Refined Computations for Points of the Form 2<I><SUP>k</SUP>P</I> Based on Montgomery Trick

Daisuke ADACHI; Tomio HIRATA

doi:10.1093/ietfec/e89-a.1.334

Refined Computations for Points of the Form 2^kP Based on Montgomery Trick

Daisuke ADACHI, Tomio HIRATA

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.1 pp.334-339

Publication Date: 2006/01/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.1.334

Type of Manuscript: LETTER

Category: Information Security

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Daisuke ADACHI, Tomio HIRATA, "Refined Computations for Points of the Form 2kP Based on Montgomery Trick" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 1, pp. 334-339, January 2006, doi: 10.1093/ietfec/e89-a.1.334.
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.1.334/_p

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@ARTICLE{e89-a_1_334,
author={Daisuke ADACHI, Tomio HIRATA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Refined Computations for Points of the Form 2kP Based on Montgomery Trick},
year={2006},
volume={E89-A},
number={1},
pages={334-339},
abstract={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.},
keywords={},
doi={10.1093/ietfec/e89-a.1.334},
ISSN={1745-1337},
month={January},}

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TY - JOUR
TI - Refined Computations for Points of the Form 2kP Based on Montgomery Trick
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 334
EP - 339
AU - Daisuke ADACHI
AU - Tomio HIRATA
PY - 2006
DO - 10.1093/ietfec/e89-a.1.334
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2006
AB - 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.
ER -