Research Communication | Open Access
Volume 2021 | Communication ID 83
Volume 2021 | Communication ID 83
| Twisted Edwards Curves over the Ring? Fq[e],e?^2=e |
Moha Ben Taleb Elhamam, Abdelhakim Chillali Chillali, Lhoussain El Fadil
Received |
Accepted |
Published |
January 26, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: Let Fq be a finite field of q elements, where q is a power of a prime number p≠2. In this paper, we study the Twisted Edwards Curves over the ring Fq[e], where e^2=e, denoted by E_(E,a,d) (Fq[e]); (a;d) ∈〖(Fq[e])〗^2 . Using the Twisted Edwards equation, we define the Twisted Edwards Curves E_(E,a,d) (Fq[e]) and we will show that E_(E,π_0 (a),π_0 (d)) (Fq[e]) and E_(E,π_1 (a),π_1 (d)) (Fq[e]) are two Twisted Edwards Curves over the field Fq, where π_0 and π_1are respectively the canonical projection and the sum projection of coordinates from Fq[e] to Fq. Precisely, we give ...