Twisted Edwards Curves

机译：扭曲的爱德华兹曲线

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This paper introduces "twisted Edwards curves," a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents fast explicit formulas for twisted Edwards curves in projective and inverted coordinates; and shows that twisted Edwards curves save time for many curves that were already expressible as Edwards curves.

机译：本文介绍了“扭曲的爱德华兹曲线”，它是最近引入的爱德华兹曲线的概括。表明扭曲的爱德华兹曲线包括有限域上的更多曲线，尤其是蒙哥马利形式的每个椭圆曲线；展示了如何通过等轴线覆盖更多曲线；给出了投影和倒转坐标系中扭曲的爱德华兹曲线的快速显式公式；并显示了扭曲的Edwards曲线可节省许多已经可以表示为Edwards曲线的曲线的时间。

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来源
《Progress in Cryptology - AFRICACRYPT 2008》|2008年|P.389-405|共17页
会议地点 Casablanca(MA);Casablanca(MA)
作者
Daniel J. Bernstein; Peter Birkner; Marc Joye; Tanja Lange; Christiane Peters;
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会议组织
原文格式 PDF
正文语种 eng
中图分类密码、密码机;
关键词
elliptic curves; edwards curves; twisted edwards curves; montgomery curves; isogenies;

机译：椭圆曲线;爱德华曲线;扭曲爱德华曲线;蒙哥马利曲线;同质性;

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专利

1. SUPERSINGULAR TWISTED EDWARDS CURVES OVER PRIME FIELDS. Ⅱ. SUPERSINGULAR TWISTED EDWARDS CURVES WITH THE j-INVARIANT EQUAL TO 66~3 [J] . Bessalov A. V, Kovalchuk L. V Cybernetics and Systems Analysis . 2019,第5期

机译：超奇异的扭曲爱德华兹曲线遍及主要领域。 Ⅱ。 j不等式等于66〜3的超奇异扭曲爱德华曲线
2. SUPERSINGULAR TWISTED EDWARDS CURVES OVER PRIME FIELDS.I. SUPERSINGULAR TWISTED EDWARDS CURVES WITH j-INVARIANTS EQUAL TO ZERO AND 12～(3) [J] . A.V.Bessalov, L.V.Kovalchuk Cybernetics and Systems Analysis . 2019,第3期

机译：超出扭曲的爱德华兹曲线在素质领域。我。具有j-funoriants的超旋转的爱德华州曲线等于零和12〜（3）
3. METHOD FOR DETERMINING THE ORDER OF THE POINT ON A TWISTED EDWARDS CURVE [J] . A.V. Bessalov Telecommunications and Radio Engineering . 2017,第6期

机译：确定扭转爱德华曲线上点阶的方法
4. Coordinate system for elliptic curve cryptosystem on twisted Edwards curve [C] . Masaaki Shirase IEEE International Conference on Consumer Electronics-Taiwan . 2016

机译：椭圆形爱德华兹曲线上的椭圆曲线密码系统的坐标系
5. Zeta functions of twisted modular curves and twisted quaternionic Shimura varieties. [D] . Virdol, Cristian. 2005

机译：扭曲的模块曲线和扭曲的四元Shimura品种的Zeta函数。
6. Energy/Area-Efficient Scalar Multiplication with Binary Edwards Curves for the IoT [O] . Carlos Andres Lara-Nino, Arturo Diaz-Perez, Miguel Morales-Sandoval 2019

机译：IoT的能源/面积有效标量乘法与二进制Edwards曲线
7. A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem [O] . Brian Baldwin, Richard Moloney, Andrew Byrne, 2012

机译：椭圆曲线密码系统的扭曲爱德华兹曲线的硬件分析

Twisted Edwards Curves

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