On the elliptic curve endomorphism generator

Merai Laszlo

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On the elliptic curve endomorphism generator

机译：椭圆曲线同态生成器

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摘要

For an elliptic curve over a finite field we define the point sequence recursively by with an endomorphism and with some initial point on . We study the distribution and the linear complexity of sequences obtained from (P-n).

机译：对于有限域上的椭圆曲线，我们用同胚态和上的一些初始点递归定义点序列。我们研究了从（P-n）获得的序列的分布和线性复杂度。

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来源
《Designs, Codes and Crytography》 |2018年第5期|1113-1129|共17页
作者
Merai Laszlo;
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作者单位

Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, Altenbergerstr 69, A-4040 Linz, Austria;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Elliptic curves; Complex multiplication; Character sums; Linear complexity; Power generator;

机译：椭圆曲线;复数乘法;字符和;线性复杂度;发电机;

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专利

1. The -curve Construction for Endomorphism-Accelerated Elliptic Curves [J] . Smith Benjamin Journal of Cryptology . 2016,第4期

机译：内胚加速椭圆曲线的曲线构造
2. Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves [J] . Steven D. Galbraith, Xibin Lin, Michael Scott Journal of Cryptology . 2011,第3期

机译：大类曲线上更快椭圆曲线密码学的内态
3. Endomorphism rings of supersingular elliptic curves over F_p [J] . Li Songsong, Ouyang Yi, Xu Zheng Finite fields and their applications . 2020,第Feba期

机译：F_P超出椭圆曲线的子宫内膜环
4. Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves [C] . Steven D. Galbraith, Xibin Lin, Michael Scott Advances in cryptology - EUROCRYPT 2009 . 2009

机译：大类曲线上更快椭圆曲线密码学的内态
5. Endomorphism rings of elliptic curves over finite fields [D] . Kohel, David Russell 1996

机译：有限域上椭圆曲线的同胚环
6. Colloquium Paper: Parametrizations of elliptic curves by Shimura curves and by classical modular curves [O] . Kenneth A. Ribet, Shuzo Takahashi 1997

机译：座谈会论文：Shimura曲线和by的椭圆曲线参数化经典模曲线
7. On the elliptic curve endomorphism generator [O] . Mérai, László 2017

机译：关于椭圆曲线内同生成器

On the elliptic curve endomorphism generator

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