Twisted Edwards Curve Over the Ring

Taleb El Hamam, Moha Ben; Chillali, Abdelhakim; El Fadil, Lhoussain

doi:10.2478/tmmp-2023-0004

Abstract

Let 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_E_a,d over the local ring 𝔽_q[e], where e² = 0. In the first time, we study the arithmetic of the ring 𝔽_q[e], e² = 0. After that we define the twisted Edwards curves E_E_a,d over this ring and we give essential properties and we define the group E_E_a,d , these properties. Precisely, we give a bijection between the groups E_E_a,d and E_E_a,d₀ × F_q,where E_E_a,d₀ is the twisted Edwards curves over the finite field 𝔽_q.

References

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Twisted Edwards Curve Over the Ring

Abstract

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