扭曲的爱德华兹曲线在环上

Q4 Mathematics

Tatra Mountains Mathematical Publications Pub Date : 2023-02-01 DOI:10.2478/tmmp-2023-0004

Moha Ben Taleb El Hamam, A. Chillali, L. El Fadil

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引用次数: 0

摘要

抽象Let𝔽q是q个元素的有限域，其中q是奇数素数的幂。在本文中，我们研究了局部环上表示为EEa，d的扭曲Edwards曲线𝔽q[e]，其中e2=0。我们第一次研究了环的算术𝔽q[e]，e2=0。然后我们定义了这个环上的扭曲Edwards曲线EEa，d，我们给出了本质性质，我们定义了群EEa，d，这些性质。精确地说，我们给出了群EEa，d和EEa，d0×Fq之间的双射，其中EEa，d0是有限域上扭曲的Edwards曲线𝔽q

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Twisted Edwards Curve Over the Ring

Abstract Let 𝔽q be a finite field of q elements, where q is a power of an odd prime number. In this paper, we study the twisted Edwards curves denoted EEa,d over the local ring 𝔽q[e], where e2 = 0. In the first time, we study the arithmetic of the ring 𝔽q[e], e2 = 0. After that we define the twisted Edwards curves EEa,d over this ring and we give essential properties and we define the group EEa,d , these properties. Precisely, we give a bijection between the groups EEa,d and EEa,d0 × Fq,where EEa,d0 is the twisted Edwards curves over the finite field 𝔽q.

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来源期刊

Tatra Mountains Mathematical Publications Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

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