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Упрощённое доказательство формулы Ворда для эллиптических последовательностей
Дальневосточный математический журнал. 2019. Т. 19. № 1. С. 84–87.
Ustinov A.
Kiritchenko V., Tsfasman M., Vladuts S. et al., Finite Fields and Their Applications 2025 Vol. 101 Article 102517
Quadratic residue patterns modulo a prime are studied since 19th century. In the first part we extend existing results on the number of consecutive ℓ-tuples of quadratic residues, studying corresponding algebraic curves and their Jacobians, which happen to be products of Jacobians of hyperelliptic curves. In the second part we state the last unpublished result of ...
Added: November 17, 2024
Illarionov A., Математические заметки 2020 Т. 107 № 1 С. 80–92
Решается функциональное уравнение, связанное с теоремами сложения и эллиптическими функциями ...
Added: November 15, 2023
Shirokov N. A., Синцова К. А., Вестник Санкт-Петербургского университета. Серия 1. Математика. Механика. Астрономия 2023 Т. 10 № 1 С. 61–72
The problem of describing classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, splines entered in the theory of approximation more than 100 years ago and still retains its relevance. Among a large number of problems related to approximation, we considered the problem of polynomial approximation in ...
Added: May 24, 2023
Nesterenko A., Математические вопросы криптографии 2019 Vol. 10 No. 2 P. 135–144
An algorithm for the construction of elliptic curves satisfying special requirements is presented. The choice of requirements aims to prevent known attacks on the elliptic curve discrete logarithm problem in special cases. The results of practical experiments are discussed, some parameters of concrete elliptic curves are given. ...
Added: August 26, 2019
Bogomolov F. A., Fu H., Tschinkel Y., / 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., / Series arXiv "math". 2017.
We explicitly construct pairs of elliptic curves defined over the algebraic numbers with large intersection of projective torsion points. ...
Added: June 20, 2017
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
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
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
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
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., / 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
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
Buff X., Goncharuk N. B., / 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
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
Lebedev P., 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
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
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
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