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Refined Computations for Points of the Form 2kP Based on Montgomery Trick
Daisuke ADACHI Tomio HIRATA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2006/01/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Security
scalar multiplication, elliptic curve arithmetic, Montgomery trick, window method,
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This paper focuses on algorithms for an efficient scalar multiplication. It proposes two algorithms for computing points of the form 2kP in affine coordinates. One works for k=2, and the other works for an arbitrary natural number k. The efficiency of these algorithms is based on a trade-off between a field inversion and several field multiplications. Montgomery trick is used to implement this trade-off. Since a field inversion is usually more expensive than 10 field multiplications, the proposed algorithms are efficient in comparison with existing ones.