Twisted Jacobi Intersections Curves

机译：扭曲的Jacobi相交曲线

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In this paper, the twisted Jacobi intersections which contains Jacobi intersections as a special case is introduced. We show that every elliptic curve over the prime field with three points of order 2 is isomor-phic to a twisted Jacobi intersections curve. Some fast explicit formulae for twisted Jacobi intersections curves in projective coordinates are presented. These explicit formulae for addition and doubling are almost as fast as the Jacobi intersections. In addition, the scalar multiplication can be more effective in twisted Jacobi intersections than in Jacobi intersections. Moreover, we propose new addition formulae which are independent of parameters of curves and more effective in reality than the previous formulae in the literature.

机译：在本文中，介绍了包含Jacobi交点的特例的扭曲Jacobi交点。我们证明，素数场上具有2个三阶点的每条椭圆曲线对于扭曲的Jacobi相交曲线都是同构的。给出了投影坐标系中扭曲的Jacobi相交曲线的一些快速显式公式。这些用于加法和加倍的显式公式几乎与Jacobi交集一样快。此外，与雅可比相交相比，扭曲雅可比相交中的标量乘法更有效。此外，我们提出了新的加法公式，该公式与曲线的参数无关，并且在实际中比文献中的先前公式更有效。

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来源
《Theory and application of models of computation》|2010年|p.199-210|共12页
会议地点 Prague(CZ);Prague(CZ);Prague(CZ)
作者
Rongquan Feng; Menglong Nie; Hongfeng Wu;
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作者单位

LMAM, School of Mathematical Sciences, Peking University,Beijing 100871, P.R. China;

LMAM, School of Mathematical Sciences, Peking University,Beijing 100871, P.R. China;

Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing 100190, P.R. China;

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会议组织
原文格式 PDF
正文语种 eng
中图分类计算技术、计算机技术;
关键词
elliptic curves; jacobi intersections; twisted jacobi intersec-tions; scalar multiplication; cryptography;

机译：椭圆曲线雅各比路口；扭曲的雅各比相交；标量乘法密码学;

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专利

1. Twisted Jacobi intersections curves [J] . Rongquan Feng, Menglong Nie, Hongfeng Wu Theoretical computer science . 2013,第Null期

机译：扭曲的Jacobi相交曲线
2. On twisted contact groupoids and on integration of twisted Jacobi manifolds [J] . symplectic groupoids Bulletin des sciences mathematiques . 2010,第5期

机译：关于扭曲的接触类群和扭曲的Jacobi流形的积分
3. 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
4. Hashing into Twisted Jacobi Intersection Curves [C] . Xiaoyang He, Wei Yu, Kunpeng Wang International conference on information security and cryptology . 2018

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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. Isogeny formulas for Jacobi intersection and twisted hessian curves [O] . João Paulo da Silva, Julio López, Ricardo Dahab 2019

机译：雅典交叉路口和扭曲黑森州曲线的基因源性公式

Twisted Jacobi Intersections Curves

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