Efficient Window-Based Scalar Multiplication on Elliptic Curves Using Double-Base Number System
In a recent paper , Mishra and Dimitrov have proposed a window-based Elliptic Curve (EC) scalar multiplication using double-base number representation. Their methods were rather heuristic. In this paper, given the window lengths w 2 and w 3 for the bases 2 and 3, we first show how to fix the number of windows, ρ, 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.
KeywordsElliptic Curve Elliptic Curf Scalar Multiplication Window Length Point Doubling
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