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Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three

机译：特征3场上椭圆曲线的有效算法。

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摘要

This paper presents new explicit formulae for the point doubling, tripling and addition for ordinary Weierstrafi elliptic curves with a point of order 3 and their equivalent Hessian curves over finite fields of characteristic three. The cost of basic point operations is lower than that of all previously proposed ones. The new doubling, mixed addition and tripling formulae in projective coordinates require 3M + 2C, 8M + 1C + 1D and 4M + 4C + 1D respectively, where M, C and D is the cost of a field multiplication, a cubing and a multiplication by a constant. Finally, we present several examples of ordinary elliptic curves in characteristic three for high security levels.

机译：本文针对特征为3的有限域上的普通Weierstrafi椭圆曲线（点数为3）及其等效的Hessian曲线，给出了新的显式公式，用于加倍，加倍和加倍。基本点操作的成本低于以前提出的所有操作。投影坐标系中新的加倍，混合加法和三重公式分别需要3M + 2C，8M + 1C + 1D和4M + 4C + 1D，其中M，C和D是场乘法，求和和乘以的成本一个常数。最后，针对高安全级别，我们提供了特征3中的普通椭圆曲线的几个示例。

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来源
《Selected areas in cryptography》|2012年|135-148|共14页
会议地点 Windsor(CA)
作者
Reza R. Farashahi; Hongfeng Wu; Chang-An Zhao;
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作者单位

Dept. of Computing, Macquarie University, Sydney, NSW 2109, Australia,Dept. of Mathematical Sciences, Isfahan University of Technology,84156-83111 Isfahan, Iran;

College of Sciences, North China University of Technology, Beijing 100144, China;

School of Computer Science and Educational Software, Guangzhou University,Guangzhou 510006, China;

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会议组织
原文格式 PDF
正文语种 eng
中图分类
关键词
Elliptic curve; Hessian curve; scalar multiplication; cryptography;

机译：椭圆曲线黑森曲线标量乘法密码学;

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1. Efficient arithmetic on subfield elliptic curves over small finite fields of odd characteristic [J] . Keisuke Hakuta, Hisayoshi Sato, Tsuyoshi Takagi Journal of mathematical cryptology . 2010,第3期

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2. Efficient arithmetic on subfield elliptic curves over small finite fields of odd characteristic [J] . Keisuke Hakuta, Hisayoshi Sato, Tsuyoshi Takagi Journal of mathematical cryptology . 2010,第3期

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3. Efficient Arithmetic in Finite Field Extensions with Application in Elliptic Curve Cryptography [J] . Daniel V.Bailey, Christof Paar Journal of Cryptology . 2001,第3期

机译：有限域扩展中的有效算术及其在椭圆曲线密码学中的应用
4. Efficient Arithmetic on Subfield Elliptic Curves over Small Finite Fields of Odd Characteristic [C] . Keisuke Hakuta, Hisayoshi Sato, Tsuyoshi Takagi Information Security Practice and Experience . 2008

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5. Fast algorithms for arithmetic on elliptic curves over prime fields. [D] . Sullivan, Nicholas T. 2007

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6. Numerical Study of Paramagnetic Elliptical Microparticles in Curved Channels and Uniform Magnetic Fields [O] . Christopher Sobecki, Jie Zhang, Cheng Wang 2020

机译：弯曲通道和均匀磁场中顺磁性椭圆形微粒的数值研究
7. Efficient arithmetic on elliptic curves over fields of characteristic three [O] . Rezaeian Farashahi, Reza, Wu, Hongfeng, Zhao, Chang-An 2013

机译：特征三场上椭圆曲线的高效算法

Efficient Arithmetic on Elliptic Curves over Fields of Characteristic Three

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