Results 21 to 30 of about 2,144,780 (355)
Local and global densities for Weierstrass models of elliptic curves [PDF]
Mathematical Research Letters, 2020 We prove local results on the $p$-adic density of elliptic curves over $\mathbb{Q}_p$ with different reduction types, together with global results on densities of elliptic curves over $\mathbb{Q}$ with specified reduction types at one or more (including ...
John Cremona, Mohammad Sadek
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Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography
Cybernetics and Information Technologies, 2021 Short Weierstrass elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problem (ECDLP) are widely used in cryptographic applications. A notion of security called Elliptic Curve Cryptography (ECC) security is also suggested in literature
Abhishek Kunal +1 more
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ELLIPTIC CURVES PUBLIC KEY TRAITOR TRACING SCHEME [PDF]
مجلة جامعة الانبار للعلوم الصرفة, 2008 In this paper we use the elliptic curves system in the Public Key Traitor Tracing Scheme. The Elliptic Curve points form Abelian group that used in the Public Key Traitor Tracing Scheme.
Ali M. Sagheer
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The Arithmetic of Elliptic Curves
Elliptic Curves, 2020 Our research focuses on 9 specific elliptic curves E over Q, each with complex multiplication by the maximal order in an imaginary quadratic field. Viewed over C, each E gives rise to tori, defined by the generators ω1, ω2 ∈ C of the period lattice ...
G. Ballew, James Duncan May
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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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Combined small subgroups and side-channel attack on elliptic curves with cofactor divisible by 2m [PDF]
International Journal of Electronics and Telecommunications, 2019 Nowadays, alternative models of elliptic curves like Montgomery, Edwards, twisted Edwards, Hessian, twisted Hessian, Huff’s curves and many others are very popular and many people use them in cryptosystems which are based on elliptic curve cryptography ...
Michał Wrońska
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Evaluation of Computational Approaches of Short Weierstrass Elliptic Curves for Cryptography
Cybernetics and Information Technologies, 2021 The survey presents the evolution of Short Weierstrass elliptic curves after their introduction in cryptography. Subsequently, this evolution resulted in the establishment of present elliptic curve computational standards.
Abhishek Kunal +1 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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On the algebra of elliptic curves [PDF]
Proceedings of the Edinburgh Mathematical Society, 2023 AbstractIt is argued that a nonsingular elliptic curve admits a natural or fundamental abelian heap structure uniquely determined by the curve itself. It is shown that the set of complex analytic or rational functions from a nonsingular elliptic curve to itself is a truss arising from endomorphisms of this heap.
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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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