The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Nous introduisons des algorithmes efficaces pour la multiplication scalaire sur des courbes elliptiques définies sur FP. Les algorithmes calculent 2k P directement à partir P, Où P est un point aléatoire sur une courbe elliptique, sans calculer les points intermédiaires, ce qui est plus rapide que k doublements répétés. De plus, nous appliquons les algorithmes à la multiplication scalaire sur des courbes elliptiques et analysons leur complexité de calcul. Grâce à leur implémentation par rapport aux coordonnées affines (resp. projectives pondérées), nous avons obtenu un facteur de performance accru de 1.45 (45%) (resp. 1.15 (15%)) dans la multiplication scalaire de la courbe elliptique de taille 160. -peu.
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Copier
Yasuyuki SAKAI, Kouichi SAKURAI, "Efficient Scalar Multiplications on Elliptic Curves with Direct Computations of Several Doublings" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 1, pp. 120-129, January 2001, doi: .
Abstract: We introduce efficient algorithms for scalar multiplication on elliptic curves defined over FP. The algorithms compute 2k P directly from P, where P is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves, and analyze their computational complexity. As a result of their implementation with respect to affine (resp. weighted projective) coordinates, we achieved an increased performance factor of 1.45 (45%) (resp. 1.15 (15%)) in the scalar multiplication of the elliptic curve of size 160-bit.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_1_120/_p
Copier
@ARTICLE{e84-a_1_120,
author={Yasuyuki SAKAI, Kouichi SAKURAI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Efficient Scalar Multiplications on Elliptic Curves with Direct Computations of Several Doublings},
year={2001},
volume={E84-A},
number={1},
pages={120-129},
abstract={We introduce efficient algorithms for scalar multiplication on elliptic curves defined over FP. The algorithms compute 2k P directly from P, where P is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves, and analyze their computational complexity. As a result of their implementation with respect to affine (resp. weighted projective) coordinates, we achieved an increased performance factor of 1.45 (45%) (resp. 1.15 (15%)) in the scalar multiplication of the elliptic curve of size 160-bit.},
keywords={},
doi={},
ISSN={},
month={January},}
Copier
TY - JOUR
TI - Efficient Scalar Multiplications on Elliptic Curves with Direct Computations of Several Doublings
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 120
EP - 129
AU - Yasuyuki SAKAI
AU - Kouichi SAKURAI
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2001
AB - We introduce efficient algorithms for scalar multiplication on elliptic curves defined over FP. The algorithms compute 2k P directly from P, where P is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves, and analyze their computational complexity. As a result of their implementation with respect to affine (resp. weighted projective) coordinates, we achieved an increased performance factor of 1.45 (45%) (resp. 1.15 (15%)) in the scalar multiplication of the elliptic curve of size 160-bit.
ER -