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Published in:
2005 | OriginalPaper | Chapter
A Note on Signed Binary Window Algorithm for Elliptic Curve Cryptosystems
Authors : Fanyu Kong, Daxing Li
Published in: Cryptology and Network Security
Publisher: Springer Berlin Heidelberg
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The window algorithms for various signed binary representations have been used to speed up point multiplication on elliptic curves. While there’s been extensive research on the non-adjacent form, little attention has been devoted to non-sparse optimal signed binary representations. In the paper, we prove some properties of non-sparse optimal signed binary representations and present a precise analysis of the non-sparse signed window algorithm. The main contributions are described as follows. Firstly, we attain the lower bound
k
+1/3 of the expected length of non-sparse optimal signed binary representations of
k
-bit positive integers. Secondly, we propose a new non-sparse signed window partitioning algorithm. Finally, we analyze Koyama-Tsuruoka’s non-sparse signed window algorithm and the proposed algorithm and compare them with other methods. The upper bound
$\frac{5}{6}\cdot 2^{w-1} -1+\frac{(-1)^{w}}{3}$
of the number of precomputed windows of the non-sparse signed window algorithms is attained.