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Elliptic Curves with Large Intersection of Projective Torsion Points
Cornell University
,
2017.
Bogomolov F. A., Fu H.
We explicitly construct pairs of elliptic curves defined over the algebraic numbers with large intersection of projective torsion points.
Publication based on the results of:
Bogomolov F. A., Fu H., Tschinkel Y., / Cornell University. Series arXiv "math". 2017.
We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line. ...
Added: July 31, 2017
Bogomolov F. A., Fu H., European Journal of Mathematics 2016 Vol. 2 No. 3 P. 644-660
Given two elliptic curves, each of which is associated with a projection map that identifies opposite elements with respect to the natural group structure, we investigate how their corresponding projective images of torsion points intersect. ...
Added: August 31, 2016
Nesterenko A., Математические вопросы криптографии 2014 Vol. 5 No. 2 P. 99-102
In this article we present an algorithm for constructing an elliptic curve endomorphism for given complex irrationality. This endomorphism can be used for speeding up a group operation on elliptic curve. ...
Added: February 2, 2015
Poberezhny V. A., / ИТЭФ. Series "Препринты ИТЭФ". 2012. No. 57/12.
In this work we investigate the action of generalized Schlesinger transformation on the isomonodromic families of meromorphic connections on the linear bundles of rank two and degree zero over an elliptic curve. The main interest is the action of the gauge transformation on the moduli space of vector bundles. the central result is the explicit ...
Added: March 31, 2014
Lvovsky S., / Cornell University. Series arXiv "math". 2018.
We show that if we are given a smooth non-isotrivial family of elliptic curves over ℂ with a smooth base B for which the general fiber of the mapping J:B→𝔸^1 (assigning j-invariant of the fiber to a point) is connected, then the monodromy group of the family (acting on H1(⋅,ℤ) of the fibers) coincides with SL(2,ℤ); if the general fiber has m≥2 connected components, then the ...
Added: December 5, 2018
Goncharuk N. B., Функциональный анализ и его приложения 2012 Т. 46 № 1 С. 13-30
По заданному диффеоморфизму окружности f можно построить отображение, переводящее вещественное число a в число вращения диффеоморфизма f+a. В 1978 г. В. И. Арнольд предложил комплексный аналог этого отображения: каждое число z, Imz>0, переходит в модуль μ(z) эллиптической кривой, которая строится по отображению f+z. В предлагаемой статье исследовано поведение отображения μ вблизи отрезков вещественной оси, на ...
Added: February 18, 2013
A. Yu. Nesterenko, Journal of Mathematical Sciences 2012 Vol. 182 No. 4 P. 518-526
In this article we present several algorithms for solution a cycle detection problem. We give proof of correctness for these algorithms, complexity bounds and some number theory applications, like integer factorization and discrete logarithm. ...
Added: February 27, 2014
Brown F., / arxive. Series math "nt". 2013. No. arXiv:1110.6917v2.
Abstract. We study the de Rham fundamental group of the configuration space
E (n) of n + 1 marked points on a complex elliptic curve E, and define multiple
elliptic polylogarithms. These are multivalued functions on E (n) with unipotent
monodromy, and are constructed by a general averaging procedure. We show
that all iterated integrals on E (n) , ...
Added: May 14, 2014
Nesterenko A., Математические вопросы криптографии 2016 Vol. 7 No. 2 P. 115-120
We propose an algorithm for solving the discrete logarithm problem on the elliptic curve. This algorithm uses additional information on the multiplicative order of the solution and may be realised in parallel. ...
Added: November 16, 2016
Nesterenko A., Системы высокой доступности 2012 № 2 С. 81-90
We present a new variant of Diffie-Hellman protocol, which is realized in a group of points of elliptic curve over finite field and contains a possibility of key confirmation. An important feature of this protocol is mutual authentication of protocol entities. We make some security demands to the protocol such as key security, long-term keys ...
Added: November 30, 2012
Lebedev P. A., Nesterenko A., Чебышевский сборник 2012 Т. 13 № 2 (42) С. 91-105
We consider different parallel algortihms for operations in prime fields and their applications for operations on points of elliptic curves. The work provides results for implementations of these algorithms on NVIDIA graphical processors. ...
Added: February 25, 2013
Nabebin A. A., Ученые записки Российского государственного социального университета 2014 № 2(124) С. 51-57
Определяются эллиптические кривые над конечными полями и группы точек эллиптических кривых. Приведены алгоритмы, обеспечивающие построение криптографических протоколов на группе точек эллиптических кривых. Рассматриваются шифросистемы и электронные цифровые подписи ЭльГамаля, основанные на группе точек эллиптических кривых. ...
Added: June 21, 2016
Takebe T., International Journal of Modern Physics A 2004 Vol. 19, May suppl. P. 418-435
Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is described by the degeneration of the twisted WZW model on elliptic curves. The spaces of conformal blocks and conformal coinvariants of the degenerate model are factorised into those of the orbifold WZW model. ...
Added: August 14, 2014
Rybakov S., Mathematical notes 2016 Vol. 99 No. 3 P. 397-405
Let S be a bielliptic surface over a finite field, and let an elliptic curve B be the Albanese variety of S; then the zeta function of the surface S is equal to the zeta function of the direct product P1 × B. Therefore, the classification problem for the zeta functions of bielliptic surfaces is ...
Added: July 8, 2016
Brown F., / arxive. Series math "nt". 2013. No. 1110.6917.
Abstract. We study the de Rham fundamental group of the configuration space
E (n) of n + 1 marked points on a complex elliptic curve E, and define multiple
elliptic polylogarithms. These are multivalued functions on E (n) with unipotent
monodromy, and are constructed by a general averaging procedure. We show
that all iterated integrals on E (n) , ...
Added: May 14, 2014
Pavlov A., Mathematische Zeitschrift 2021 No. 297 P. 223-254
We show that for maximal Cohen–Macaulay modules over the homogeneous coordinate ring of a smooth Calabi–Yau varieties X, the computation of Betti numbers can be reduced to computations of dimensions of certain HomHom spaces in the bounded derived category Db(X). In the simplest case of a smooth elliptic curve E embedded in P2 as a smooth cubic, we get explicit values for Betti ...
Added: October 31, 2020
Takebe T., Kuroki G., Journal of Physics A: Mathematical and Theoretical 2001 Vol. 34 No. 11 P. 2403-2413
We construct a Gaudin type lattice model as the Wess-Zumino-Witten model on elliptic curves at the critical level. Bethe eigenvectors are obtained by the bosonisation technique. ...
Added: August 14, 2014
Bogomolov F. A., Fu H., European Journal of Mathematics 2018 Vol. 4 No. 2 P. 555-560
We construct pairs of elliptic curves over number fields with large intersection of projective torsion points. ...
Added: September 13, 2018
Nesterenko A., Проблемы информационной безопасности. Компьютерные системы 2012 № 2 С. 76-82
In this work we present two new protocols for secure management of remote objects. These protocols are released in group of points of elliptic curve, defined over finite field, with usage of russian cryptography standards. ...
Added: November 27, 2012
Nesterenko A., Фундаментальная и прикладная математика 2010 Т. 16 № 6 С. 109-122
В работе рассматриваются алгоритмы поиска длин циклов в последовательностях. Приводится обоснование изложенных алгоритмов, сравнение оценок их трудоёмкости, а также результаты их практического применения для решения задачи дискретного логарифмирования в группе точек эллиптической кривой ...
Added: March 3, 2013
Buff X., Goncharuk N. B., / Cornell University. Series math "arxiv.org". 2013. No. 1308.3510.
We investigate the notion of complex rotation number which was introduced by V.I.Arnold in 1978. Let f: R/Z \to R/Z be an orientation preserving circle diffeomorphism and let {\omega} \in C/Z be a parameter with positive imaginary part. Construct a complex torus by glueing the two boundary components of the annulus {z \in C/Z | ...
Added: December 12, 2013
Brown F., Levin A., / Cornell University. Series arXiv "math". 2013. No. 1110.6917 [.
Abstract. We study the de Rham fundamental group of the configuration sp ace of several marked points on a complex elliptic curve, and define multiple elliptic polylogarithms. These are multivalued functions with unipotent monodromy, and are constructed by a general averaging proce dure. We show that all iterated integrals on this configuration space can be ...
Added: October 4, 2013
Nesterenko A., Пугачев А. В., Прикладная дискретная математика 2015 № 4 С. 56-71
A new hybrid encryption scheme based on ElGamal asymmetric encryption scheme with distributed secret keys is presented. The keys are used for defence against unauthorised intrusion of encrypted messages. The security of the scheme is based on elliptic curve discrete logarithm problem. The main feature of the scheme is the fact that plain message is ...
Added: March 14, 2016
Netay I. V., Савватеев А. В., / Cornell University. Series math "arxiv.org". 2016.
The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles.
We call them Sharygin triangles.
It turns out that they are parametrized by an open subset of an elliptic curve.
Also we prove that there are infinitely many non-similar integer ...
Added: October 19, 2016