INDOCRYPT 2007: Progress in Cryptology – INDOCRYPT 2007 pp 351-360

Efficient Window-Based Scalar Multiplication on Elliptic Curves Using Double-Base Number System

• Rana Barua
• Sumit Kumar Pandey
• Ravi Pankaj
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4859)

Abstract

In a recent paper [10], 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.

Keywords

Elliptic Curve Elliptic Curf Scalar Multiplication Window Length Point Doubling
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

• Rana Barua
• 1
• Sumit Kumar Pandey
• 1
• Ravi Pankaj
• 1
1. 1.Indian Statistical Institute, 205, B.T. Road, KolkataIndia