Elliptic curve cryptosystems are widespread in everyday-life, its efficiency is also an important area for researchers also for industrial applications. Among the all algorithms used in elliptic curves, the scalar multiplication computation in elliptic curve is the most consuming step, researchers have been studied for decades, and a lot method have been made to accelerate scalar multiplication. There are mainly three method were used in computing point multiplication, the first is na ıve double-and-add approach, the second method is Windowed method, the third method called GLV(Gallant, Lambert and Vanstone) method which is our study based on, was proposed in 2002, and since then it becomes an important tool for speeding up scalar multiplication for Elliptic Curves that have efficient computable endomorphisms.
Keywords: Elliptic curve cryptography Finite field arithmetic Coordinate system GLV method GLS curves