Faster Scalar Multiplication for Elliptic Curve Cryptosystems

In Elliptic Curve Cryptosystems (ECC), a scalar multiplication of a base point is the most time-consuming operation. Thus, a lot of improvemnets on the scalar multiplication algorithms have been proposed. In TwC 2013, Shirase introduced a new strategy for computing a scalar multiplication efficiently by transforming a base point to a new base point with its x-coordinate value 0 [Shi13]. In fact, Shirase showed that the strategy is efficient for ECADD in the projective coordinates. This paper applies Shirase´s strategy to ECDBL in the projective coordinates, and to ECADD and ECDBL in the Jacobian coordinates, and evaluates the efficiency of Shirase´s strategy for computing a scalar multiplication.