Results 41 to 50 of about 2,536,804 (344)
Families of elliptic curves with rational 3-torsion
Journal of Mathematical Cryptology, 2012 In this paper we look at three families of elliptic curves with rational 3-torsion over a finite field. These families include Hessian curves, twisted Hessian curves, and a new family we call generalized DIK curves. We find the number of -isogeny classes
Moody Dustin, Wu Hongfeng
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Elliptic curves with a pre-determined embedding degree [PDF]
, 2009 A pairing over an elliptic curve E(F_) to an extension field of F_ has begun to be attractive in cryptosystems, where k is called the embedding degree. The cryptosystems using a pairing are called the pairing-based cryptosystems.
Atsuko Miyaji +3 more
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Optimal Locally Repairable Codes Via Elliptic Curves [PDF]
IEEE Transactions on Information Theory, 2017 Constructing locally repairable codes achieving Singleton-type bound (we call them optimal codes in this paper) is a challenging task and has attracted great attention in the last few years. Tamo and Barg first gave a breakthrough result in this topic by
Xudong Li, Liming Ma, C. Xing
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Nonlinearities in Elliptic Curve Authentication [PDF]
Entropy, 2014 In order to construct the border solutions for nonsupersingular elliptic curve equations, some common used models need to be adapted from linear treated cases for use in particular nonlinear cases. There are some approaches that conclude with these solutions.
Ramzi Alsaedi +2 more
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TORSION OF ELLIPTIC CURVES OVER QUADRATIC CYCLOTOMIC FIELDS
, 2010 In this paper we study the possible torsions of elliptic curves over ℚ(i) and ℚ(√−3)
Najman, Filip, Filip Najman
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Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves [PDF]
Journal of The American Mathematical Society, 2017 We prove the first known nontrivial bounds on the sizes of the 2-torsion subgroups of the class groups of cubic and higher degree number fields K K (the trivial bound being O ϵ ,
M. Bhargava +5 more
semanticscholar +1 more source
Euler characteristics and elliptic curves [PDF]
Proceedings of the National Academy of Sciences, 1997 Let E be a modular elliptic curve over ℚ, without complex multiplication; let p be a prime number where E has good ordinary reduction; and let F ∞ be the field obtained by adjoining to ℚ all p -power ...
Coates, John, Howson, Susan
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Scalar multiplication on Weierstraß elliptic curves from Co-Z arithmetic [PDF]
, 2011 In 2007, Meloni introduced a new type of arithmetic on elliptic curves when adding projective points sharing the same Z-coordinate.This paper presents further co-Z addition formula (and register allocations) for various point additions on Weierstrass ...
Atsuko Miyaji +9 more
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Triangles and elliptic curves, V
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994 The author continues his work on elliptic curves associated to triangles as described in part I, ibid. 70, No. 4, 106-108; part II, ibid., No. 7, 223-225; and part III, ibid., No. 10, 311-314 (1994); see respectively Zbl 0824.14028 and 14029 and Zbl 0832.14021).
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On the Density of Elliptic Curves [PDF]
Compositio Mathematica, 2001 We show that 17.9% of all elliptic curves over Q , ordered by their exponential height, are semistable, and that there is a positive density subset of elliptic curves for which the root numbers are uniformly distributed. Moreover, for any α > 1/6 (resp. α > 1/12) the set of Frey curves (
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