Refined computations for points of the form 2kP based on Montgomery trick

被引：1

作者：

Adachi, D ^{[1
]}

Hirata, T

机构：

[1] Nagoya Univ, Grad Sch Engn, Nagoya, Aichi 4648603, Japan

[2] Nagoya Univ, Grad Sch Informat Sci, Nagoya, Aichi 4648603, Japan

来源：

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES | 2006年 / E89A卷 / 01期

关键词：

scalar multiplication; elliptic curve arithmetic; Montgomery trick; window method;

D O I：

10.1093/ietfec/e89-a.1.334

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper focuses on algorithms for an efficient scalar multiplication. It proposes two algorithms for computing points of the form 2(k)p 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.

引用

页码：334 / 339

页数：6

共 5 条

[1] Testing numbers of the form N = 2kp(m) - 1 for primality
Sadovnik, E. V.
DISCRETE MATHEMATICS AND APPLICATIONS, 2006, 16 (02): : 99 - 108
[2] A NEW MESHLESS "FRAGILE POINTS METHOD (FPM)" BASED ON A GALERKIN WEAK- FORM FOR 2D FLEXOELECTRIC ANALYSIS
Guan, Yue
Dong, Leiting
Atluri, Satya N.
PROCEEDINGS OF THE ASME 2020 INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, IMECE2020, VOL 12, 2020,
[3] Higher order approximation in exponential form based on half-step grid-points for 2D quasilinear elliptic BVPs on a variant domain
Setia, Nikita
Mohanty, R. K.
METHODSX, 2023, 10
[4] A New Spline-in-Tension Method of O (k2 + h4) Based on Off-step Grid Points for the Solution of 1D Quasi-linear Hyperbolic Partial Differential Equations in Vector Form
Mohanty, R. K.
Khurana, Gunjan
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS, 2019, 27 (1-3) : 141 - 168
[5] A New Spline-in-Tension Method of O(k2+h4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k^{2}+h^{4})$$\end{document} Based on Off-step Grid Points for the Solution of 1D Quasi-linear Hyperbolic Partial Differential Equations in Vector Form
R. K. Mohanty
Gunjan Khurana
Differential Equations and Dynamical Systems, 2019, 27 (1-3) : 141 - 168

← 1 →