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Published in:
2012 | OriginalPaper | Chapter
Improved Fixed-Base Comb Method for Fast Scalar Multiplication
Authors : Nashwa A. F. Mohamed, Mohsin H. A. Hashim, Michael Hutter
Published in: Progress in Cryptology - AFRICACRYPT 2012
Publisher: Springer Berlin Heidelberg
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Computing elliptic-curve scalar multiplication is the most time consuming operation in any elliptic-curve cryptosystem. In the last decades, it has been shown that pre-computations of elliptic-curve points improve the performance of scalar multiplication especially in cases where the elliptic-curve point
P
is fixed. In this paper, we present an improved fixed-base comb method for scalar multiplication. In contrast to existing comb methods such as proposed by Lim and Lee or Tsaur and Chou, we make use of a width-
ω
non-adjacent form representation and restrict the number of rows of the comb to be greater or equal
ω
. The proposed method shows a significant reduction in the number of required elliptic-curve point addition operation. The computational complexity is reduced by 33 to 38,% compared to Tsaur and Chou method even for devices that have limited resources. Furthermore, we propose a constant-time variation of the method to thwart simple-power analysis attacks.