椭圆曲线群法的基本方法

IF 0.5 4区数学 Q3 MATHEMATICS Archiv der Mathematik Pub Date : 2024-09-20 DOI:10.1007/s00013-024-02041-6

Sander Zwegers

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引用次数: 0

摘要

我们重温了椭圆曲线上的群结构，并给出了加法关联性的简单而基本的证明。为此，我们仅使用群结构的明确定义，就给出了三点之和的明确公式。在此过程中，我们发现了椭圆曲线上三点之和的一种很好的几何解释

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An elementary approach to the group law on elliptic curves

We revisit the group structure on elliptic curves and give a simple and elementary proof of the associativity of the addition. We do this by providing an explicit formula for the sum of three points, only using the explicit definition of the group structure. In the process, we find a nice geometric interpretation of the sum of three points on the elliptic curve

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.

期刊最新文献

Correction to: Combinatorial constructions of repairable threshold schemes Elementary divisors, Hochster duality, and spectra An elementary approach to the group law on elliptic curves The relation between the gonality and the Clifford index of a chain of cycles Rationality of extended unipotent characters