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Elliptic curves over a nonlocal ring ????2d[????],????2 = ????
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In this work, we came to present the elliptic curves over a nonlocal ring [Formula: see text] where [Formula: see text] is a finite field of characteristic 2, and [Formula: see text] is a prime integer. We consider an elliptic curve given by the Weierstrass equation of the form [Formula: see text] such that [Formula: see text] are in the ring [Formula: see text] and b is invertible in [Formula: see text] see Tadmori et al. [Normal form of the elliptic curves over the finite ring, J. Math. Syst. Sci. 4 (2014) 194–196]. More precisely, we give a classification of elements of the elliptic curve over this ring, and we construct the group law over it, which allows us to prove same properties of the elliptic group [Formula: see text] by showing the isomorphism [Formula: see text]
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Title: Elliptic curves over a nonlocal ring ????2d[????],????2 = ????
Description:
In this work, we came to present the elliptic curves over a nonlocal ring [Formula: see text] where [Formula: see text] is a finite field of characteristic 2, and [Formula: see text] is a prime integer.
We consider an elliptic curve given by the Weierstrass equation of the form [Formula: see text] such that [Formula: see text] are in the ring [Formula: see text] and b is invertible in [Formula: see text] see Tadmori et al.
[Normal form of the elliptic curves over the finite ring, J.
Math.
Syst.
Sci.
4 (2014) 194–196].
More precisely, we give a classification of elements of the elliptic curve over this ring, and we construct the group law over it, which allows us to prove same properties of the elliptic group [Formula: see text] by showing the isomorphism [Formula: see text].
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