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Published in:
2010 | OriginalPaper | Chapter
Efficient Scalar Multiplications for Elliptic Curve Cryptosystems Using Mixed Coordinates Strategy and Direct Computations
Authors : Roghaie Mahdavi, Abolghasem Saiadian
Published in: Cryptology and Network Security
Publisher: Springer Berlin Heidelberg
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Scalar multiplication is the heart of elliptic curve cryptosystems. Several techniques have been proposed for efficient scalar multiplication. Mixed coordinate strategy is a useful technique for implementing efficient scalar multiplication. It splits a scalar multiplication into a few parts, and performs each part in the best coordinate. Also, the running time of scalar multiplication can be reduced by applying direct computations in the evaluation stage. This technique directly computes points of the form 2
P
+
Q
from points
P
and
Q
on the elliptic curve. In this paper, we apply mixed coordinate strategy and direct computations to various scalar multiplication algorithms such as binary method, NAF and window NAF methods, MOF and window MOF methods to find the best combinations of mixed coordinates strategy and direct computations for scalar multiplication with respect to the computational costs and memory consumption.