Twisted Edwards curve over the ring $\mathbb{F}_q[e], e²=0$

Rok, strany: 2023, 43 - 50

Let $\mathbb{F}_q$ 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 $E_Ea,d$ over the local ring $\mathbb{F}_q[e]$, where $e²=0$. In the first time, we study the arithmetic of the ring $\mathbb{F}_q[e]$, $e²=0$. After that we define the twisted Edwards curves $E_Ea,d$ over this ring and we give essential properties and we define the group $E_Ea,d$, these properties. Precisely, we give a bijection between the groups $E_Ea,d$ and $E_Ea0,d0× \mathbb{F}_q$, where $E_Ea0,d0$ is the twisted Edwards curves over the finite field $ \mathbb{F}_q$.

ISO 690:

Hamam, M., Chillali, A., El Fadil, L. 2023. Twisted Edwards curve over the ring $\mathbb{F}_q[e], e²=0$. In Tatra Mountains Mathematical Publications, vol. 83, no.1, pp. 43-50. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2023-0004

APA:

Hamam, M., Chillali, A., El Fadil, L. (2023). Twisted Edwards curve over the ring $\mathbb{F}_q[e], e²=0$. Tatra Mountains Mathematical Publications, 83(1), 43-50. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2023-0004

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

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