Efficient window-based scalar multiplication on elliptic curves using double-base number system

Abstract

In a recent paper [10], Mishra and Dimitrov have proposed a window-based Elliptic Curve (EC) scalar multiplication using doublebase number representation. Their methods were rather heuristic. In this paper, given the window lengths ω2 and ω3 for the bases 2 and 3, we first show how to fix the number of windows, p, and then obtain a Double Base Number System (DBNS) representation of the scalar n suitable for window-based EC scalar multiplication. Using the DBNS representation, we obtain our first algorithm that uses a small table of precomputed EC points. We then modify this algorithm to obtain a faster algorithm by reducing the number of EC additions at the cost of storing a larger number of precomputed points in a table. Explicit constructions of the tables are also given. © Springer-Verlag Berlin Heidelberg 2007.