CONSTRUCTION OF METRICS ON THE SET OF ELLIPTIC CURVES OVER A FINITE FIELD

被引：0

作者：

Hakuta, Keisuke ^{[1
]}

机构：

[1] Shimane Univ, Acad Assembly, Inst Sci & Engn, Matsue, Shimane, Japan

来源：

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2021年 / 109卷 / 123期

关键词：

elliptic curves; isomorphism; metric;

D O I：

10.2298/PIM2123125H

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider metrics on the set of elliptic curves in short Weierstrass form over a finite field of characteristic greater than three. The metrics have been first found by Mishra and Gupta (2008). Vetro (2011) constructs other metrics which are independent on the choice of a generator of the multiplicative group of the underlying finite field, whereas the metrics found by Mishra and Gupta, are dependent on the choice of a generator of the multiplicative group of the underlying finite field. Hakuta (2015, 2018) constructs metrics on the set of non-supersingular elliptic curves in short Weierstrass form over a finite field of characteristic two and three, respectively. The aim of this paper is to point out that the metric found by Mishra and Gupta is in fact not a metric. We also construct new metrics which are slightly modified versions of the metric found by Mishra and Gupta.

引用

页码：125 / 141

页数：17

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