The Weil pairing on elliptic curves over C
نویسنده
چکیده
To help motivate the Weil pairing, we discuss it in the context of elliptic curves over the field of complex numbers.
منابع مشابه
Complete characterization of the Mordell-Weil group of some families of elliptic curves
The Mordell-Weil theorem states that the group of rational points on an elliptic curve over the rational numbers is a finitely generated abelian group. In our previous paper, H. Daghigh, and S. Didari, On the elliptic curves of the form $ y^2=x^3-3px$, Bull. Iranian Math. Soc. 40 (2014), no. 5, 1119--1133., using Selmer groups, we have shown that for a prime $p...
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By the Mordell-Weil theorem, the group of rational points on an elliptic curve over a number field is a finitely generated abelian group. There is no known algorithm for finding the rank of this group. This paper computes the rank of the family $ E_p:y^2=x^3-3px $ of elliptic curves, where p is a prime.
متن کاملA WEIL PAIRING ON THE p-TORSION OF ORDINARY ELLIPTIC CURVES OVER K[ǫ]
For an elliptic curve E over any field K, the Weil pairing en is a bilinear map on n-torsion. For K of characteristic p > 0, the map en is degenerate if and only if n is divisible by p. In this paper, we consider E over the dual numbers K[ǫ] and define a non-degenerate “Weil pairing on ptorsion” which shares many of the same properties of the Weil pairing. We also show that the discrete logarit...
متن کاملA Weil pairing on the p-torsion of ordinary elliptic curves over K[ ]
For an elliptic curve E over any field K, the Weil pairing en is a bilinear map on n-torsion. For K of characteristic p > 0, the map en is degenerate if and only if n is divisible by p. In this paper, we consider E over the dual numbers K[ ] and define a non-degenerate “Weil pairing on p-torsion” which shares many of the same properties of the Weil pairing. We also show that the discrete logari...
متن کاملElliptic Curves over Finite Fields
In this chapter, we study elliptic curves defined over finite fields. Our discussion will include the Weil conjectures for elliptic curves, criteria for supersingularity and a description of the possible groups arising as E(Fq). We shall use basic algebraic geometry of elliptic curves. Specifically, we shall need the notion and properties of isogenies of elliptic curves and of the Weil pairing....
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ورودعنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2005 شماره
صفحات -
تاریخ انتشار 2005