Field inversion and point halving revisited
Fong, K.
Hankerson, D.
Lopez, J.
Menezes, A.
Dept. of Comput. Sci., Southern Illinois Univ., Carbondale, IL, USA;
This paper appears in: Computers, IEEE Transactions on
Publication Date: Aug. 2004
Volume: 53,
Issue: 8
On page(s): 1047- 1059
ISSN: 0018-9340
INSPEC Accession Number: 8034967
Digital Object Identifier: 10.1109/TC.2004.43
Current Version Published: 2004-06-21
Abstract
We present a careful analysis of elliptic curve point multiplication methods that use the point halving technique of Knudsen and Schroeppel and compare these methods to traditional algorithms that use point doubling. The performance advantage of halving methods is clearest in the case of point multiplication kP, where P is not known in advance and smaller field inversion to multiplication ratios generally favor halving. Although halving essentially operates on affine coordinate representations, we adapt an algorithm of Knuth to allow efficient use of projective coordinates with halving-based windowing methods for point multiplication.
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