computation of scalar multiplication kP. In this paper, a window technic is applied to the φ -NAF representation, which gets the φ -NAF w decomposition of k and can obtain better result than φ -NAF representation with the cost of some quantities of storages. The length and the density of the expansion is accurately estimated.