Results 21 to 30 of about 699,908 (302)
Isogenies on twisted Hessian curves
Journal of Mathematical Cryptology, 2021 Elliptic curves are typically defined by Weierstrass equations. Given a kernel, the well-known Vélu's formula shows how to explicitly write down an isogeny between Weierstrass curves. However, it is not clear how to do the same on other forms of elliptic
Perez Broon Fouazou Lontouo +3 more
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Regulators of Elliptic Curves [PDF]
International Mathematics Research Notices, 2018 Abstract We study the regulator of the Mordell–Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic $p>0$. We prove a new Northcott property for the regulator of elliptic curves of rank at least 4 defined over a number field.
Autissier, Pascal +2 more
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Quadratic Hamiltonians on non-Euclidean spaces of arbitrary constant curvature [PDF]
, 2013 This paper derives explicit solutions for Riemannian and sub-Riemannian curves on non-Euclidean spaces of arbitrary constant cross-sectional curvature.
Biggs, James
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Generalized Fibonacci Sequences for Elliptic Curve Cryptography
Mathematics, 2023 The Fibonacci sequence is a well-known sequence of numbers with numerous applications in mathematics, computer science, and other fields. In recent years, there has been growing interest in studying Fibonacci-like sequences on elliptic curves.
Zakariae Cheddour +2 more
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Twists of Elliptic Curves [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2017 In this note we extend the theory of twists of elliptic curves as presented in various standard texts for characteristic not equal to two or three to the remaining characteristics. For this, we make explicit use of the correspondence between the twists and the Galois cohomology set $H^1\big(\operatorname{G}_{\overline{K}/K}, \operatorname{Aut}_ ...
Kronberg, M., Soomro, M.A., Top, J.
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Elliptic curve cryptography [PDF]
Ubiquity, 2008 This paper describes the Elliptic Curve Cryptography algorithm and its suitability for smart cards.
Vivek Kapoor +2 more
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A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves
Transactions of the London Mathematical Society, 2021 Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves ...
Garen Chiloyan, Álvaro Lozano‐Robledo
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TORSION OF ELLIPTIC CURVES OVER QUADRATIC CYCLOTOMIC FIELDS [PDF]
, 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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Some Families of Elliptic Curves [PDF]
, 2023 Elliptic curves, intricate mathematical structures, form a nexus between number theory, alge- braic geometry, and cryptography. This paper offers a thorough exploration of these curves, delving into their foundational properties, historical origins, and ...
Shah, Sudev
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Elliptic curves and the congruent number problem [PDF]
, 2023 openIn this thesis we will introduce some basic notions on the arithmetic theory of elliptic curves and show how this theory is connected to the congruent number problem, a classical problem in arithmetic.
BARBAN, FRANCESCO
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