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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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Elliptic Curves with Complex Multiplication [PDF]
, 2022 openAn elliptic curve has complex multiplication if its ring of endomorphisms is stricly larger than $\mathbb{Z}$, in this case special simmetry arises from the additional structure.
MARCHESINI, LUCA
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On the ρ-values of complete families of pairing-friendly elliptic curves
Journal of Mathematical Cryptology, 2012 The parameter ρ of a complete family of pairing-friendly elliptic curves represents how suitable some given elliptic curves are in pairing-based cryptographic schemes. The superiority of the curves depends on how close ρ is to 1.
Okano Keiji
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International Journal of Mathematics and Mathematical Sciences, 2015 Elliptic curves have a wide variety of applications in computational number theory such as elliptic curve cryptography, pairing based cryptography, primality tests, and integer factorization.
Keisuke Hakuta
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Classification of Elliptic Cubic Curves Over The Finite Field of Order Nineteen
مجلة بغداد للعلوم, 2016 Plane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen,
Baghdad Science Journal
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Cauchy: Jurnal Matematika Murni dan Aplikasi, 2022 Elliptic curve cryptography includes symmetric key cryptography systems that base their security on mathematical problems of elliptic curves. There are several ways that can be used to define the elliptic curve equation that depends on the infinite field
Juhari Juhari, Mohamad Febry Andrean
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On the Generalizations of Universality Theorem for L-Functions of Elliptic Curves
Jaunųjų Mokslininkų Darbai, 2017 In the paper, the continuous type’s universality theorem for L-functions of elliptic curves is discussed and its generalizations in three directions – for positive integer powers and derivatives of L-functions of elliptic curves as well as the weighted ...
Virginija Garbaliauskienė
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Hardware Accelerators for Elliptic Curve Cryptography [PDF]
, 2008 Puttmann C, Shokrollahi J, Porrmann M, Rückert U. Hardware Accelerators for Elliptic Curve Cryptography. Advances in Radio Science. 2008;6:259-264.In this paper we explore different hardware accelerators for cryptography based on elliptic curves ...
U. Rückert +7 more
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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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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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