Improving Random Point Scalar Multiplication ThroughComputing Directly 2~kP on GF(2~m)
Zhang Ru · Acta Armamentarii · 2005
Random point scalar multiplication on binary field GF(2 m) is one of the costliest computations in elliptic curve cryptography. According to the formulas to compute directly 4P, 8P, 16P and 32P, formulas to compute directly 2 kP were deduced. And combining them with the existing ω-width signed window method, the method of directly computing the 2 kP signed windows was given in this paper. This improved method keeps the features of ω-width signed window method, decreases the number of doubling, and ultimately improves the speed of scalar multiplication. When tested on a 200MHz DSP, it is proved that the new method greatly speeds up scalar multiplication, and when compared with the method put forward by Yasuyuki Sakai etc, the speed of the arithmetic is increased about 20%.