Speeding up the elliptic curve scalar multiplication using the window- w non adjacent form

Nowadays, elliptic curve based cryptosystem is an efficient public key cryptosystem, The very expensive operation in this cryptographic protocol is the elliptic curve scalar multiplication (elliptic curve point multiplication). Efforts have been mainly focused on developing efficient algorithms for representing the scalar which is involved of elliptic curve scalar multiplication. One of these is using the window- w non adjacent form method. In the present work, the accelerating elliptic curve scalar multiplication using the window- w non adjacent form method is proposed, where the number of operations in the elliptic curve scalar multiplication has been reduced. The expected gain is about 20%, 14% and 7.6% comparing with using the anther methods to compute the elliptic curve scalar multiplication. 20%.