@article{oai:nagoya.repo.nii.ac.jp:00013170, author = {ADACHI, Daisuke and HIRATA, Tomio}, issue = {1}, journal = {IEICE transactions on fundamentals of electronics, communications and computer sciences}, month = {Jan}, note = {This paper focuses on algorithms for an efficient scalar multiplication. It proposes two algorithms for computing points of the form 2^kP 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.}, pages = {334--339}, title = {Refined Computations for Points of the Form 2kP Based on Montgomery Trick}, volume = {E89-A}, year = {2006} }