Efficient scalar multiplication based on window algorithm with 2´s complement applied for elliptic curve cryptosystems

In this paper we propose an efficient and secure elliptic curve scalar multiplication algorithm over odd prime fields. For this purpose, we propose an explicit algorithm for short addition-subtraction chain method which utilizes a 2´s Complement with window method. We term it as W2CASC. Our proposed scalar multiplication algorithm based on W2CASC algorithm has preceded by 12.7% to 28% 160 bit multiplier over similar techniques. Hence scalar multiplication utilizing W2CASC algorithm shows significance in application to elliptic curve cryptosystems. Also our algorithm has preceded by 26% to 28% in context of Elliptic Curve Cryptosystems (ECC).