Public key cryptosystem and binary Edwards curves on the ring F2 n[e], e2 =e for data management
Moha Ben Taleb El Hamam, Abdelhakim Chillali, Lhoussain El Fadil · 2022 2nd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) · 2022
Let$\mathbb{F}_{2^{n}}[e]$be a finite ring of characteristic 2, where$e^{2}=e$and$n$is a positive integer. Let$(a, d) \in\left(\mathbb{F}_{2^{n}}[e]\right)^{2}$, sach that$a$and$d+a^{2}+a$are invertible in$\mathbb{F}_{2^{n}}[e]$. In the present paper, we study$E_{B, a, d}\left(\mathbb{F}_{2^{n}}[e]\right)$, the binary Edwards curve over the ring$\mathbb{F}_{2^{n}}[e]$. More precisely, we give a bijection between this curve and the product of two binary Edwards curves defined on the finite field$\mathbb{F}_{2^{n}}$. Afterthat we study the addition law of binary Edwards curves over the ring$\mathbb{F}_{2^{n}}[e]$. We end this work with cryptography applications, ElGamal binary Edwards curve cryptosystem and Cramer-Shoup binary Edwards curve cryptosystem.