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Speeding Up Elliptic Scalar Multiplication Using Multidoubling

Yasuyuki SAKAI, Kouichi SAKURAI

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Summary :

We discuss multidoubling methods for efficient elliptic scalar multiplication. The methods allows computation of 2k P directly from P without computing the intermediate points, where P denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic curves with Montgomery form and Weierstrass form defined over finite fields with characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves and analyze computational complexity. As a result of our implementation with respect to the Montgomery and Weierstrass forms in terms of affine coordinates, we achieved running time reduced by 28% and 31%, respectively, in the scalar multiplication of an elliptic curve of size 160-bit over finite fields with characteristic greater than 3.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E85-A No.5 pp.1075-1083
Publication Date
2002/05/01
Publicized
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Type of Manuscript
Special Section LETTER (Special Section on Discrete Mathematics and Its Applications)
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