Výsledky vyhledávání - "Counting points on elliptic curves"

Counting rational points on smooth cubic curves

Autor: Manh Hung Tran

Publikováno v: Journal of Number Theory. 189:138-146

We use a global version of Heath-Brown's $p-$adic determinant method developed by Salberger to give upper bounds for the number of rational points of height at most $B$ on non-singular cubic curves defined over $\mathbb{Q}$. The bounds are uniform in

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::33abb056398bf1d608f9050c92f87073
https://doi.org/10.1016/j.jnt.2017.12.001

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Rational families of 17-torsion points of elliptic curves over number fields

Autor: Sheldon Kamienny, Maarten Derickx, Barry Mazur

Publikováno v: Number Theory Related to Modular Curves. :81-104

3 Brill–Noether Varieties 6 3.1 The canonical involution v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Basic Brill–Noether varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 The Basic Brill

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https://doi.org/10.1090/conm/701/14142

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High performance hardware support for elliptic curve cryptography over general prime field

Autor: Khalid Javeed, Michael Scott, Xiaojun Wang

Publikováno v: Microprocessors and Microsystems. 51:331-342

Secure information exchange in resource constrained devices can be accomplished efficiently through elliptic curve cryptography (ECC). Due to the high computational complexity of ECC arithmetic, a high performance dedicated hardware architecture is e

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::14c27675f649175abe9d4a7b12a25353
https://doi.org/10.1016/j.micpro.2016.12.005

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Counting points on curves using a map to P1, II

Autor: Jan Tuitman

Publikováno v: Finite Fields and Their Applications. 45:301-322

We introduce a new algorithm to compute the zeta function of a curve over a finite field. This method extends previous work of ours to all curves for which a good lift to characteristic zero is known. We develop all the necessary bounds, analyse the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a2b3440752c6daba90d7d79bf398a21b
https://doi.org/10.1016/j.ffa.2016.12.008

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Rational points on, and the arithmetic of, elliptic curves: A tale of two books (and an article)

Autor: Joseph H. Silverman

Publikováno v: Bulletin of the American Mathematical Society. 54:591-594

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::47faa5a6dcbc24e5ee15134905d77bef
https://doi.org/10.1090/bull/1542

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A JOINT ELLIOTT TYPE THEOREM FOR TWISTS OF L-FUNCTIONS OF ELLIPTIC CURVES

Autor: Antanas Laurinčikas, Virginija Garbaliauskienė

Publikováno v: Mathematical modelling and analysis, Vilnius : Technika, 2016, Vol. 21, no. 6, p. 752-761
Mathematical Modelling and Analysis; Vol 21 No 6 (2016); 752-761
Mathematical Modelling and Analysis, Vol 21, Iss 6 (2016)

We consider a collection of L-functions of elliptic curves twisted by a Dirichlet character modulo q (q is a prime number), and prove for this collection a joint limit theorem for weakly convergent probability measures in the space of analytic functi

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https://doi.org/10.3846/13926292.2016.1241191

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Pseudo-random Sequence Generation from Elliptic Curves over a Finite Field of Characteristic 2

Autor: Zbigniew Kotulski, Omar Reyad

Publikováno v: Annals of computer science and information systems, Vol 8, Pp 991-998 (2016)
FedCSIS

In this paper, the randomness of binary sequences generated from elliptic curves over a finite field of characteristic 2 is studied. A scheme of construction based on the Chaos-Driven Elliptic Curve Pseudo-random Number Generator (C-D ECPRNG) is prop

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https://doaj.org/article/b4ad209a3b6c45cd94b7480e9d22040f

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An Improvement of the Elliptic Net Algorithm

Autor: Bing-Long Chen, Chang-An Zhao

Publikováno v: IEEE Transactions on Computers. 65:2903-2909

In this paper we propose a modified Elliptic Net algorithm to compute pairings. By reducing the number of the intermediate variables which should be updated in the iteration loop of the Elliptic Net algorithm, we speed up the computation of pairings.

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https://doi.org/10.1109/tc.2015.2498556

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Some consequences of Masser’s counting theorem on elliptic curves

Autor: Aurélien Galateau, Valéry Mahé

Publikováno v: Mathematische Zeitschrift. 285:613-629

We use Masser’s counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser’s result with bounds on the rank and t

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https://doi.org/10.1007/s00209-016-1728-4

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