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.